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Numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition

โœ Scribed by R. C. Mehta

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
421 KB
Volume
20
Category
Article
ISSN
0029-5981

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โœฆ Synopsis

A finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed. An implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces. A two-time level implicit method is used, while Taylor's forward projection method is employed for taking account of the nonlinearities. An iterative method is described which predicts unknown surface conditions. An example is illustrated which is typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitation.

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## Abstract The aim of this article is to study the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing a new variable, we reformulate the problem as a nonclassical parabolic equation along with the in