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Application of the Boltzmann transformation and the method of successive approximations to solve a heat conduction problem with a temperature dependent thermal conductivity

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
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The notebook provides the solutions to two heat conduction problems where the thermal conductivity varies with temperature. The author starts by using the shooting technique and NDSolve to get the exact numerical solutions to the nonlinear boundary value problems. The governing equation is derived using the Boltzmann transformation. Then, the method of successive approximations, described in M. N. Özisik, Heat Conduction, Wiley, New York, 1980, is used to obtain the same solutions. Convergence of this method is achieved after only two iterations.

*Applied Mathematics
*Applied Mathematics > Numerical Methods
*Engineering > Chemical Engineering

Temperature dependent thermal conductivity, heat conduction problem, shooting method, split boundary value problem, NDSolve, method of successive approximations, Boltzmann transformation
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Successive_Approximations_1F.nb (151.5 KB) - Mathematica Notebook
Successive_Approximations_2F.nb (152.5 KB) - Mathematica Notebook