Transient heating in a spherical tissue due to thermal therapy in the context of memory-dependent heat transport law

Abstract

The objective of the present study is to formulate the bio-heat model to study the variations of temperature profile and thermal damages within a spherical living tissue subjected to a thermal therapy, whose outer surface is thermally insulated. The heat conduction equation is formulated in the context of convolution-type Dual-phase (DP) lag memory-dependent derivative, having kernels to be power functions, from which, the Lord–Shulman model can be obtained as a particular case. The Laplace transform technique is implemented to solve the governing equations. The influences of the memory-dependent derivative and effect of time-delay parameters on the temperature of skin tissues and the thermal injuries are precisely demonstrated. The thermal injuries of the tissue are assessed by the denatured protein range. The numerical inversion of the Laplace transform is performed with the help of Zakian methods. The numerical outcomes of thermal injuries and temperatures have been represented graphically. Excellent predictive capability is demonstrated to identify an appropriate therapy to select different kernel functions for effective heating in hyperthermia treatment. Significant effect of the thermal therapy is reported due to the effect of delay time also.

Keywords:

• Spherical skin tissue
• memory-dependent derivative
• bioheat equation
• Laplace transform
• time-dependent heat source
• delay time

Acknowledgments

The authors are grateful to the Editor and Reviewers for their valuable suggestions for the improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors received no financial support for this research.