Thermobiological Mathematical Model for the Study of Temperature Response After Cooling Effects

International Journal of Applied Physics
© 2022 by SSRG - IJAP Journal
Volume 9 Issue 2
Year of Publication : 2022
Authors : Vivek Kumar, S. R. Shah

How to Cite?

Vivek Kumar, S. R. Shah, "Thermobiological Mathematical Model for the Study of Temperature Response After Cooling Effects," SSRG International Journal of Applied Physics, vol. 9,  no. 2, pp. 7-11, 2022. Crossref,


An thermobiological mathematical model is developed to study the recovery of skin tissue to the ambient temperature after the exposure of skin to cold temperature till the skin reaches externally applied temperature. This model is based on Pennes heat balance equation. The Laplace transform method and boundary condition of core temperature are used. The study shows the linear dependence of steady-state temperature on blood perfusion rate. It can be concluded that the skin starts to recover to the ambient temperature above 800 seconds. The recovery profile or temperature profile of skin is not constant but depends on various physical parameters of skin tissue. Therefore, the temperature profile is studied for different parameters like tissue thermal conductivity, perfusion rate of blood, and metabolic heat generation. It is found that skin temperature reaches ambient temperature soon if thermal conductivity & metabolic heat generation is high and blood perfusion is low. This study also finds the steady state temperature of the tissue, i.e., when too much time is passed, the temperature is calculated. It is found that the value of steady state temperature is different for different values of blood perfusion rate.


Ambient temperature, Blood perfusion, Laplace transform method, Metabolic heat generation, Perfusion rate. Thermal conductivity.


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