Radiation interaction between two solid half-spaces

Author:
G. Kleinstein

Journal:
Quart. Appl. Math. **28** (1971), 527-537

DOI:
https://doi.org/10.1090/qam/99771

MathSciNet review:
QAM99771

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Abstract | References | Additional Information

Abstract: A solution to the radiation interaction problem between two solid half-spaces is obtained. A Green's function method reduces the problem to the solution of two nonlinear integral equations for the surface temperatures which are solved by utilizing analytical and numerical techniques.

**[1]**J. C. Jaeger,*Conduction of heat in a solid with a power law of heat transfer at its surface*, Proc. Cambridge Philos. Soc.**46**, 634-641 (1950) MR**0037455****[2]**W. R. Mann and F. Wolf,*Heat transfer between solid and gasses under nonlinear boundary conditions*, Quart. Appl. Math.**9**, 163-184 (1950) MR**0042596****[3]**H. S. Carslaw and J. C. Jaeger,*Conduction of heat in solids*, 2nd ed., Clarendon Press, Oxford, 1959 MR**959730****[4]**J. H. Roberts and W. R. Mann,*On a certain nonlinear integral equation of the Volterra type*, Pacific J. Math.**1**, 431-445 (1951) MR**0044009****[5]**A. Friedman,*Partial differential equations of parabolic type*, Prentice--Hall, Englewood Cliffs, N. J., (1964) (especially Chapter 6) MR**0181836****[6]**A. Friedman,*On integral equations of Volterra type*, J. Analyse Math.**11**, 381-413 (1963) MR**0158232****[7]**K. Padmavally,*On a non-linear integral equation*, J. Math. Mech.**7**, 533-555 (1958) MR**0103400****[8]**M. Abramowitz and I. A. Stegun (Editors),*Handbook of mathematical functions with formulas, graphs, and mathematical tables*, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964; 3rd printing with corrections, 1965, p. 17 MR**0167642**

Additional Information

DOI:
https://doi.org/10.1090/qam/99771

Article copyright:
© Copyright 1971
American Mathematical Society