Modelling transient heat transfer through the skin and a contact material

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Abstract
Two thermal models of the skin and superficial tissues are described, both of which incorporate the thermal effects of subcutaneous and dermal blood flow through temperature-dependent heat sources. The model which represents the dermal blood flow as the perfusion of a region of finite thickness gives rise to purely numerical solutions for the transient temperatures. Representing the dermal blood flow by a heat generating surface gives rise to a model which yields explicitly analytical expressions. Although these analytical expressions require numerical integration techniques to finally evaluate them, they are of a form which allows temperature values to be derived more efficiently than by the purely numerical method. Both models are used to predict the time-dependent temperature profiles resulting with the skin surface. The predictions of the two models are compared and the limitations of the analytical model highlighted.