Damped wave conduction and relaxation in the human skin layer and thermal fabric layer are modeled with a temperature dependent heat source in the human tissue layer. Steady state temperature profiles are derived from the Fourier heat conduction equation. The general solution for the temperature is assumed to be a sum of the transient temperature and steady state temperature. This makes the boundary conditions in space for the skin and fabric layers homogeneous for the transient temperarature. The hyperbolic PDE is solved for by the method of separation of variables. The use of final condition in time in addition to the initial temperature condition leads to bounded infinite Fourier series solutions. These solutions are bounded and does not violate second law of thermodynamics. The model can be used to interpret experimental observations of maximum heat flux that is a parameter of the warm/cool feeling of human skin in winter. For large relaxation times of human skin tissue,
the transient temperature can be expected to undergo oscillations. These oscillations will be supercritical and grow with time for strong heat sources, U* > 1 and may be subcritical damped oscillatory for weak heat sources, U* < 1. For large thermal relaxation times of thermal fabric material,
the transient temperature in the thermal fabric layer may be expected to be subcritical damped oscillatory.
Volume Subject Area:Heat Transfer Theory and Fundamental Research
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