Heat Transfer With Pulsatile Flow in a Tube: A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy

Dr. Terry Moschandreou

doi:10.34257/HTPFT2026

Heat Transfer With Pulsatile Flow in a Tube: A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy

Authors

Dr. Terry Moschandreou

Published May 12, 2026

E-ISBN 978-1-7340132-4-5

DOI: https://doi.org/10.34257/HTPFT2026

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Pages342

LanguageEnglish

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Keywords

pulsatile flow Nusselt number Navier-Stokes equations perturbation method Poiseuille flow oscillatory flow Green's function Bessel functions Graetz problem Reynolds number

Synopsis

The partial differential equations governing heat transfer with pulsatile flow in a tube, which serves as a model of a simple heat exchange device are solved in this thesis. The governing equations are the Navier Stokes equations and the convection diffusion equation. Two boundary value problems are solved. In the first case a Neumann boundary condition is specified which represents constant heat flux at the wall of the tube with fluid entering a thermal region at a constant temperature. A regular perturbation expansion is used to obtain higher order harmonics downstream for the temperature field. The main assumption is that the temperature field becomes fully developed downstream as the velocity field becomes fully developed downstream. The perturbation parameter is the ratio of pressure gradient amplitudes of unsteady flow to that of steady flow. Using a Green’s function the first order solution is obtained. As a measure of heat transfer enhancement, a bulk temperature is formulated for the convective process involved and a change in unsteady Nusselt number to that of steady Nusselt number is evaluated analytically. In the second part of the thesis the more difficult problem of heat transfer in pulsatile flow with constant wall temperature is considered. Although a complete solution is not possible as in the first part, it is possible to use a combination of the Generalized Integral Transform Techniques and Laplace transforms to solve this problem upstream and downstream in the thermal region of the tube. The approximate solution indicates that a plane wave propogates down the tube and the phase of the wave defines critical values in frequency and time along the tube. Use of Dirac’s distribution makes it possible to define a bulk temperature and a change in unsteady bulk temperature from that of steady bulk temperature is presented. By means of classical analysis an inequality involving the two quantities is presented. As a result a measure of heat transfer in pulsatile flow compared to that of steady flow is presented.

Author Biography

Dr. Terry Moschandreou

Dr. Terry E. Moschandreou is currently working for Thames Valley District School Board as Intermediate/ Senior Teacher in Mathematics and Science. He has been a professor in applied mathematics at the University of Western Ontario in the School of Mathematical and Statistical Sciences where he has taught for several years. He received his PhD degree in Applied Mathematics from the University of Western Ontario in 1996. The greater part of his professional life has been spent at the University of Western Ontario and Fanshawe College in London, Ontario, Canada. For a short period, he worked at the NationalrnTechnical University of Athens, Greece. Dr. Moschandreou is the author of several research articles in blood flow and oxygen transport in the microcirculation, general fluid dynamics, and theory of differential equations.

Academic Disclosures

Ethical Approval

Not applicable for this article.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability

Not applicable for this article.

Acknowledgement

I would like to express my thanks and appreciation to my supervisor Dr. M. Zamir for his guidance and direction over the past few years. I also appreciate helpful discussions with Dr. Stan Deakin. I also would like to thank National Sciences and Engineering Research Council of Canada for their financial support.

Dedication

To My Father and Mother

AI Use Disclosure

No generative AI was used for analysis or results.

Trial Registration

Null — Not applicable for mathematical/engineering research

Funding

NSERC Canada mentioned explicitly in acknowledgements

References

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GENIN, L. et al. Hydrodynamics and heat transfer with pulsating fluid flow in tubes. Thermal Engineering, v. 39, n. 5, 1992.

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LEVEQUE, A. Les lois de la transmission de chaleur par convection. Annls Mines. Paris, v. 13, n. Mem. Ser. 12, p. 283–290, 1928.

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NUSSELT, W. The dependence of the heat-transfer coefficient on tube length. Zeit. Ver. deut. Ing., v. 54, p. 1154–1158, 1910.

PEATTIE, R.; BUDWIG, R. Heat Transfer in laminar, oscillatory flow in cylindrical and conical tubes. Int. J. Heat Mass Transfer, v. 32, n. 5, p. 923–934, 1989.

PEREZ GUERRERO, J.; COTTA, R. Integral transform method for Navier-Stokes equations in stream-function only formulation. Int. J. Num. Meth. Fluids, v. 15, p. 399–409, 1992.

SELLARS, J.; TRIBUS, M.; KLEIN, J. Heat Transfer to Laminar Flow in a Round tube or Flat Conduit - The Graetz Problem Extended. Trans. Am. Soc. Mech. Engrs., p. 441, 1956.

SERFATY, R.; COTTA, R. Integral transform solutions of diffusion problems with nonlinear equation coefficients. Int. Comm. Heat Mass Transfer, v. 17, p. 852–864, 1990.

SERFATY, R.; COTTA, R. Hybrid analysis of transient nonlinear convection-diffusion problems. Int. J. Num. Meth. Heat Fluid Flow, v. 2, p. 55–62, 1992.

SERFATY, R.; COTTA, R. Hybrid analysis of transient non-linear convection-diffusion problems. Int. J. Num. Meth. Heat Fluid Flow, v. 2, p. 55–62, 1992.

SIEGEL, R.; PERLMUTTER, M. Heat Transfer for pulsating Laminar duct flow. Trans. ASME J. Heat Trans, v. 84, n. 2, p. 111–123, 1962.

UCHIDA, S. The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe. ZAMP, v. VII, 1956.

VAN DYKE, M. Perturbation Methods in Fluid Mechanics. [s.l.] The Parabolic Press, 1975.

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ZEMANIAN, A. Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications. [s.l.] Dover Publications Inc., 1987.

[1]1987. IMSL Library, MATH/LIB. IMSL.

[2]1929. The Transverse Velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established. Proc. Roy. Soc. 42, pt.1 (1929), 1–15.

[3]Ahlfors, L.V. Complex Analysis: An introduction to the theory of analytic functions of one complex variable. McGraw-Hill.

[4]Andre, P. et al. 1981. Etude des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique. Int. J. Heat Mass Transfer. 24, No.1 (1981), 1211–1219.

[5]Atabek, H., Chang, C. 1961. Oscillatory flow near the entry of a circular tube. ZAMP. 12, (1961), 185–201.

[6]Barnett, D., Vachon, R. 1970. An Analysis of convective heat transfer for pulsating flow in a tube. Proc. 4th Int. Heat Transfer Conference, Paris (1970), 1–11.

[7]Base, T. et al. 1995. The effects of a pulsating flow on the forced convection heat transfer inside a circular heated tube. Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95 (1995), 612–613.

[8]Cho, H., Hyun, J. 1990. Numerical solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe. Int. J. Heat and Fluid Flow. 11, 4 (1990).

[9]Cotta, R. 1994. Benchmark results in computational heat and fluid flow: the integral transform method. Int. J. Heat Mass Transfer. 37, Suppl.1 (1994), 381–393.

[10]Cotta, R. 1992. Computational integral transform approach in nonlinear diffusion and convection-diffusion problems. Serie Scientifica LIN-1202. Laboratorio di Ingegneria Nucleare di Montecuccolino, Universita degli Studi di Bologna.

[11]Cotta, R. 1993. Integral Transforms in Computational Heat and Fluid Flow. CRC Press.

[12]Cotta, R. et al. 1992. Hybrid solution of the incompressible Navier-Stokes equations via integral transformation. Proc. of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy (1992), 135–150.

[13]Cotta, R. et al. 1990. Integral transform solution of a class of transient convection-diffusion problems. Proc. of the Int. Conf. on Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK (1990), 239–250.

[14]Cotta, R. et al. 1992. Steady-State Diffusion Problems with Variable Equation Coefficients. Int. J. Heat and Technology. 10, 3-4 (1992), 104.

[15]Cotta, R., Carvalho, T. 1991. Hybrid analysis of boundary layer equations for internal flow problems. Proc. of the 7th Int. Conf. on Num. Meth. in Laminar and Turbulent Flow, Stanford, CA (1991), 106–115.

[16]Cotta, R., Mikhailov, M. 1993. The integral transform method. Appl. Math. Modelling. 17, (1993), 156–161.

[17]Cotta, R., Ozisik, M. 1987. Diffusion Problems with General Time-Dependent Coefficients. J. Braz. Assoc. Mech. Sciences. 9, 4 (1987), 269–292.

[18]Cotta, R., Ozisik, M. 1986. Transient Forced Convection in Laminar Channel Flow with Stepwise Variations of Wall Temperature. Can. J. Chem. Eng. 64, (1986), 734–742.

[19]Cotta, R., Serfaty, R. 1991. Integral transform algorithm for parabolic diffusion problems with nonlinear boundary and equation source terms. Proc. of the 8th Int. Conf. on Num. Meth. for Thermal Problems, Stanford, CA (1991), 916–926.

[20]Courant, R., Hilbert, D. 1962. Methods of Mathematical Physics, Volume II. Wiley.

[21]Creff, R., Andre, P. 1985. Dynamic and Convective Results for a Developing Laminar unsteady Flow. International Journal for Numerical Methods in Fluids. 5, (1985), 145–160.

[22]Fallen, M. 1982. Heat Transfer in a Pipe with Superimposed Pulsating Flow. Warme und Stoffubertragung. 16, (1982), 89–99.

[23]Genin, L. et al. 1992. Hydrodynamics and heat transfer with pulsating fluid flow in tubes. Thermal Engineering. 39, 5 (1992).

[24]Graetz, L. 1885. Uber die Warmeleitungsfahigkeit von Flussigkeiten. Annalen der Physik Chem. 25, (1885), 337–357.

[25]Haneke, H. et al. 1992. Advanced Computational Methods in Heat Transfer II, Vol.2: Natural/Forced Convection and Combustion Simulation. Advanced Computational Methods in Heat Transfer II. Computational Mechanics Publications.

