An estimation of temperature in living tissue using a fractional model with sinusoidal heat flux conditions on the skin surface

Abstract

An accurate and quantitative description of the thermal responses of skin tissue under sinusoidal heat flux conditions on the skin surface is provided in this study using a fractional model of the bioheat transfer equation. The governing fractional one-dimensional bio-heat transfer equation was transformed into a dimensionless form to get closed solution by the Caputo-Fabrizio time-fractional derivative technique. The proposed technique, with the aid of symbolic computation, provides an impressive solution for the bioheat transfer equation. Numerical simulations were performed with the aid of Mathcad software to study the behavior of temperature transients on the skin surface exposed to instantaneous surface heating. To investigate the thermal impacts of various control factors on tissue temperature, sensitivity analysis is carried out. We found that the effects of the fractional derivative and the moving heat source velocity on the temperature of the tissue and thermal injuries are enormous, and are shown graphically for an explicit and detail discussion. Observations from the graphical representation of results, show clearly that increasing pressure term leads to increase in velocity distribution of temperature and the effect is maximum towards the center in most cases. The study reveals that bio-thermal research can help with skin burn evaluation, clinical thermal treatment equipment design, and thermal protection from various risks of skin heat injuries. In conclusion, the results of this investigation will be very helpful and useful to both clinical-therapeutic applications and medical sciences.