Abstract
A review is made of certain analytical methods used in heat transfer. Singular perturbation methods, asymptotic methods, and methods associated with the solution of integral equations are considered for the purpose of solving problems in various types of heat transfer.
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Literature cited
J. P. Hartnett and F. Irvine, Jr. (editors), Advances in Heat Transfer, Vol. 1, Academic Press, New York-London (1964).
J. P. Hartnett and F. Irvine, Jr. (editors), Advances in Heat Transfer, Vol. 2, Academic Press, New York-London (1965).
J. P. Hartnett and F. Irvine, Jr. (editors), Advances in Heat Transfer, Vol. 3, Academic Press, New York-London (1966).
J. P. Hartnett and F. Irvine, Jr. (editors), Advances in Heat Transfer, Vol. 4, Academic Press, New York-London (1967).
J. P. Hartnett and F. Irvine, Jr. (editors), Advances in Heat Transfer, Vol. 5, Academic Press, New York-London (1967).
W. Bele (editor), Modern Developments in Heat Transfer, Academic Press, New York-London (1963).
W. M. Rohsenow (editor), Developments in Heat Transfer, Edward Arnold Ltd., London (1964).
B. A. Finlayson and L. E. Scriven, Appl. Math. Rev.,19, 735–748 (1966).
T. R. Goodman, Cited in [1] (1964), pp. 52–122.
G. Karslou and D. Eger, Thermal Conductivity of Solids [in Russian], Nauka, Moscow (1964).
A. V. Lykov, Theory of Thermal Conductivity [in Russian], Vysshaya Shkola (1967).
A. V. Lykov and Yu. A. Mikhailov, Theory of Heat and Mass Transfer [in Russian], Gosenergoizdat (1963).
M. J. Lighthill, Philos. Mag.,40, 1179–1201 (1949).
H. S. Tsien, Advances in Applied Mechanics, Vol. 4, Academic Press, New York (1956), pp. 281–349.
Y. H. Kuo, J. Math. Phys.,32, 83–101 (1953).
Y. H. Kuo, J. Aeronaut. Sci.,23, 125–136 (1956).
M. van Dyke, Perturbation Methods in the Mechanics of Fluids [in Russian], Mir, Moscow (1967).
M. J. Lighthill, Philos. Mag.,40, 1202–1223 (1949).
J. Legras, Comptes Rendues, Acad. Sci. Paris,233, 1005–1008 (1951).
J. Legras, ONERA Publ., No. 66 (1953).
M. J. Lighthill, Z. Flugwiss,9, 267–275 (1961).
T. R. Goodman and J. J. She, J. Appl. Mech.,27, 16 (1960).
K. L. Ahuja and I. J. Kumar, Def. Sci. J., India,16, 203 (1966).
W. D. Morris, J. Fluid Mech.,21, 453–464 (1965).
W. B. Olstad, Heat Transfer, Fl. Mech. Inst., Stanford Univ. Press, 138 (1965).
P. A. Lagerstrom and J. D. Cole, AEChRat. Mech. Anal.,4, 817–822 (1955).
P. A. Lagerstrom, J. Math. Mech.,6, 605 (1957).
S. Kaplun, Z. Ang. Math. Physik,5, 111–135 (1954).
S. Kaplun, J. Math. Mech.,6, 595–603 (1957).
A. Erdelyi, J. Soc. Indus. Appl. Math.,11, 105–116 (1963).
S. H. Lam, Heat Transfer, Fl. Mech. Inst, Stanford Univ. Press, 44–47 (1965).
R. M. Terrill and G. M. Shresgta, Appl. Sci. Res.,A15, 440 (1965).
R. K. Varma and M. P. Murgai, Quart. Appl. Math.,22, 345–353 (1965).
H. F. Mueller, N. D. Malmuth, Int. J. Heat Mass Transfer,8, 915–920 (1965).
R. D. Cess, Int. J. Heat Mass Transfer,9, 1269–1277 (1966).
O. R. Burgraff, AIAA J.,4, 1725 (1966).
G. R. Inger, J. Fluid Mech.,26, 793 (1966).
J. W. E. Ellinwood, J. Math. Phys.,46, 281–298 (1967).
D. G. Drake and P. C. Rhodes, Z. Ang. Math. Physik,3, 342–353 (1967).
D. E. Coles, Heat Transfer, Fl. Mech. Inst., Stanford “Univ. Press, 119–137 (1957).
I. E. Bekweth and N. B. Cohen, NASA, TN-D-625 (1961).
P. A. Lagerstrom, in: High Speed Aerodynamics and Jet Propulsion, F. K. Moor (editor), Vol. 4, Princeton Univ. Press, Princeton (1964), pp. 125.