[26]Hapke, J. 1974. Warmeubergang bei pulsierender laminarer Stromung. Brennst.-Warme-Kraft. 26, (1974).

[27]Jakob, M. 1949. Heat Transfer. John Wiley.

[28]Kim, S. et al. 1993. Heat Transfer in the thermally developing region of a pulsating channel flow. Int. J. Heat Mass Transfer. 36, 17 (1993), 4257–4266.

[29]Kim, W., Ozisik, M. 1987. Transient Laminar Forced Convection in Ducts with Suddenly Applied Uniform Wall Heat Flux. Int. J. Heat and Mass Transfer. 30, (1987), 1753–1756.

[30]Leiroz, A., Cotta, R. 1993. On the solution of nonlinear elliptic convection-diffusion problems through the integral transform method. Num. Heat Transfer, Part B-Fundamentals. 23, (1993), 401–411.

[31]Leveque, A. 1928. Les lois de la transmission de chaleur par convection. Annls Mines. Paris. 13, Mem. Ser. 12 (1928), 283–290.

[32]Luikov, A. 1973. Heat and Mass Transfer. Mir Publishers.

[33]Mikhailov, M., Cotta, R. 1990. Unified integral transform method. J. Braz. Assoc. Mech. Sci., RBCM. 12, 3 (1990), 301–310.

[34]Mikhailov, M., Ozisik, M. 1984. Unified analysis and Solutions of Heat and Mass Diffusion. Wiley.

[35]Nusselt, W. 1910. The dependence of the heat-transfer coefficient on tube length. Zeit. Ver. deut. Ing. 54, (1910), 1154–1158.

[36]Peattie, R., Budwig, R. 1989. Heat Transfer in laminar, oscillatory flow in cylindrical and conical tubes. Int. J. Heat Mass Transfer. 32, 5 (1989), 923–934.

[37]Perez Guerrero, J., Cotta, R. 1992. Integral transform method for Navier-Stokes equations in stream-function only formulation. Int. J. Num. Meth. Fluids. 15, (1992), 399–409.

[38]Sellars, J. et al. 1956. Heat Transfer to Laminar Flow in a Round tube or Flat Conduit - The Graetz Problem Extended. Trans. Am. Soc. Mech. Engrs. (1956), 441.

[39]Serfaty, R., Cotta, R. 1992. Hybrid analysis of transient non-linear convection-diffusion problems. Int. J. Num. Meth. Heat Fluid Flow. 2, (1992), 55–62.

[40]Serfaty, R., Cotta, R. 1992. Hybrid analysis of transient nonlinear convection-diffusion problems. Int. J. Num. Meth. Heat Fluid Flow. 2, (1992), 55–62.

[41]Serfaty, R., Cotta, R. 1990. Integral transform solutions of diffusion problems with nonlinear equation coefficients. Int. Comm. Heat Mass Transfer. 17, (1990), 852–864.

[42]Siegel, R., Perlmutter, M. 1962. Heat Transfer for pulsating Laminar duct flow. Trans. ASME J. Heat Trans. 84, 2 (1962), 111–123.

[43]Uchida, S. 1956. The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe. ZAMP. VII, (1956).

[44]Van Dyke, M. 1975. Perturbation Methods in Fluid Mechanics. The Parabolic Press.

[45]Womersley, J. 1955. Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx. Phil. Mag. 46, (1955), 199–221.

[46]Zemanian, A. 1987. Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications. Dover Publications Inc.

(1)The Transverse Velocity Gradient Near the Mouths of Pipes in Which an Alternating or Continuous Flow of Air Is Established. Proc. Roy. Soc. 1929, 42 (pt.1), 1-15.

(2)Uchida, S. The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe. ZAMP 1956, VII.

(3)Womersley, J. Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx. Phil. Mag. 1955, 46, 199-221.

(4)Atabek, H.; Chang, C. Oscillatory Flow Near the Entry of a Circular Tube. ZAMP 1961, 12, 185-201.

(5)Siegel, R.; Perlmutter, M. Heat Transfer for Pulsating Laminar Duct Flow. Trans. ASME J. Heat Trans 1962, 84 (2), 111-123.

(6)Barnett, D.; Vachon, R. An Analysis of Convective Heat Transfer for Pulsating Flow in a Tube. In Proc. 4th Int. Heat Transfer Conference, Paris; 1970; pp. 1-11.

(7)Creff, R.; Andre, P. Dynamic and Convective Results for a Developing Laminar Unsteady Flow. International Journal for Numerical Methods in Fluids 1985, 5, 145-160.

(8)Cho, H.; Hyun, J. Numerical Solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe. Int. J. Heat and Fluid Flow 1990, 11 (4).

(9)Haneke, H.; Laschefski, H.; Grobe-Gorgemann, A.; Mitra, N. Advanced Computational Methods in Heat Transfer II, Vol.2: Natural Forced Convection and Combustion Simulation. Advanced Computational Methods in Heat Transfer II. Computational Mechanics Publications 1992, pp. 287-298.

(10)Kim, S.; Kang, B.; Hyun, J. Heat Transfer in the Thermally Developing Region of a Pulsating Channel Flow. Int. J. Heat Mass Transfer 1993, 36 (17), 4257-4266.

(11)Base, T.; Campbell, M.; Hobbs, J. The Effects of a Pulsating Flow on the Forced Convection Heat Transfer Inside a Circular Heated Tube. In Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95; 1995; Vol. 2, pp. 612-613.

(12)Fallen, M. Heat Transfer in a Pipe With Superimposed Pulsating Flow. Warme und Stoffubertragung 1982, 16, 89-99.

(13)Genin, L.; Loval, A.; Manchkha, S.; Sviridov, V. Hydrodynamics and Heat Transfer With Pulsating Fluid Flow in Tubes. Thermal Engineering 1992, 39 (5).

(14)Hapke, J. Warmeubergang Bei Pulsierender Laminarer Stromung. Brennst.-Warme-Kraft 1974, 26.

(15)Andre, P.; Creff, R.; Crabol, J. Etude Des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique. Int. J. Heat Mass Transfer 1981, 24 (No.1), 1211-1219.

(16)Peattie, R.; Budwig, R. Heat Transfer in Laminar, Oscillatory Flow in Cylindrical and Conical Tubes. Int. J. Heat Mass Transfer 1989, 32 (5), 923-934.

(17)Van Dyke, M. Perturbation Methods in Fluid Mechanics; The Parabolic Press, 1975.

(18)Graetz, L. Uber Die Warmeleitungsfahigkeit Von Flussigkeiten. Annalen der Physik Chem. 1885, 25, 337-357.

(19)Nusselt, W. The Dependence of the Heat-Transfer Coefficient on Tube Length. Zeit. Ver. deut. Ing. 1910, 54, 1154-1158.

(20)Leveque, A. Les Lois de la Transmission de Chaleur Par Convection. Annls Mines. Paris 1928, 13 (Mem. Ser. 12), 283-290.

(21)Sellars, J.; Tribus, M.; Klein, J. Heat Transfer to Laminar Flow in a Round Tube or Flat Conduit - The Graetz Problem Extended. Trans. Am. Soc. Mech. Engrs. 1956, 441.

(22)Ahlfors, L. V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable; McGraw-Hill.

(23)Cotta, R. Integral Transforms in Computational Heat and Fluid Flow; CRC Press, 1993.

(24)Cotta, R. Benchmark Results in Computational Heat and Fluid Flow: The Integral Transform Method. Int. J. Heat Mass Transfer 1994, 37 (Suppl.1), 381-393.

(25)Cotta, R.; Mikhailov, M. The Integral Transform Method. Appl. Math. Modelling 1993, 17, 156-161.

(26)Zemanian, A. Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, With Applications; Dover Publications Inc., 1987.

(27)Luikov, A. Heat and Mass Transfer; Mir Publishers, 1973.

(28)Mikhailov, M.; Ozisik, M. Unified Analysis and Solutions of Heat and Mass Diffusion; Wiley, 1984.

(29)Cotta, R. Computational Integral Transform Approach in Nonlinear Diffusion and Convection-Diffusion Problems. Serie Scientifica LIN-1202. Laboratorio di Ingegneria Nucleare di Montecuccolino, Universita degli Studi di Bologna 1992.

(30)Mikhailov, M.; Cotta, R. Unified Integral Transform Method. J. Braz. Assoc. Mech. Sci., RBCM 1990, 12 (3), 301-310.

(31)Serfaty, R.; Cotta, R. Integral Transform Solutions of Diffusion Problems With Nonlinear Equation Coefficients. Int. Comm. Heat Mass Transfer 1990, 17, 852-864.

(32)Cotta, R.; Serfaty, R. Integral Transform Algorithm for Parabolic Diffusion Problems With Nonlinear Boundary and Equation Source Terms. In Proc. of the 8th Int. Conf. on Num. Meth. for Thermal Problems, Stanford, CA; 1991; pp. 916-926.

(33)Cotta, R.; Serfaty, R.; Guedes, R. Integral Transform Solution of a Class of Transient Convection-Diffusion Problems. In Proc. of the Int. Conf. on Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK; 1990; Vol. 1, pp. 239-250.

(34)Serfaty, R.; Cotta, R. Hybrid Analysis of Transient Nonlinear Convection-Diffusion Problems. Int. J. Num. Meth. Heat Fluid Flow 1992, 2, 55-62.

(35)Leiroz, A.; Cotta, R. On the Solution of Nonlinear Elliptic Convection-Diffusion Problems through the Integral Transform Method. Num. Heat Transfer, Part B-Fundamentals 1993, 23, 401-411.

(36)Perez Guerrero, J.; Cotta, R. Integral Transform Method for Navier-Stokes Equations in Stream-Function only Formulation. Int. J. Num. Meth. Fluids 1992, 15, 399-409.

(37)Cotta, R.; Perez Guerrero, J.; Scofano Neto, F. Hybrid Solution of the Incompressible Navier-Stokes Equations via Integral Transformation. In Proc. of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy; 1992; Vol. 1, pp. 135-150.

