Research On The Related Application Of Heat Transfer Equation

With the rise of heat therapy such as lasers,it is particularly important to understand and master the heat transfer mechanism of biological tissues under different heat flow and temperature conditions.At present,the researches on heat flow conditions mainly focus on the Fourier model-based Pennes equation and the non-Fourier model-based thermal wave equation solution and comparison of results under constant or positive and cosine heat flow loading conditions.The researches on different temperature boundary conditions also focus on the solution and comparison of the Pennes model and the thermal wave model.Therefore,there is a lack of a general formula to avoid saluting of the Pennes equation and the thermal wave equation more times when the boundary conditions are changed.In this paper,the generalized solutions of the Pennes equation and the thermal wave equation under various periodic heat flow boundary conditions and various periodic temperature boundary conditions are obtained,respectively,and the obtained analytical formulas are verified and analyzed.For the arbitrary periodic heat flow boundary conditions,the analytical solutions of Pennes and thermal fluctuations under arbitrary periodic heat flow are obtained based on Laplace transform and Fourier transform.Based on the analytical solution,the temperature field distribution of the skin at different depths and the temperature field distribution along the depth at a certain time are studied in detail.It is found that the thermal wave equation has obvious delay characteristics compared with the Pennes equation.Furthermore,the effect of heat perfusion rate on skin temperature field was studied,and it was found that skin temperature was negatively correlated with heat perfusion rate at a certain depth.The response of the periodic loading of different frequencies to the skin temperature field when the total heat load is applied is studied,which indicates that the skin response temperature is positively correlated with the heating frequency at the near skin surface.For the arbitrary periodic temperature boundary conditions,the analytical solutions of Pennes equation and thermal wave equation of skin tissue under arbitrary periodic surface temperature thermal perturbation are derived based on the variable separation and Duhamel integral method.Then,by comparing with the literature results to verify the correctness of the analytical solution,the periodic triangular temperature heat wave is taken as an example to discuss the differences between the Fourier-based Pennes equation and the non-Fourier-based thermal wave equation and the effects of various parameterchanges on skin temperature disturbance are discussed.