C. F. Dewey and J. F. Gross, Cited in [4] (1967), pp. 317–446.
J. L. Novotany and K. T. Yang, J. Heat Transfer, Trans. ASME, C.89, 309–313 (1967).
F. E. Fendell, J. Fluid Mech.,34, 163–176 (1968).
T. Kubota and F. L. Fernandez, AIAA J.,6, 22 (1968).
H. F. Mueller and N. D. Malmuth, AIAA J.,7, 1631 (1969).
H. K. Kueken, J. Fluid. Mech.,37, 785 (1969).
A. B. Vasil'eva, USSR Computational Math., Mathematical Phys.,3, 823 (1963).
R. K. Varma and M. P. Murgai, Proc. Roy. Soc., (to be published).
R. O'Mailey and J. R. Keller, Comm. Pure Appl. Math.,21, 263–270 (1968).
L. E. Frankel, Proc. Camb. Phil. Soc.,65, 209–232, 233–263, 264–284 (1969).
J. Cochran, A New Approach to Singular Perturbation Problems, Ph. D. Dissertation, Stanford Univ. (1962).
J. J. Mahony, J. Austral. Math. Soc.,2, 440–463 (1962).
J. D. Cole and J. Kevorkian, in: Nonlinear Differential Equations and Nonlinear Mechanics, J. B. Laselle and S. Lefschetz (editors), Academic Press, New York (1963), pp. 113–120.
N. D. Fowkes, Quart. Appl. Math.,26, 57–70, 71–87 (1968).
S. Kaplun, Collected Papers, P. A. Langstrom, L. N. Howard, and Ching-Shi Liu (editors), Academic Press, New York (1967).