(38)IMSL Library, MATH LIB. IMSL 1987.

(39)Cotta, R.; Ozisik, M. Diffusion Problems With General Time-Dependent Coefficients. J. Braz. Assoc. Mech. Sciences 1987, 9 (4), 269-292.

(40)Cotta, R.; Leiroz, A.; Aparecido, J. Steady-State Diffusion Problems With Variable Equation Coefficients. Int. J. Heat and Technology 1992, 10 (3-4), 104.

(41)Cotta, R.; Ozisik, M. Transient Forced Convection in Laminar Channel Flow With Stepwise Variations of Wall Temperature. Can. J. Chem. Eng. 1986, 64, 734-742.

(42)Kim, W.; Ozisik, M. Transient Laminar Forced Convection in Ducts With Suddenly Applied Uniform Wall Heat Flux. Int. J. Heat and Mass Transfer 1987, 30, 1753-1756.

(43)Serfaty, R.; Cotta, R. Hybrid Analysis of Transient Non-Linear Convection-Diffusion Problems. Int. J. Num. Meth. Heat Fluid Flow 1992, 2, 55-62.

(44)Cotta, R.; Carvalho, T. Hybrid Analysis of Boundary Layer Equations for Internal Flow Problems. In Proc. of the 7th Int. Conf. on Num. Meth. in Laminar and Turbulent Flow, Stanford, CA; 1991; pp. 106-115.

(45)Courant, R.; Hilbert, D. Methods of Mathematical Physics, Volume II; Wiley, 1962; Vol. II.

(46)Jakob, M. Heat Transfer; John Wiley, 1949.

1.The Transverse Velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established. Proc. Roy. Soc. 1929;42(pt.1):1-15.

2.Uchida S. The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe. ZAMP. 1956;VII.

3.Womersley J. Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx. Phil. Mag. 1955;46:199-221.

4.Atabek H, Chang C. Oscillatory flow near the entry of a circular tube. ZAMP. 1961;12:185-201.

5.Siegel R, Perlmutter M. Heat Transfer for pulsating Laminar duct flow. Trans. ASME J. Heat Trans. 1962;84(2):111-123.

6.Barnett D, Vachon R. An Analysis of convective heat transfer for pulsating flow in a tube. In: Proc. 4th Int. Heat Transfer Conference, Paris. ; 1970:1-11.

7.Creff R, Andre P. Dynamic and Convective Results for a Developing Laminar unsteady Flow. International Journal for Numerical Methods in Fluids. 1985;5:145-160.

8.Cho H, Hyun J. Numerical solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe. Int. J. Heat and Fluid Flow. 1990;11(4).

9.Haneke H, Laschefski H, Grobe-Gorgemann A, Mitra N. Advanced Computational Methods in Heat Transfer II, Vol.2: Natural/Forced Convection and Combustion Simulation. Advanced Computational Methods in Heat Transfer II. 1992;2:287-298.

10.Kim S, Kang B, Hyun J. Heat Transfer in the thermally developing region of a pulsating channel flow. Int. J. Heat Mass Transfer. 1993;36(17):4257-4266.

11.Base T, Campbell M, Hobbs J. The effects of a pulsating flow on the forced convection heat transfer inside a circular heated tube. In: Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95. Vol. 2. ; 1995:612-613.

12.Fallen M. Heat Transfer in a Pipe with Superimposed Pulsating Flow. Warme und Stoffubertragung. 1982;16:89-99.

13.Genin L, Loval A, Manchkha S, Sviridov V. Hydrodynamics and heat transfer with pulsating fluid flow in tubes. Thermal Engineering. 1992;39(5).

14.Hapke J. Warmeubergang bei pulsierender laminarer Stromung. Brennst.-Warme-Kraft. 1974;26.

15.Andre P, Creff R, Crabol J. Etude des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique. Int. J. Heat Mass Transfer. 1981;24(No.1):1211-1219.

16.Peattie R, Budwig R. Heat Transfer in laminar, oscillatory flow in cylindrical and conical tubes. Int. J. Heat Mass Transfer. 1989;32(5):923-934.

17.Van Dyke M. Perturbation Methods in Fluid Mechanics. The Parabolic Press; 1975.

18.Graetz L. Uber die Warmeleitungsfahigkeit von Flussigkeiten. Annalen der Physik Chem. 1885;25:337-357.

19.Nusselt W. The dependence of the heat-transfer coefficient on tube length. Zeit. Ver. deut. Ing. 1910;54:1154-1158.

20.Leveque A. Les lois de la transmission de chaleur par convection. Annls Mines. Paris. 1928;13(Mem. Ser. 12):283-290.

21.Sellars J, Tribus M, Klein J. Heat Transfer to Laminar Flow in a Round tube or Flat Conduit - The Graetz Problem Extended. Trans. Am. Soc. Mech. Engrs. Published online 1956:441.

22.Ahlfors LV. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. McGraw-Hill

23.Cotta R. Integral Transforms in Computational Heat and Fluid Flow. CRC Press; 1993.

24.Cotta R. Benchmark results in computational heat and fluid flow: the integral transform method. Int. J. Heat Mass Transfer. 1994;37(Suppl.1):381-393.

25.Cotta R, Mikhailov M. The integral transform method. Appl. Math. Modelling. 1993;17:156-161.

26.Zemanian A. Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, With Applications. Dover Publications Inc.; 1987.

27.Luikov A. Heat and Mass Transfer. Mir Publishers; 1973.

28.Mikhailov M, Ozisik M. Unified Analysis and Solutions of Heat and Mass Diffusion. Wiley; 1984.

29.Cotta R. Computational integral transform approach in nonlinear diffusion and convection-diffusion problems. Serie Scientifica LIN-1202. Published online 1992.

30.Mikhailov M, Cotta R. Unified integral transform method. J. Braz. Assoc. Mech. Sci., RBCM. 1990;12(3):301-310.

31.Serfaty R, Cotta R. Integral transform solutions of diffusion problems with nonlinear equation coefficients. Int. Comm. Heat Mass Transfer. 1990;17:852-864.

32.Cotta R, Serfaty R. Integral transform algorithm for parabolic diffusion problems with nonlinear boundary and equation source terms. In: Proc. of the 8th Int. Conf. on Num. Meth. For Thermal Problems, Stanford, CA. ; 1991:916-926.

33.Cotta R, Serfaty R, Guedes R. Integral transform solution of a class of transient convection-diffusion problems. In: Proc. of the Int. Conf. On Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK. Vol. 1. ; 1990:239-250.

34.Serfaty R, Cotta R. Hybrid analysis of transient nonlinear convection-diffusion problems. Int. J. Num. Meth. Heat Fluid Flow. 1992;2:55-62.

35.Leiroz A, Cotta R. On the solution of nonlinear elliptic convection-diffusion problems through the integral transform method. Num. Heat Transfer, Part B-Fundamentals. 1993;23:401-411.

36.Perez Guerrero J, Cotta R. Integral transform method for Navier-Stokes equations in stream-function only formulation. Int. J. Num. Meth. Fluids. 1992;15:399-409.

37.Cotta R, Perez Guerrero J, Scofano Neto F. Hybrid solution of the incompressible Navier-Stokes equations via integral transformation. In: Proc. Of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy. Vol. 1. ; 1992:135-150.

38.IMSL Library, MATH/LIB. Published online 1987.

39.Cotta R, Ozisik M. Diffusion Problems with General Time-Dependent Coefficients. J. Braz. Assoc. Mech. Sciences. 1987;9(4):269-292.

40.Cotta R, Leiroz A, Aparecido J. Steady-State Diffusion Problems with Variable Equation Coefficients. Int. J. Heat and Technology. 1992;10(3-4):104.

41.Cotta R, Ozisik M. Transient Forced Convection in Laminar Channel Flow with Stepwise Variations of Wall Temperature. Can. J. Chem. Eng. 1986;64:734-742.

42.Kim W, Ozisik M. Transient Laminar Forced Convection in Ducts with Suddenly Applied Uniform Wall Heat Flux. Int. J. Heat and Mass Transfer. 1987;30:1753-1756.

43.Serfaty R, Cotta R. Hybrid analysis of transient non-linear convection-diffusion problems. Int. J. Num. Meth. Heat Fluid Flow. 1992;2:55-62.

44.Cotta R, Carvalho T. Hybrid analysis of boundary layer equations for internal flow problems. In: Proc. of the 7th Int. Conf. on Num. Meth. In Laminar and Turbulent Flow, Stanford, CA. ; 1991:106-115.

45.Courant R, Hilbert D. Methods of Mathematical Physics, Volume II. Vol. II. Wiley; 1962.

46.Jakob M. Heat Transfer. John Wiley; 1949.

Ahlfors, L. V. (n.d.). Complex Analysis: An introduction to the theory of analytic functions of one complex variable. McGraw-Hill.

Andre, P., Creff, R., & Crabol, J. (1981). Etude des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique. Int. J. Heat Mass Transfer, 24(No.1), 1211-1219.

Atabek, H., & Chang, C. (1961). Oscillatory flow near the entry of a circular tube. ZAMP, 12, 185-201.

Barnett, D., & Vachon, R. (1970). An Analysis of convective heat transfer for pulsating flow in a tube. Proc. 4th Int. Heat Transfer Conference, Paris, 1-11.

Base, T., Campbell, M., & Hobbs, J. (1995). The effects of a pulsating flow on the forced convection heat transfer inside a circular heated tube. Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95, 2, 612-613.

Cho, H., & Hyun, J. (1990). Numerical solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe. Int. J. Heat and Fluid Flow, 11(4).

Cotta, R. (1992). Computational integral transform approach in nonlinear diffusion and convection-diffusion problems. In Serie Scientifica LIN-1202. Laboratorio di Ingegneria Nucleare di Montecuccolino, Universita degli Studi di Bologna.

Cotta, R. (1993). Integral Transforms in Computational Heat and Fluid Flow. CRC Press.

