Abstract.
This paper considers the inverse determination of the positive unknown thermal properties K(T), C(T) and the unknown temperature T( x, t ) in the nonlinear transient heat conduction equation. In addition to prescribed initial and/or boundary values, specified continuously differentiable temperature data T(x 0, t) with non-zero derivative at a single sensor location x = x 0 is given. When K(T) and C(T) obey a certain relationship which enables one to linearise exactly the nonlinear heat equation then their dependence upon T is obtained explicitly, whilst the unknown temperature T(x, t) is obtained implicitly and is then calculated numerically. Results are presented and discussed for infinite, semi-infinite and finite slabs.
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Received: September 20, 2000
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Lesnic, D. The determination of the thermal properties of a heat conductor in a nonlinear heat conduction problem. Z. angew. Math. Phys. 53, 175–196 (2002). https://doi.org/10.1007/s00033-002-8151-x
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DOI: https://doi.org/10.1007/s00033-002-8151-x