THE EFFECT OF FRACTIONAL ORDER DERIVATIVE ON HUMAN HEAD SKIN TISSUE IN RESPONSE TO THERMAL DIFFUSION

In this manuscript, the Caputo-Fabrizio fractional order model is used to study the effects of thermal diffusion in human head skin tissue. This leads to analyzing variations in the concentration distribution of the diffusive material in skin tissue and the temperature distribution function with relaxation time due to the chemical potential function, which depends on time and thermal diffusion on the bounding plane. The Laplace transform technique is employed to compute the results, which show a significant effect of the Caputo-Fabrizio fractional order parameter, distance, and time. The procured results have been illustrated graphically using MATLAB, where the influence of a non-singular memory kernel has been observed, which implies a more realistic description of the thermal process in skin tissue. The numerical results for concentration and temperature distribution functions are obtained using the method of numerical inversion based on the Tzou method. The validity of this intended model is assessed by comparing it with previously published results. Significantly, the infinite memory effects have been avoided by introducing a smooth, non-singular kernel. The accumulation of heat by the skin tissue over time is realistically modeled. Observing the more realistic treatment of memory effects, according to the authors, the Caputo-Fabrizio approach provides a more refined and realistic model, which is explicitly suited for precision heat application in thermal therapies like cryosurgery and hyperthermia treatments for tumors, also enhancing the accuracy of simulations related to thermal damage, skin burn, and pain response in heterogeneous tissue.