Cotta, R. (1994). Benchmark results in computational heat and fluid flow: the integral transform method. Int. J. Heat Mass Transfer, 37(Suppl.1), 381-393.

Cotta, R., & Carvalho, T. (1991). Hybrid analysis of boundary layer equations for internal flow problems. Proc. of the 7th Int. Conf. on Num. Meth. In Laminar and Turbulent Flow, Stanford, CA, Part 1, 106-115.

Cotta, R., & Mikhailov, M. (1993). The integral transform method. Appl. Math. Modelling, 17, 156-161.

Cotta, R., & Ozisik, M. (1986). Transient Forced Convection in Laminar Channel Flow with Stepwise Variations of Wall Temperature. Can. J. Chem. Eng., 64, 734-742.

Cotta, R., & Ozisik, M. (1987). Diffusion Problems with General Time-Dependent Coefficients. J. Braz. Assoc. Mech. Sciences, 9(4), 269-292.

Cotta, R., & Serfaty, R. (1991). Integral transform algorithm for parabolic diffusion problems with nonlinear boundary and equation source terms. Proc. of the 8th Int. Conf. on Num. Meth. For Thermal Problems, Stanford, CA, part 2, 916-926.

Cotta, R., Leiroz, A., & Aparecido, J. (1992). Steady-State Diffusion Problems with Variable Equation Coefficients. Int. J. Heat and Technology, 10(3-4), 104.

Cotta, R., Perez Guerrero, J., & Scofano Neto, F. (1992). Hybrid solution of the incompressible Navier-Stokes equations via integral transformation. Proc. Of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy, 1, 135-150.

Cotta, R., Serfaty, R., & Guedes, R. (1990). Integral transform solution of a class of transient convection-diffusion problems. Proc. of the Int. Conf. On Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK, 1, 239-250.

Courant, R., & Hilbert, D. (1962). Methods of Mathematical Physics, Volume II (Vol. II). Wiley.

Creff, R., & Andre, P. (1985). Dynamic and Convective Results for a Developing Laminar unsteady Flow. International Journal for Numerical Methods in Fluids, 5, 145-160.

Fallen, M. (1982). Heat Transfer in a Pipe with Superimposed Pulsating Flow. Warme Und Stoffubertragung, 16, 89-99.

Genin, L., Loval, A., Manchkha, S., & Sviridov, V. (1992). Hydrodynamics and heat transfer with pulsating fluid flow in tubes. Thermal Engineering, 39(5).

Graetz, L. (1885). Uber die Warmeleitungsfahigkeit von Flussigkeiten. Annalen Der Physik Chem., 25, 337-357.

Haneke, H., Laschefski, H., Grobe-Gorgemann, A., & Mitra, N. (1992). Advanced Computational Methods in Heat Transfer II, Vol.2: Natural/Forced Convection and Combustion Simulation. In Advanced Computational Methods in Heat Transfer II (Vols. 2, pp. 287-298). Computational Mechanics Publications.

Hapke, J. (1974). Warmeubergang bei pulsierender laminarer Stromung. Brennst.-Warme-Kraft, 26.

IMSL Library, MATH/LIB. (1987). IMSL.

Jakob, M. (1949). Heat Transfer. John Wiley.

Kim, S., Kang, B., & Hyun, J. (1993). Heat Transfer in the thermally developing region of a pulsating channel flow. Int. J. Heat Mass Transfer, 36(17), 4257-4266.

Kim, W., & Ozisik, M. (1987). Transient Laminar Forced Convection in Ducts with Suddenly Applied Uniform Wall Heat Flux. Int. J. Heat and Mass Transfer, 30, 1753-1756.

Leiroz, A., & Cotta, R. (1993). On the solution of nonlinear elliptic convection-diffusion problems through the integral transform method. Num. Heat Transfer, Part B-Fundamentals, 23, 401-411.

Leveque, A. (1928). Les lois de la transmission de chaleur par convection. Annls Mines. Paris, 13(Mem. Ser. 12), 283-290.

Luikov, A. (1973). Heat and Mass Transfer. Mir Publishers.

Mikhailov, M., & Cotta, R. (1990). Unified integral transform method. J. Braz. Assoc. Mech. Sci., RBCM, 12(3), 301-310.

Mikhailov, M., & Ozisik, M. (1984). Unified analysis and Solutions of Heat and Mass Diffusion. Wiley.

Nusselt, W. (1910). The dependence of the heat-transfer coefficient on tube length. Zeit. Ver. Deut. Ing., 54, 1154-1158.

Peattie, R., & Budwig, R. (1989). Heat Transfer in laminar, oscillatory flow in cylindrical and conical tubes. Int. J. Heat Mass Transfer, 32(5), 923-934.

Perez Guerrero, J., & Cotta, R. (1992). Integral transform method for Navier-Stokes equations in stream-function only formulation. Int. J. Num. Meth. Fluids, 15, 399-409.

Sellars, J., Tribus, M., & Klein, J. (1956). Heat Transfer to Laminar Flow in a Round tube or Flat Conduit - The Graetz Problem Extended. Trans. Am. Soc. Mech. Engrs., 441.

Serfaty, R., & Cotta, R. (1990). Integral transform solutions of diffusion problems with nonlinear equation coefficients. Int. Comm. Heat Mass Transfer, 17, 852-864.

Serfaty, R., & Cotta, R. (1992). Hybrid analysis of transient non-linear convection-diffusion problems. Int. J. Num. Meth. Heat Fluid Flow, 2, 55-62.

Serfaty, R., & Cotta, R. (1992). Hybrid analysis of transient nonlinear convection-diffusion problems. Int. J. Num. Meth. Heat Fluid Flow, 2, 55-62.

Siegel, R., & Perlmutter, M. (1962). Heat Transfer for pulsating Laminar duct flow. Trans. ASME J. Heat Trans, 84(2), 111-123.

The Transverse Velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established. (1929). Proc. Roy. Soc., 42(pt.1), 1-15.

Uchida, S. (1956). The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe. ZAMP, VII.

Van Dyke, M. (1975). Perturbation Methods in Fluid Mechanics. The Parabolic Press.

Womersley, J. (1955). Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx. Phil. Mag., 46, 199-221.

Zemanian, A. (1987). Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications. Dover Publications Inc.

1929. “The Transverse Velocity Gradient Near the Mouths of Pipes in Which an Alternating or Continuous Flow of Air Is Established”. Proc. Roy. Soc. 42 (pt.1): 1-15.

Ahlfors, Lars V. n.d. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. McGraw-Hill.

Andre, P., R. Creff, and J. Crabol. 1981. “Etude Des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique”. Int. J. Heat Mass Transfer 24 (No.1): 1211-19.

Atabek, H.B., and C.C. Chang. 1961. “Oscillatory Flow Near the Entry of a Circular Tube”. ZAMP 12: 185-201.

Barnett, D.O., and R.I. Vachon. 1970. “An Analysis of Convective Heat Transfer for Pulsating Flow in a Tube”. In Proc. 4th Int. Heat Transfer Conference, Paris, 1-11.

Base, T.E., M.R. Campbell, and J. Hobbs. 1995. “The Effects of a Pulsating Flow on the Forced Convection Heat Transfer Inside a Circular Heated Tube”. In Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95, 2:612-13.

Cho, H.W., and J.M. Hyun. 1990. “Numerical Solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe”. Int. J. Heat and Fluid Flow 11 (4).

Cotta, R.M. 1992. “Computational Integral Transform Approach in Nonlinear Diffusion and Convection-Diffusion Problems”. Serie Scientifica LIN-1202. Laboratorio di Ingegneria Nucleare di Montecuccolino, Universita degli Studi di Bologna.

Cotta, R.M. 1993. Integral Transforms in Computational Heat and Fluid Flow. CRC Press.

Cotta, R.M., A.J.K. Leiroz, and J.B. Aparecido. 1992. “Steady-State Diffusion Problems With Variable Equation Coefficients”. Int. J. Heat and Technology 10 (3-4): 104.

Cotta, R.M., and M.D. Mikhailov. 1993. “The Integral Transform Method”. Appl. Math. Modelling 17: 156-61.

Cotta, R.M., and M.N. Ozisik. 1986. “Transient Forced Convection in Laminar Channel Flow With Stepwise Variations of Wall Temperature”. Can. J. Chem. Eng. 64: 734-42.

Cotta, R.M., and M.N. Ozisik. 1987. “Diffusion Problems With General Time-Dependent Coefficients”. J. Braz. Assoc. Mech. Sciences 9 (4): 269-92.

Cotta, R.M., and T.M.B. Carvalho. 1991. “Hybrid Analysis of Boundary Layer Equations for Internal Flow Problems”. In Proc. of the 7th Int. Conf. on Num. Meth. In Laminar and Turbulent Flow, Stanford, CA, 106-15.

Cotta, R.M., J.S. Perez Guerrero, and F. Scofano Neto. 1992. “Hybrid Solution of the Incompressible Navier-Stokes Equations via Integral Transformation”. In Proc. Of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy, 1:135-50.

Cotta, R.M., R. Serfaty, and R.O.C. Guedes. 1990. “Integral Transform Solution of a Class of Transient Convection-Diffusion Problems”. In Proc. of the Int. Conf. On Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK, 1:239-50.

Courant, R., and D. Hilbert. 1962. Methods of Mathematical Physics, Volume II. Vol. II. Wiley.

Creff, R., and P. Andre. 1985. “Dynamic and Convective Results for a Developing Laminar Unsteady Flow”. International Journal for Numerical Methods in Fluids 5: 145-60.

Fallen, M. 1982. “Heat Transfer in a Pipe With Superimposed Pulsating Flow”. Warme Und Stoffubertragung 16: 89-99.

Genin, L.G., A.P. Loval, S.P. Manchkha, and V.G. Sviridov. 1992. “Hydrodynamics and Heat Transfer With Pulsating Fluid Flow in Tubes”. Thermal Engineering 39 (5).

