A BOUNDARY CONDITION DISSECTION METHOD FOR THE SOLUTION OF BOUNDARY-VALUE HEAT CONDUCTION PROBLEMS WITH POSITION-DEPENDENT CONVECTIVE COEFFICIENTS

Abstract

A boundary condition dissection method is developed on the postulation that a condition imposed on the boundary of a heat conduction problem may be realized in practice by using conditions not of the imposed kind. Thus, a Robin condition imposed on the boundary may be dissected as a linear combination of the boundary heal flux and temperature, arid by doing so, heat conduction problems with position-dependent convective coefficients can be solved by the separation-of-variables technique. The method leads to the solution of a Fredholm integral equation of the second kind with a degenerate kernel, and this equation may be solved by using simultaneous algebraic equations. The method is superior to the finite-difference method and the methods of weighted residuals, which have been conventionally used in solving suck problems. Extension of the method to the solution of other heat conduction problems is also possible and mentioned in the paper.

Notes

Hanji Shang's present address is Mathematics Department, Fudan University, Shanghai, People's Republic of China.