The Heat-Balance Integral—Further Considerations and Refinements

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Abstract
Integral methods have previously been applied to transient heat conduction in a slab with constant thermal properties. In this paper the method is extended so as to include temperature-dependent thermal properties in the analysis. In addition, it is shown how to improve the accuracy of a solution by increasing the order of the polynomial used to represent the temperature profile. For the case of a prescribed step surface temperature in a semi-infinite slab, a quartic profile is shown to give excellent accuracy.

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