Graetz, L. 1885. “Uber Die Warmeleitungsfahigkeit Von Flussigkeiten”. Annalen Der Physik Chem. 25: 337-57.

Haneke, H., H. Laschefski, A. Grobe-Gorgemann, and N.K. Mitra. 1992. “Advanced Computational Methods in Heat Transfer II, Vol.2: Natural Forced Convection and Combustion Simulation”. Advanced Computational Methods in Heat Transfer II. Computational Mechanics Publications.

Hapke, J. 1974. “Warmeubergang Bei Pulsierender Laminarer Stromung”. Brennst.-Warme-Kraft 26.

Jakob, M. 1949. Heat Transfer. John Wiley.

Kim, S.Y., B.H. Kang, and J.M. Hyun. 1993. “Heat Transfer in the Thermally Developing Region of a Pulsating Channel Flow”. Int. J. Heat Mass Transfer 36 (17): 4257-66.

Kim, W.S., and M.N. Ozisik. 1987. “Transient Laminar Forced Convection in Ducts With Suddenly Applied Uniform Wall Heat Flux”. Int. J. Heat and Mass Transfer 30: 1753-56.

Leiroz, A.J.K., and R.M. Cotta. 1993. “On the Solution of Nonlinear Elliptic Convection-Diffusion Problems through the Integral Transform Method”. Num. Heat Transfer, Part B-Fundamentals 23: 401-11.

Leveque, A. 1928. “Les Lois de la Transmission de Chaleur Par Convection”. Annls Mines. Paris 13 (Mem. Ser. 12): 283-90.

Luikov, A.V. 1973. Heat and Mass Transfer. Mir Publishers.

Mikhailov, M.D., and M.N. Ozisik. 1984. Unified Analysis and Solutions of Heat and Mass Diffusion. Wiley.

Mikhailov, M.D., and R.M. Cotta. 1990. “Unified Integral Transform Method”. J. Braz. Assoc. Mech. Sci., RBCM 12 (3): 301-10.

Nusselt, W. 1910. “The Dependence of the Heat-Transfer Coefficient on Tube Length”. Zeit. Ver. Deut. Ing. 54: 1154-58.

Peattie, R., and R. Budwig. 1989. “Heat Transfer in Laminar, Oscillatory Flow in Cylindrical and Conical Tubes”. Int. J. Heat Mass Transfer 32 (5): 923-34.

Perez Guerrero, J.S., and R.M. Cotta. 1992. “Integral Transform Method for Navier-Stokes Equations in Stream-Function only Formulation”. Int. J. Num. Meth. Fluids 15: 399-409.

Sellars, J.R., M. Tribus, and J.S. Klein. 1956. “Heat Transfer to Laminar Flow in a Round Tube or Flat Conduit - The Graetz Problem Extended”. Trans. Am. Soc. Mech. Engrs., 441.

Serfaty, R., and R.M. Cotta. 1990. “Integral Transform Solutions of Diffusion Problems With Nonlinear Equation Coefficients”. Int. Comm. Heat Mass Transfer 17: 852-64.

Serfaty, R., and R.M. Cotta. 1992. “Hybrid Analysis of Transient Non-Linear Convection-Diffusion Problems”. Int. J. Num. Meth. Heat Fluid Flow 2: 55-62.

Serfaty, R., and R.M. Cotta. 1992. “Hybrid Analysis of Transient Nonlinear Convection-Diffusion Problems”. Int. J. Num. Meth. Heat Fluid Flow 2: 55-62.

Siegel, R., and M. Perlmutter. 1962. “Heat Transfer for Pulsating Laminar Duct Flow”. Trans. ASME J. Heat Trans 84 (2): 111-23.

Uchida, S. 1956. “The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe”. ZAMP VII.

Van Dyke, M. 1975. Perturbation Methods in Fluid Mechanics. The Parabolic Press.

Womersley, J.R. 1955. “Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx”. Phil. Mag. 46: 199-221.

Zemanian, A.H. 1987. Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, With Applications. Dover Publications Inc.

Cotta, R.M., and R. Serfaty. 1991. “Integral Transform Algorithm for Parabolic Diffusion Problems With Nonlinear Boundary and Equation Source Terms”. In Proc. of the 8th Int. Conf. on Num. Meth. For Thermal Problems, Stanford, CA, 916-26.

Cotta, R.M. 1994. “Benchmark Results in Computational Heat and Fluid Flow: The Integral Transform Method”. Int. J. Heat Mass Transfer 37 (Suppl.1): 381-93.

“IMSL Library, MATH LIB”. 1987. IMSL.

(1929) “The Transverse Velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established”, Proc. Roy. Soc., 42(pt.1), pp. 1–15.

Ahlfors, L.V. (no date) Complex Analysis: An introduction to the theory of analytic functions of one complex variable. McGraw-Hill.

Andre, P., Creff, R., Crabol, J. (1981) “Etude des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique”, Int. J. Heat Mass Transfer, 24(No.1), pp. 1211–1219.

Atabek, H., Chang, C. (1961) “Oscillatory flow near the entry of a circular tube”, ZAMP, 12, pp. 185–201.

Barnett, D., Vachon, R. (1970) “An Analysis of convective heat transfer for pulsating flow in a tube”, in Proc. 4th Int. Heat Transfer Conference, Paris, pp. 1–11.

Base, T., Campbell, M., Hobbs, J. (1995) “The effects of a pulsating flow on the forced convection heat transfer inside a circular heated tube”, in Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95, pp. 612–613.

Cho, H., Hyun, J. (1990) “Numerical solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe”, Int. J. Heat and Fluid Flow, 11(4).

Cotta, R. (1992) “Computational integral transform approach in nonlinear diffusion and convection-diffusion problems”, Serie Scientifica LIN-1202 [Preprint]. Laboratorio di Ingegneria Nucleare di Montecuccolino, Universita degli Studi di Bologna.

Cotta, R. (1993) Integral Transforms in Computational Heat and Fluid Flow. CRC Press.

Cotta, R. (1994) “Benchmark results in computational heat and fluid flow: the integral transform method”, Int. J. Heat Mass Transfer, 37(Suppl.1), pp. 381–393.

Cotta, R., Carvalho, T. (1991) “Hybrid analysis of boundary layer equations for internal flow problems”, in Proc. of the 7th Int. Conf. on Num. Meth. in Laminar and Turbulent Flow, Stanford, CA, pp. 106–115.

Cotta, R., Leiroz, A., Aparecido, J. (1992) “Steady-State Diffusion Problems with Variable Equation Coefficients”, Int. J. Heat and Technology, 10(3-4), p. 104.

Cotta, R., Mikhailov, M. (1993) “The integral transform method”, Appl. Math. Modelling, 17, pp. 156–161.

Cotta, R., Ozisik, M. (1986) “Transient Forced Convection in Laminar Channel Flow with Stepwise Variations of Wall Temperature”, Can. J. Chem. Eng., 64, pp. 734–742.

Cotta, R., Ozisik, M. (1987) “Diffusion Problems with General Time-Dependent Coefficients”, J. Braz. Assoc. Mech. Sciences, 9(4), pp. 269–292.

Cotta, R., Perez Guerrero, J., Scofano Neto, F. (1992) “Hybrid solution of the incompressible Navier-Stokes equations via integral transformation”, in Proc. of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy, pp. 135–150.

Cotta, R., Serfaty, R. (1991) “Integral transform algorithm for parabolic diffusion problems with nonlinear boundary and equation source terms”, in Proc. of the 8th Int. Conf. on Num. Meth. for Thermal Problems, Stanford, CA, pp. 916–926.

Cotta, R., Serfaty, R., Guedes, R. (1990) “Integral transform solution of a class of transient convection-diffusion problems”, in Proc. of the Int. Conf. on Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK, pp. 239–250.

Courant, R., Hilbert, D. (1962) Methods of Mathematical Physics, Volume II. Wiley.

Creff, R., Andre, P. (1985) “Dynamic and Convective Results for a Developing Laminar unsteady Flow”, International Journal for Numerical Methods in Fluids, 5, pp. 145–160.

Fallen, M. (1982) “Heat Transfer in a Pipe with Superimposed Pulsating Flow”, Warme und Stoffubertragung, 16, pp. 89–99.

Genin, L. et al. (1992) “Hydrodynamics and heat transfer with pulsating fluid flow in tubes”, Thermal Engineering, 39(5).

Graetz, L. (1885) “Uber die Warmeleitungsfahigkeit von Flussigkeiten”, Annalen der Physik Chem., 25, pp. 337–357.

Haneke, H. et al. (1992) “Advanced Computational Methods in Heat Transfer II, Vol.2: Natural/Forced Convection and Combustion Simulation”, Advanced Computational Methods in Heat Transfer II. Computational Mechanics Publications, pp. 287–298.

Hapke, J. (1974) “Warmeubergang bei pulsierender laminarer Stromung”, Brennst.-Warme-Kraft, 26.

Jakob, M. (1949) Heat Transfer. John Wiley.

Kim, S., Kang, B., Hyun, J. (1993) “Heat Transfer in the thermally developing region of a pulsating channel flow”, Int. J. Heat Mass Transfer, 36(17), pp. 4257–4266.

Kim, W., Ozisik, M. (1987) “Transient Laminar Forced Convection in Ducts with Suddenly Applied Uniform Wall Heat Flux”, Int. J. Heat and Mass Transfer, 30, pp. 1753–1756.

Leiroz, A., Cotta, R. (1993) “On the solution of nonlinear elliptic convection-diffusion problems through the integral transform method”, Num. Heat Transfer, Part B-Fundamentals, 23, pp. 401–411.

Leveque, A. (1928) “Les lois de la transmission de chaleur par convection”, Annls Mines. Paris, 13(Mem. Ser. 12), pp. 283–290.

Luikov, A. (1973) Heat and Mass Transfer. Mir Publishers.

Mikhailov, M., Cotta, R. (1990) “Unified integral transform method”, J. Braz. Assoc. Mech. Sci., RBCM, 12(3), pp. 301–310.

