A new global time treatment is proposed and demonstrated for inverse heat conduction problems. This exposition illustrates the methodology by carefully and meticulously investigating the classic Beck’s problem. It is shown that accurate and stable numerical results occur without resorting to any stabilizing scheme beyond the implementation of a global basis representation for the temperature distribution. As a global time method the entire space-time domain is resolved in a simultaneous fashion. The approach is also extendable to multidimensional and multiprobe situations without difficulty. In direct problems the method has been successively applied to initial value problems, Volterra integral equations, and parabolic and hyperbolic partial and integro-partial differential equations.

Issue Section:
Conduction Heat Transfer
Keywords:
Conduction, Materials Processing and Manufacturing Process, Numerical Methods
Topics:
Heat conduction
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