Abstract
In this work, the new concept of “memory dependent derivative” in the Pennes’ bio-heat transfer process of skin tissues is employed to investigate the one-dimensional problem of a skin tissue under sinusoidal heat flux conditions. Laplace transform technique is utilized to solve the problem. We investigate, numerically, the bio-heat transfer equation with memory-dependent derivative to find the effect on the tissue temperature of the kernel function and the time-delay parameter which are characteristic of memory dependent derivative heat transfer. Correlations are made with the results obtained in the case of the absence of memory-dependent derivative parameters. The effects of the time-delay on the temperature distribution in skin tissue for different forms of kernel functions are examined.
•Memory dependent derivative of Pennes' bio-heat transfer equation is constructed.•The analytical solution of MDD bio-heat equation is presented.•The thermal responses of skin tissue under sinusoidal heat flux conditions are investigated.•The effects of time-delay and the forms of kernel function on the thermal injury are examined.•The memory-dependent derivatives are better than the fractional one for reflecting the memory effect.