Mikhailov, M., Ozisik, M. (1984) Unified analysis and Solutions of Heat and Mass Diffusion. Wiley.

Nusselt, W. (1910) “The dependence of the heat-transfer coefficient on tube length”, Zeit. Ver. deut. Ing., 54, pp. 1154–1158.

Peattie, R., Budwig, R. (1989) “Heat Transfer in laminar, oscillatory flow in cylindrical and conical tubes”, Int. J. Heat Mass Transfer, 32(5), pp. 923–934.

Perez Guerrero, J., Cotta, R. (1992) “Integral transform method for Navier-Stokes equations in stream-function only formulation”, Int. J. Num. Meth. Fluids, 15, pp. 399–409.

Sellars, J., Tribus, M., Klein, J. (1956) “Heat Transfer to Laminar Flow in a Round tube or Flat Conduit - The Graetz Problem Extended”, Trans. Am. Soc. Mech. Engrs., p. 441.

Serfaty, R., Cotta, R. (1990) “Integral transform solutions of diffusion problems with nonlinear equation coefficients”, Int. Comm. Heat Mass Transfer, 17, pp. 852–864.

Serfaty, R., Cotta, R. (1992) “Hybrid analysis of transient non-linear convection-diffusion problems”, Int. J. Num. Meth. Heat Fluid Flow, 2, pp. 55–62.

Serfaty, R., Cotta, R. (1992) “Hybrid analysis of transient nonlinear convection-diffusion problems”, Int. J. Num. Meth. Heat Fluid Flow, 2, pp. 55–62.

Siegel, R., Perlmutter, M. (1962) “Heat Transfer for pulsating Laminar duct flow”, Trans. ASME J. Heat Trans, 84(2), pp. 111–123.

Uchida, S. (1956) “The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe”, ZAMP, VII.

Van Dyke, M. (1975) Perturbation Methods in Fluid Mechanics. The Parabolic Press.

Womersley, J. (1955) “Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx”., Phil. Mag., 46, pp. 199–221.

Zemanian, A. (1987) Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications. Dover Publications Inc.

“IMSL Library, MATH/LIB” (1987). IMSL.

[1]“The Transverse Velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established”, Proc. Roy. Soc., vol. 42, no. pt.1, pp. 1–15, 1929.

[2]S. Uchida, “The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe”, ZAMP, vol. VII, 1956.

[3]J. Womersley, “Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx”., Phil. Mag., vol. 46, pp. 199–221, 1955.

[4]H. Atabek and C. Chang, “Oscillatory flow near the entry of a circular tube”, ZAMP, vol. 12, pp. 185–201, 1961.

[5]R. Siegel and M. Perlmutter, “Heat Transfer for pulsating Laminar duct flow”, Trans. ASME J. Heat Trans, vol. 84, no. 2, pp. 111–123, 1962.

[6]D. Barnett and R. Vachon, “An Analysis of convective heat transfer for pulsating flow in a tube”, in Proc. 4th Int. Heat Transfer Conference, Paris, 1970, pp. 1–11.

[7]R. Creff and P. Andre, “Dynamic and Convective Results for a Developing Laminar unsteady Flow”, International Journal for Numerical Methods in Fluids, vol. 5, pp. 145–160, 1985.

[8]H. Cho and J. Hyun, “Numerical solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe”, Int. J. Heat and Fluid Flow, vol. 11, no. 4, 1990.

[9]H. Haneke, H. Laschefski, A. Grobe-Gorgemann, and N. Mitra, “Advanced Computational Methods in Heat Transfer II, Vol.2: Natural/Forced Convection and Combustion Simulation”, Advanced Computational Methods in Heat Transfer II, vol. 2. Computational Mechanics Publications, pp. 287–298, 1992.

[10]S. Kim, B. Kang, and J. Hyun, “Heat Transfer in the thermally developing region of a pulsating channel flow”, Int. J. Heat Mass Transfer, vol. 36, no. 17, pp. 4257–4266, 1993.

[11]T. Base, M. Campbell, and J. Hobbs, “The effects of a pulsating flow on the forced convection heat transfer inside a circular heated tube”, in Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95, 1995, vol. 2, pp. 612–613.

[12]M. Fallen, “Heat Transfer in a Pipe with Superimposed Pulsating Flow”, Warme und Stoffubertragung, vol. 16, pp. 89–99, 1982.

[13]L. Genin, A. Loval, S. Manchkha, and V. Sviridov, “Hydrodynamics and heat transfer with pulsating fluid flow in tubes”, Thermal Engineering, vol. 39, no. 5, 1992.

[14]J. Hapke, “Warmeubergang bei pulsierender laminarer Stromung”, Brennst.-Warme-Kraft, vol. 26, 1974.

[15]P. Andre, R. Creff, and J. Crabol, “Etude des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique”, Int. J. Heat Mass Transfer, vol. 24, no. No.1, pp. 1211–1219, 1981.

[16]R. Peattie and R. Budwig, “Heat Transfer in laminar, oscillatory flow in cylindrical and conical tubes”, Int. J. Heat Mass Transfer, vol. 32, no. 5, pp. 923–934, 1989.

[17]M. Van Dyke, Perturbation Methods in Fluid Mechanics. The Parabolic Press, 1975.

[18]L. Graetz, “Uber die Warmeleitungsfahigkeit von Flussigkeiten”, Annalen der Physik Chem., vol. 25, pp. 337–357, 1885.

[19]W. Nusselt, “The dependence of the heat-transfer coefficient on tube length”, Zeit. Ver. deut. Ing., vol. 54, pp. 1154–1158, 1910.

[20]A. Leveque, “Les lois de la transmission de chaleur par convection”, Annls Mines. Paris, vol. 13, no. Mem. Ser. 12, pp. 283–290, 1928.

[21]J. Sellars, M. Tribus, and J. Klein, “Heat Transfer to Laminar Flow in a Round tube or Flat Conduit - The Graetz Problem Extended”, Trans. Am. Soc. Mech. Engrs., p. 441, 1956.

[22]L. V. Ahlfors, Complex Analysis: An introduction to the theory of analytic functions of one complex variable. McGraw-Hill.

[23]R. Cotta, Integral Transforms in Computational Heat and Fluid Flow. CRC Press, 1993.

[24]R. Cotta, “Benchmark results in computational heat and fluid flow: the integral transform method”, Int. J. Heat Mass Transfer, vol. 37, no. Suppl.1, pp. 381–393, 1994.

[25]R. Cotta and M. Mikhailov, “The integral transform method”, Appl. Math. Modelling, vol. 17, pp. 156–161, 1993.

[26]A. Zemanian, Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications. Dover Publications Inc., 1987.

[27]A. Luikov, Heat and Mass Transfer. Mir Publishers, 1973.

[28]M. Mikhailov and M. Ozisik, Unified analysis and Solutions of Heat and Mass Diffusion. Wiley, 1984.

[29]R. Cotta, “Computational integral transform approach in nonlinear diffusion and convection-diffusion problems”, Serie Scientifica LIN-1202. Laboratorio di Ingegneria Nucleare di Montecuccolino, Universita degli Studi di Bologna, 1992.

[30]M. Mikhailov and R. Cotta, “Unified integral transform method”, J. Braz. Assoc. Mech. Sci., RBCM, vol. 12, no. 3, pp. 301–310, 1990.

[31]R. Serfaty and R. Cotta, “Integral transform solutions of diffusion problems with nonlinear equation coefficients”, Int. Comm. Heat Mass Transfer, vol. 17, pp. 852–864, 1990.

[32]R. Cotta and R. Serfaty, “Integral transform algorithm for parabolic diffusion problems with nonlinear boundary and equation source terms”, in Proc. of the 8th Int. Conf. on Num. Meth. for Thermal Problems, Stanford, CA, 1991, no. part 2, pp. 916–926.

[33]R. Cotta, R. Serfaty, and R. Guedes, “Integral transform solution of a class of transient convection-diffusion problems”, in Proc. of the Int. Conf. on Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK, 1990, vol. 1, pp. 239–250.

[34]R. Serfaty and R. Cotta, “Hybrid analysis of transient nonlinear convection-diffusion problems”, Int. J. Num. Meth. Heat Fluid Flow, vol. 2, pp. 55–62, 1992.

[35]A. Leiroz and R. Cotta, “On the solution of nonlinear elliptic convection-diffusion problems through the integral transform method”, Num. Heat Transfer, Part B-Fundamentals, vol. 23, pp. 401–411, 1993.

[36]J. Perez Guerrero and R. Cotta, “Integral transform method for Navier-Stokes equations in stream-function only formulation”, Int. J. Num. Meth. Fluids, vol. 15, pp. 399–409, 1992.

[37]R. Cotta, J. Perez Guerrero, and F. Scofano Neto, “Hybrid solution of the incompressible Navier-Stokes equations via integral transformation”, in Proc. of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy, 1992, vol. 1, pp. 135–150.

[38]“IMSL Library, MATH/LIB”. IMSL, 1987.

[39]R. Cotta and M. Ozisik, “Diffusion Problems with General Time-Dependent Coefficients”, J. Braz. Assoc. Mech. Sciences, vol. 9, no. 4, pp. 269–292, 1987.

[40]R. Cotta, A. Leiroz, and J. Aparecido, “Steady-State Diffusion Problems with Variable Equation Coefficients”, Int. J. Heat and Technology, vol. 10, no. 3-4, p. 104, 1992.

[41]R. Cotta and M. Ozisik, “Transient Forced Convection in Laminar Channel Flow with Stepwise Variations of Wall Temperature”, Can. J. Chem. Eng., vol. 64, pp. 734–742, 1986.

[42]W. Kim and M. Ozisik, “Transient Laminar Forced Convection in Ducts with Suddenly Applied Uniform Wall Heat Flux”, Int. J. Heat and Mass Transfer, vol. 30, pp. 1753–1756, 1987.