R. O'Malley and J. R. Keller, J. Math. Anal. Appl.,19, 291–308 (1967).
R. O'Malley and J. R. Keller, J. Math. Mech.,16, 1143–1164 (1967).
J. D. Murray, J. Math. Phys.,47, 111–133 (1968).
A. Erdelyi, J. Inst. Math. Appl.4, 113–119 (1968).
A. Erdelyi, Arch. Rat. Mech. Anal.,29, 1–17 (1968).
A. B. Vasil'eva, Uspekhi Matemat. Nauk,18, 15–86 (1963).
M. I. Vishik and L. A. Lyusternik, Uspekh Matemat. Nauk,12, 3–122 (1957).
M. I. Vishik and L. A. Lyusternik, Dokl. Akad. Nauk SSSR,121, 778 (1958).
A. Friedman, Arch. Rat. Mech. Anal.,29, 289 (1968).
P. C. Fife, Arch. Rat. Mech. Anal.,28, 184 (1968).
J. W. Mackie, Arch. Rat. Mech. Anal.,24, 219 (1967).
R. J. Swigart, AIAA J.,1, 1034 (1963).
A. P. Bazzhin and A. A. Gladkov, Inzh. Zhurnal.,3, 517 (1963).
H. C. Kao, AIAA J.,2, 1802 (1964).
R. J. Conti, J. Fluid Mech.,24, 65 (1966).
M. van Dyke, J. de Mecanique,4, 477 (1965).
P. Cheng and W. G. Vincenti, J. Fluid Mech.,27, 625–646 (1967).
H. C. Kao, J. Fluid Mech.,27, 789–813 (1967).
B. A. Ton, J. Math. Anal. Appl.,14, 341–358 (1966).
W. Eckhans and E. M. de Jager, Arch. Rat. Mech. Anal.,23, 26–56 (1966).
R. Vishkanta and R. J. Grosh, Appl. Mech. Rev.,17, 91–100 (1964).
R. Vishkanta, Cited in [3] (1966), pp. 176–251.
S. Chandrashekhar, Radiative Transfer, Dover, New York (1960).
V. Kourganoff, Basic Methods in Transfer Problems, The Clarendon Press, Oxford (1952).
L. W. Busbridge, The Mathematics of Radiative Transfer, Cambridge Univ. Press, London (1960).
E. M. Sparrow, Cited in [2] (1965), pp. 399–452.
J. R. Howell and R. Siegel, Thermal Radiation Heat Transfer, 11, NASA, SP-164 (1969).
G. F. Carrier, J. Soc. Indus. Appl. Math.,13, 68 (1965).
R. Kurant and D. Gil'bert, Methods of Mathematical Physics [in Russian], Vol. 1, Gostekhizdat, Moscow-Leningrad (1951).
S. G. Mikhlin, Integral Equations [in Russian], GTTI, Moscow-Leningrad (1948).
N. I. Muskhelishvili, Singular Integral Equations [in Russian], Fizmatgiz, Moscow (1962).
F. J. Tricomi, Integral Equations [Russian translation], IL, Moscow (1968).
M. L. Krasnov, A. I. Kiselev, and G. I. Makarenko, Integral Equations [in Russian], Nauka, Moscow (1968).
B. A. Boley, J. Math. Phys.,40, 300–313 (1961).
J. C. Koh and J. P. Hartnett, Int. J. Heat Transfer,2, 185–198 (1961).
E. R. G. Eckert, A. A. Hayday, and W. J. Minkowycz, Int. J. Heat Transfer,4, 17–29 (1961).
E. R. G. Eckert, A. A. Hayday, and W. J. Minkowycz, Heat and Mass Transfer, General Problems of Heat Exchange [in Russian], Vol. 3, Gosenergoizdat, Moscow (1963).
E. V. Tolubinskii, Dokl. Akad. Nauk SSSR,160, 1289 (1965).
E. V. Tolubinskii, Int. J. Heat Mass Transfer,9, 1471–1488 (1966).
V. T. Grinchenkov and A. F. Ulitko, Inzh. -Fiz. Zh.,6, 10 (1963).
K. K. Vasilevskii, TVT,2, 260–266 (1964).
S. V. Patankar, Int. J. Heat Mass Transfer,9, 829 (1966).
D. B. Spalding, International Development in Heat Transfer, Part 2, Am. Soc. Mech. Engs., New York (1963), pp. 439–446.
J. M. Savino and R. Siegel, Int. J. Heat Mass Transfer,12, 803 (1969).
N. J. Lighthill, Proc. Royal Soc. A.,202, 359 (1950).
M. W. Rubesin and M. Inouye, NASA, TN-3969 (1957).
A. N. Tifford, J. Aeronaut. Sci.,18, 283 (1951).
D. B. Spalding, J. Fluid Mech.,4, 22 (1958).
H. W. Liepmann, J. Fluid Mech.,3, 357 (1958).
D. R. Davies and D. E. Bourne, Quart. J. Mech. Appl. Math.,9, 457 (1956).
C. R. Illingworth, Quart. J. Mech. Appl. Math.,7, 8 (1954).
G. M. Lilley, College of Aeronautics Note No. 93 (1959).
N. Curie, The Laminar Boundary Layer Equations, The Clarendon Press, Oxford (1962).
P. L. Chambre and A. Acrivos, J. Appl. Phys.,27, 1322 (1956).
D. E. Rosner, J. Aerospace Sci.,26, 281 (1959).
D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Nauka, Moscow (1967).
P. L. Chambre, Appl. Sci. Res.,A 6, 97 (1956).
A. Acrivos and P. L. Chambre, Ind Engg. Chem.,49, 1025 (1957).
P. L. Chambre, J. Appl. Phys.,30, 1683 (1959).
W. R. Mann and F. Wolf, Quart. Appl. Math.,9, 163 (1951).
J. R. Jones and B. Frank, Comm. Pure Appl. Math.,16, 33 (1963).
G. T. Aldoshin, A. S. Golosov, and B. I. Zhuk, Proceedings of the Third All-Union Conference on Heat and Mass Transfer [in Russian], Vol. 8, ITMO, AN BSSR (1968).
P. M. Chung, S. W. Liu, and H. Mirels, Int. J. Heat Mass Transfer,6, 193–210 (1963).
T. L. Perel'man, in: Heat and Mass Transfer [in Russian], Vol. 5, Izd. AN BSSR, Minsk (1963), p. 79.
T. L. Perel'man, Priklad. Matemat, i Mekh.,25, No. 6 (1961).
I. J. Kumar, Inzh.-Fiz. Zh.,14, No. 5 (1968).
I. J. Kumar and A. B. Bartman, Proceedings of the Third All-Union Conference on Heat and Mass Transfer [in Russian], Vol. 9, ITMO, AN BSSR (1968).
I. J. Kumar, J. Math. Mech., (to be published).
H. Bateman, Tables of Integral Transforms, Vol. 1, McGraw-Hill Book Co. Inc. (1954), pp. 308, 311.
M. A. Evgrafov, Analytical Functions [in Russian], Nauka, Moscow (1968).
I. J. Kumar (to be published).
T. Perel'man, A. Bartman, and M. Levitan, Fourth International Conference on Heat Transfer, Paris (1970).
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Translated from Inzhenerno-Fizieheskii Zhurnal, Vol. 19, No. 3, pp. 578–593, September, 1970.
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Kumar, I.J. Modern analytical methods in heat transfer. Journal of Engineering Physics 19, 1207–1219 (1970). https://doi.org/10.1007/BF00826246
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DOI: https://doi.org/10.1007/BF00826246