On the heat transfer to constant-property laminar boundary layer with power-function free-stream velocity and wall-temperature distributions

Author:
Isao Imai

Journal:
Quart. Appl. Math. **16** (1958), 33-45

MSC:
Primary 76.00

DOI:
https://doi.org/10.1090/qam/103000

MathSciNet review:
103000

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Abstract: The heat transfer to constant-property laminar boundary layer with power-function variations of free stream velocity and of temperature difference between wall and free stream is studied by means of an improved version of the WKB method developed by the author. It is found that the local heat-transfer coefficient can be approximately given in the form

**[1]**A. Fage and V. M. Falkner,*Relation between heat transfer and surface friction for laminar flow*, A.R.C.R. & M., No. 1408, London, 1931**[2]**D. R. Hartree,*On an equation occurring in Falkner and Skan's approximate treatment of the equation of the boundary layer*, Proc. Cambridge Phil. Soc.**33**, 223-239 (1937)**[3]**Dean R. Chapman and Morris W. Rubesin,*Temperature and velocity profiles in the compressible laminar boundary layer with arbitrary distribution of surface temperature*, J. Aeronaut. Sci.**16**(1949), 547–565. MR**0032318****[4]**S. Levy,*Heat transfer to constant-property laminar boundary-layer flows with power-function free-stream velocity and wall-temperature variation*, J. Aeronaut. Sci.**19**, No. 5, 341-348 (May 1952)**[5]**H. Schuh,*On asymptotic solutions for the heat transfer at varying wall temperatures in a laminar boundary layer with Hartree’s velocity profiles*, J. Aeronaut. Sci.**20**(1953), 146–147. MR**0052280****[6]**H. Schuh,*On asymptotic solutions for the heat transfer at varying wall temperatures in a laminar boundary layer with Hartree’s velocity profiles*, J. Aeronaut. Sci.**20**(1953), 146–147. MR**0052280****[7]**Henry E. Fettis,*On a differential equation occurring in the theory of heat flow in boundary layers with Hartree’s velocity profiles*, J. Aeronaut. Sci.**21**(1954), 132–133. MR**0060099****[8]**M. J. Lighthill,*Contributions to the theory of heat transfer through a laminar boundary layer*, Proc. Roy. Soc. London. Ser. A.**202**(1950), 359–377. MR**0037147**, https://doi.org/10.1098/rspa.1950.0106**[9]**H. Tamaki,*Studies of surface heat transfer based on the boundary layer theory*, (in Japanese), Rept. Inst. Ind. Sci., Univ. of Tokyo**1**, No. 8, 239-273 (March 1951)**[10]**Isao Imai,*On a refinement of the W.K.B. method*, Physical Rev. (2)**74**(1948), 113. MR**0025653****[11]**Isao Imai,*Asymptotic solutions of ordinary linear differential equations of the second order*, Physical Rev. (2)**80**(1950), 1112. MR**0040530****[12]**I. Imai,*A refinement of the WKB method and its application to the electromagnetic wave theory*, IRE Trans.**AP-4**, No. 3, 233-239 (July 1956); proceedings of the Symposium on Electromagnetic Wave Theory held June 20-25, 1955, at the University of Michigan

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Additional Information

DOI:
https://doi.org/10.1090/qam/103000

Article copyright:
© Copyright 1958
American Mathematical Society