[43]R. Serfaty and R. Cotta, “Hybrid analysis of transient non-linear convection-diffusion problems”, Int. J. Num. Meth. Heat Fluid Flow, vol. 2, pp. 55–62, 1992.

[44]R. Cotta and T. Carvalho, “Hybrid analysis of boundary layer equations for internal flow problems”, in Proc. of the 7th Int. Conf. on Num. Meth. in Laminar and Turbulent Flow, Stanford, CA, 1991, no. Part 1, pp. 106–115.

[45]R. Courant and D. Hilbert, Methods of Mathematical Physics, Volume II, vol. II. Wiley, 1962.

[46]M. Jakob, Heat Transfer. John Wiley, 1949.

“The Transverse Velocity Gradient Near the Mouths of Pipes in Which an Alternating or Continuous Flow of Air Is Established”. Proc. Roy. Soc., vol. 42, no. pt.1, 1929, pp. 1-15.

Cotta, R.M. “Benchmark Results in Computational Heat and Fluid Flow: The Integral Transform Method”. Int. J. Heat Mass Transfer, vol. 37, no. Suppl.1, 1994, pp. 381-93.

Cotta, R.M., R. Serfaty. “Integral Transform Algorithm for Parabolic Diffusion Problems With Nonlinear Boundary and Equation Source Terms”. Proc. of the 8th Int. Conf. on Num. Meth. For Thermal Problems, Stanford, CA, no. part 2, 1991, pp. 916-2.

Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. McGraw-Hill.

Andre, P., et al. “Etude Des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique”. Int. J. Heat Mass Transfer, vol. 24, no. No.1, 1981, pp. 1211-9.

Atabek, H.B., C.C. Chang. “Oscillatory Flow Near the Entry of a Circular Tube”. ZAMP, vol. 12, 1961, pp. 185-01.

Barnett, D.O., R.I. Vachon. “An Analysis of Convective Heat Transfer for Pulsating Flow in a Tube”. Proc. 4th Int. Heat Transfer Conference, Paris, 1970, pp. 1-11.

Base, T.E., et al. “The Effects of a Pulsating Flow on the Forced Convection Heat Transfer Inside a Circular Heated Tube”. Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95, vol. 2, 1995, pp. 612-3.

Cho, H.W., J.M. Hyun. “Numerical Solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe”. Int. J. Heat and Fluid Flow, vol. 11, no. 4, 1990.

Cotta, R.M. “Computational Integral Transform Approach in Nonlinear Diffusion and Convection-Diffusion Problems”. Serie Scientifica LIN-1202, Laboratorio di Ingegneria Nucleare di Montecuccolino, Universita degli Studi di Bologna, 1992.

Cotta, R.M. Integral Transforms in Computational Heat and Fluid Flow. CRC Press, 1993.

Cotta, R.M., et al. “Hybrid Solution of the Incompressible Navier-Stokes Equations via Integral Transformation”. Proc. Of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy, vol. 1, 1992, pp. 135-50.

Cotta, R.M., et al. “Integral Transform Solution of a Class of Transient Convection-Diffusion Problems”. Proc. of the Int. Conf. On Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK, vol. 1, 1990, pp. 239-50.

Cotta, R.M., et al. “Steady-State Diffusion Problems With Variable Equation Coefficients”. Int. J. Heat and Technology, vol. 10, no. 3-4, 1992, p. 104.

Cotta, R.M., M.D. Mikhailov. “The Integral Transform Method”. Appl. Math. Modelling, vol. 17, 1993, pp. 156-61.

Cotta, R.M., M.N. Ozisik. “Diffusion Problems With General Time-Dependent Coefficients”. J. Braz. Assoc. Mech. Sciences, vol. 9, no. 4, 1987, pp. 269-92.

Cotta, R.M., M.N. Ozisik. “Transient Forced Convection in Laminar Channel Flow With Stepwise Variations of Wall Temperature”. Can. J. Chem. Eng., vol. 64, 1986, pp. 734-42.

Cotta, R.M., T.M.B. Carvalho. “Hybrid Analysis of Boundary Layer Equations for Internal Flow Problems”. Proc. of the 7th Int. Conf. on Num. Meth. In Laminar and Turbulent Flow, Stanford, CA, no. Part 1, 1991, pp. 106-15.

Courant, R., D. Hilbert. Methods of Mathematical Physics, Volume II. Wiley, 1962.

Creff, R., P. Andre. “Dynamic and Convective Results for a Developing Laminar Unsteady Flow”. International Journal for Numerical Methods in Fluids, vol. 5, 1985, pp. 145-60.

Fallen, M. “Heat Transfer in a Pipe With Superimposed Pulsating Flow”. Warme Und Stoffubertragung, vol. 16, 1982, pp. 89-99.

Genin, L.G., et al. “Hydrodynamics and Heat Transfer With Pulsating Fluid Flow in Tubes”. Thermal Engineering, vol. 39, no. 5, 1992.

Graetz, L. “Uber Die Warmeleitungsfahigkeit Von Flussigkeiten”. Annalen Der Physik Chem., vol. 25, 1885, pp. 337-5.

Haneke, H., et al. “Advanced Computational Methods in Heat Transfer II, Vol.2: Natural Forced Convection and Combustion Simulation”. Advanced Computational Methods in Heat Transfer II, vol. 2, Computational Mechanics Publications, 1992, pp. 287-98.

Hapke, J. “Warmeubergang Bei Pulsierender Laminarer Stromung”. Brennst.-Warme-Kraft, vol. 26, 1974.

IMSL Library, MATH LIB. IMSL, 1987.

Jakob, M. Heat Transfer. John Wiley, 1949.

Kim, S.Y., et al. “Heat Transfer in the Thermally Developing Region of a Pulsating Channel Flow”. Int. J. Heat Mass Transfer, vol. 36, no. 17, 1993, pp. 4257-66.

Kim, W.S., M.N. Ozisik. “Transient Laminar Forced Convection in Ducts With Suddenly Applied Uniform Wall Heat Flux”. Int. J. Heat and Mass Transfer, vol. 30, 1987, pp. 1753-6.

Leiroz, A.J.K., R.M. Cotta. “On the Solution of Nonlinear Elliptic Convection-Diffusion Problems through the Integral Transform Method”. Num. Heat Transfer, Part B-Fundamentals, vol. 23, 1993, pp. 401-1.

Leveque, A. “Les Lois de la Transmission de Chaleur Par Convection”. Annls Mines. Paris, vol. 13, no. Mem. Ser. 12, 1928, pp. 283-90.

Luikov, A.V. Heat and Mass Transfer. Mir Publishers, 1973.

Mikhailov, M.D., M.N. Ozisik. Unified Analysis and Solutions of Heat and Mass Diffusion. Wiley, 1984.

Mikhailov, M.D., R.M. Cotta. “Unified Integral Transform Method”. J. Braz. Assoc. Mech. Sci., RBCM, vol. 12, no. 3, 1990, pp. 301-10.

Nusselt, W. “The Dependence of the Heat-Transfer Coefficient on Tube Length”. Zeit. Ver. Deut. Ing., vol. 54, 1910, pp. 1154-8.

Peattie, R., R. Budwig. “Heat Transfer in Laminar, Oscillatory Flow in Cylindrical and Conical Tubes”. Int. J. Heat Mass Transfer, vol. 32, no. 5, 1989, pp. 923-34.

Perez Guerrero, J.S., R.M. Cotta. “Integral Transform Method for Navier-Stokes Equations in Stream-Function only Formulation”. Int. J. Num. Meth. Fluids, vol. 15, 1992, pp. 399-0.

Sellars, J.R., et al. “Heat Transfer to Laminar Flow in a Round Tube or Flat Conduit - The Graetz Problem Extended”. Trans. Am. Soc. Mech. Engrs., 1956, p. 441.

Serfaty, R., R.M. Cotta. “Hybrid Analysis of Transient Non-Linear Convection-Diffusion Problems”. Int. J. Num. Meth. Heat Fluid Flow, vol. 2, 1992, pp. 55-62.

Serfaty, R., R.M. Cotta. “Hybrid Analysis of Transient Nonlinear Convection-Diffusion Problems”. Int. J. Num. Meth. Heat Fluid Flow, vol. 2, 1992, pp. 55-62.

Serfaty, R., R.M. Cotta. “Integral Transform Solutions of Diffusion Problems With Nonlinear Equation Coefficients”. Int. Comm. Heat Mass Transfer, vol. 17, 1990, pp. 852-64.

Siegel, R., M. Perlmutter. “Heat Transfer for Pulsating Laminar Duct Flow”. Trans. ASME J. Heat Trans, vol. 84, no. 2, 1962, pp. 111-23.

Uchida, S. “The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe”. ZAMP, vol. VII, 1956.

Van Dyke, M. Perturbation Methods in Fluid Mechanics. The Parabolic Press, 1975.

Womersley, J.R. “Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx”. Phil. Mag., vol. 46, 1955, pp. 199-21.

Zemanian, A.H. Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, With Applications. Dover Publications Inc., 1987.

“IMSL Library, MATH LIB”. IMSL, 1987.

“The Transverse Velocity Gradient Near the Mouths of Pipes in Which an Alternating or Continuous Flow of Air Is Established”. Proc. Roy. Soc. 42, no. pt.1 (1929): 1–15.

Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. McGraw-Hill, n.d.

Andre, P., R. Creff, and J. Crabol. “Etude Des Conditions Particulieres De Frequence Favorisant Les Transferts Thermiques En Ecoulements Pulses En Canalisation Cylindrique”. Int. J. Heat Mass Transfer 24, no. No.1 (1981): 1211–1219.

Atabek, H.B., and C.C. Chang. “Oscillatory Flow Near the Entry of a Circular Tube”. ZAMP 12 (1961): 185–201.

Barnett, D.O., and R.I. Vachon. “An Analysis of Convective Heat Transfer for Pulsating Flow in a Tube”. In Proc. 4th Int. Heat Transfer Conference, Paris, 1–11, 1970.

