Finite integral transform-based analytical solutions of dual phase lag bio-heat transfer equation

Abstract

• Analytical solution of the non-Fourier bio heat transfer equation. • Finite integral transform. • Time independent/dependent boundary conditions. • Coupling of the transient RTE and non-Fourier heat conduction models. • Thermal analysis of laser-irradiated biological tissue phantoms. A finite integral transform (FIT)-based analytical solution to the dual phase lag (DPL) bio-heat transfer equation has been developed. One of the potential applications of this analytical approach is in the field of photo-thermal therapy, wherein the interest lies in determining the thermal response of laser-irradiated biological samples. In order to demonstrate the applicability of the generalized analytical solutions, three problems have been formulated: (1) time independent boundary conditions (constant surface temperature heating), (2) time dependent boundary conditions (medium subjected to sinusoidal surface heating), and (3) biological tissue phantoms subjected to short-pulse laser irradiation. In the context of the case study involving biological tissue phantoms, the FIT-based analytical solutions of Fourier, as well as non-Fourier, heat conduction equations have been coupled with a numerical solution of the transient form of the radiative transfer equation (RTE) to determine the resultant temperature distribution. Performance of the FIT-based approach has been assessed by comparing the results of the present study with those reported in the literature. A comparison of DPL-based analytical solutions with those obtained using the conventional Fourier and hyperbolic heat conduction models has been presented. The relative influence of relaxation times associated with the temperature gradients ( τ T ) and heat flux ( τ q ) on the resultant thermal profiles has also been discussed. To the best of the knowledge of the authors, the present study is the first successful attempt at developing complete FIT-based analytical solution(s) of non-Fourier heat conduction equation(s), which have subsequently been coupled with numerical solutions of the transient form of the RTE. The work finds its importance in a range of areas such as material processing, photo-thermal therapy, etc.