The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

Abstract

This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

Noninvasive and Continuous Monitoring of the Core Body Temperature through the Quantitative Measurement of Blood Perfusion Rate

“…The primary study by Pennes revealed that heat transfer within living blood-perfused tissue is governed by the following equation, which is assumed to be in steady state with cylindrical coordinates .25ex2ex .25ex2ex 0 = k true( normald 2 T normald r 2 + 1 r normald T normald r true) + q m ‴ + q b ‴ q b ‴ = ω b ρ b c italicp , b false( T normala − T false) where k is the tissue thermal conductivity, T denotes the tissue temperature, q m ‴ represents the metabolic heat generation, q b ‴ is the heat generation due to blood perfusion, ω b denotes the blood perfusion rate in units of m 3 /s/m 3 (volumetric flow rate of blood per unit volume of tissue), ρ b represents the blood density, c p ,b is the blood specific heat, and T a denotes the arterial blood temperature. Pennes’ work on bioheat transfer has inspired researchers to improve the bioheat equation, and some notable newly derived bioheat models include the two-equation bioheat model, , local thermal equilibrium equation model, three-energy equation model, , and dual phase-lag model. − The applications, benefits, and drawbacks of the various bioheat equations have been reviewed by many groups. ,, Although th...…”

Mathematical Modelling with the Exact Solution of Three Different Bioheat Conduction Models of a Skin Tissue Shocked by Thermoelectrical Effect

“…The boundary value problem (B. V. P.) in equations ( 6 )–( 8 ) contains nonhomogeneous partial differential equations with nonhomogeneous boundary conditions on the surface of the skin tissue. Hence, the differential equations must be formulated in two parts, i.e., a steady part and a transient part as follows [ 35 , 37 , 38 ]: …”

Exact solutions, spectrum properties, and hierarchical structures of the multiple temperature model

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