Base, T.E., M.R. Campbell, and J. Hobbs. “The Effects of a Pulsating Flow on the Forced Convection Heat Transfer Inside a Circular Heated Tube”. In Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95, 2:612–613, 1995.

Cho, H.W., and J.M. Hyun. “Numerical Solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe”. Int. J. Heat and Fluid Flow 11, no. 4 (1990).

Cotta, R.M. “Computational Integral Transform Approach in Nonlinear Diffusion and Convection-Diffusion Problems”. Serie Scientifica LIN-1202. Laboratorio di Ingegneria Nucleare di Montecuccolino, Universita degli Studi di Bologna, 1992.

Cotta, R.M. Integral Transforms in Computational Heat and Fluid Flow. CRC Press, 1993.

Cotta, R.M., and T.M.B. Carvalho. “Hybrid Analysis of Boundary Layer Equations for Internal Flow Problems”. In Proc. of the 7th Int. Conf. on Num. Meth. In Laminar and Turbulent Flow, Stanford, CA, 106–115, 1991.

Cotta, R.M., and M.D. Mikhailov. “The Integral Transform Method”. Appl. Math. Modelling 17 (1993): 156–161.

Cotta, R.M., and M.N. Ozisik. “Diffusion Problems With General Time-Dependent Coefficients”. J. Braz. Assoc. Mech. Sciences 9, no. 4 (1987): 269–292.

Cotta, R.M., and M.N. Ozisik. “Transient Forced Convection in Laminar Channel Flow With Stepwise Variations of Wall Temperature”. Can. J. Chem. Eng. 64 (1986): 734–742.

Cotta, R.M., A.J.K. Leiroz, and J.B. Aparecido. “Steady-State Diffusion Problems With Variable Equation Coefficients”. Int. J. Heat and Technology 10, no. 3-4 (1992): 104.

Cotta, R.M., J.S. Perez Guerrero, and F. Scofano Neto. “Hybrid Solution of the Incompressible Navier-Stokes Equations via Integral Transformation”. In Proc. Of the 2nd Int. Conf. Advanced Computational Methods in Heat Transfer, Heat Transfer 92, Milan, Italy, 1:135–150, 1992.

Cotta, R.M., R. Serfaty, and R.O.C. Guedes. “Integral Transform Solution of a Class of Transient Convection-Diffusion Problems”. In Proc. of the Int. Conf. On Advanced Computational Methods in Heat Transfer, Heat Transfer 90, Southampton, UK, 1:239–250, 1990.

Courant, R., and D. Hilbert. Methods of Mathematical Physics, Volume II. Vol. II. Wiley, 1962.

Creff, R., and P. Andre. “Dynamic and Convective Results for a Developing Laminar Unsteady Flow”. International Journal for Numerical Methods in Fluids 5 (1985): 145–160.

Fallen, M. “Heat Transfer in a Pipe With Superimposed Pulsating Flow”. Warme und Stoffubertragung 16 (1982): 89–99.

Genin, L.G., A.P. Loval, S.P. Manchkha, and V.G. Sviridov. “Hydrodynamics and Heat Transfer With Pulsating Fluid Flow in Tubes”. Thermal Engineering 39, no. 5 (1992).

Graetz, L. “Uber Die Warmeleitungsfahigkeit Von Flussigkeiten”. Annalen der Physik Chem. 25 (1885): 337–357.

Haneke, H., H. Laschefski, A. Grobe-Gorgemann, and N.K. Mitra. “Advanced Computational Methods in Heat Transfer II, Vol.2: Natural Forced Convection and Combustion Simulation”. Advanced Computational Methods in Heat Transfer II. Computational Mechanics Publications, 1992.

Hapke, J. “Warmeubergang Bei Pulsierender Laminarer Stromung”. Brennst.-Warme-Kraft 26 (1974).

Jakob, M. Heat Transfer. John Wiley, 1949.

Kim, S.Y., B.H. Kang, and J.M. Hyun. “Heat Transfer in the Thermally Developing Region of a Pulsating Channel Flow”. Int. J. Heat Mass Transfer 36, no. 17 (1993): 4257–4266.

Kim, W.S., and M.N. Ozisik. “Transient Laminar Forced Convection in Ducts With Suddenly Applied Uniform Wall Heat Flux”. Int. J. Heat and Mass Transfer 30 (1987): 1753–1756.

Leiroz, A.J.K., and R.M. Cotta. “On the Solution of Nonlinear Elliptic Convection-Diffusion Problems through the Integral Transform Method”. Num. Heat Transfer, Part B-Fundamentals 23 (1993): 401–411.

Leveque, A. “Les Lois de la Transmission de Chaleur Par Convection”. Annls Mines. Paris 13, no. Mem. Ser. 12 (1928): 283–290.

Luikov, A.V. Heat and Mass Transfer. Mir Publishers, 1973.

Mikhailov, M.D., and R.M. Cotta. “Unified Integral Transform Method”. J. Braz. Assoc. Mech. Sci., RBCM 12, no. 3 (1990): 301–310.

Mikhailov, M.D., and M.N. Ozisik. Unified Analysis and Solutions of Heat and Mass Diffusion. Wiley, 1984.

Nusselt, W. “The Dependence of the Heat-Transfer Coefficient on Tube Length”. Zeit. Ver. deut. Ing. 54 (1910): 1154–1158.

Peattie, R., and R. Budwig. “Heat Transfer in Laminar, Oscillatory Flow in Cylindrical and Conical Tubes”. Int. J. Heat Mass Transfer 32, no. 5 (1989): 923–934.

Perez Guerrero, J.S., and R.M. Cotta. “Integral Transform Method for Navier-Stokes Equations in Stream-Function only Formulation”. Int. J. Num. Meth. Fluids 15 (1992): 399–409.

Sellars, J.R., M. Tribus, and J.S. Klein. “Heat Transfer to Laminar Flow in a Round Tube or Flat Conduit - The Graetz Problem Extended”. Trans. Am. Soc. Mech. Engrs. (1956): 441.

Serfaty, R., and R.M. Cotta. “Hybrid Analysis of Transient Non-Linear Convection-Diffusion Problems”. Int. J. Num. Meth. Heat Fluid Flow 2 (1992): 55–62.

Serfaty, R., and R.M. Cotta. “Hybrid Analysis of Transient Nonlinear Convection-Diffusion Problems”. Int. J. Num. Meth. Heat Fluid Flow 2 (1992): 55–62.

Serfaty, R., and R.M. Cotta. “Integral Transform Solutions of Diffusion Problems With Nonlinear Equation Coefficients”. Int. Comm. Heat Mass Transfer 17 (1990): 852–864.

Siegel, R., and M. Perlmutter. “Heat Transfer for Pulsating Laminar Duct Flow”. Trans. ASME J. Heat Trans 84, no. 2 (1962): 111–123.

Uchida, S. “The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe”. ZAMP VII (1956).

Van Dyke, M. Perturbation Methods in Fluid Mechanics. The Parabolic Press, 1975.

Womersley, J.R. “Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx”. Phil. Mag. 46 (1955): 199–221.

Zemanian, A.H. Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, With Applications. Dover Publications Inc., 1987.

Cotta, R.M. “Benchmark Results in Computational Heat and Fluid Flow: The Integral Transform Method”. Int. J. Heat Mass Transfer 37, no. Suppl.1 (1994): 381–393.

Cotta, R.M., and R. Serfaty. “Integral Transform Algorithm for Parabolic Diffusion Problems With Nonlinear Boundary and Equation Source Terms”. In Proc. of the 8th Int. Conf. on Num. Meth. For Thermal Problems, Stanford, CA, 916–926, 1991.

1.The Transverse Velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established. Proc. Roy. Soc. 1929;42(pt.1):1-15.

2.Uchida S. The Pulsating Viscous Flow Superimposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe. ZAMP. 1956;VII.

3.Womersley J. Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube - I; The Linear Approx. Phil. Mag. 1955;46:199-221.

4.Atabek H, Chang C. Oscillatory flow near the entry of a circular tube. ZAMP. 1961;12:185-201.

5.Siegel R, Perlmutter M. Heat Transfer for pulsating Laminar duct flow. Trans. ASME J. Heat Trans. 1962;84(2):111-23.

6.Barnett D, Vachon R. An Analysis of convective heat transfer for pulsating flow in a tube. In: Proc. 4th Int. Heat Transfer Conference, Paris. 1970. pp. 1-11.

7.Creff R, Andre P. Dynamic and Convective Results for a Developing Laminar unsteady Flow. International Journal for Numerical Methods in Fluids. 1985;5:145-60.

8.Cho H, Hyun J. Numerical solutions of Pulsating Flow and Heat Transfer Characteristics in a Pipe. Int. J. Heat and Fluid Flow. 1990;11(4).

9.Haneke H, Laschefski H, Grobe-Gorgemann A, Mitra N. Advanced Computational Methods in Heat Transfer II, Vol.2: Natural/Forced Convection and Combustion Simulation. Vols. 2, Advanced Computational Methods in Heat Transfer II. Computational Mechanics Publications; 1992. pp. 287-98.

10.Kim S, Kang B, Hyun J. Heat Transfer in the thermally developing region of a pulsating channel flow. Int. J. Heat Mass Transfer. 1993;36(17):4257-66.

11.Base T, Campbell M, Hobbs J. The effects of a pulsating flow on the forced convection heat transfer inside a circular heated tube. In: Proceedings 15th Canadian Congress of Applied Mechanics, Cancam 95. 1995. pp. 612-3.

12.Fallen M. Heat Transfer in a Pipe with Superimposed Pulsating Flow. Warme und Stoffubertragung. 1982;16:89-9.

13.Genin L, Loval A, Manchkha S, Sviridov V. Hydrodynamics and heat transfer with pulsating fluid flow in tubes. Thermal Engineering. 1992;39(5).

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Heat Transfer With Pulsatile Flow in a Tube: A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy. (2026). Global Journals. https://doi.org/10.34257/HTPFT2026

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Heat Transfer With Pulsatile Flow in a Tube: A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy

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