Numerical analysis of combined-mode dual-phase-lag heat conduction and radiation in an absorbing, emitting, and scattering cylindrical medium

Thermodynamic stability analysis of non‐Fourier model‐based bio‐heat transfer in laser‐irradiated cylindrical‐shaped multilayered biological tissue

“…Figure 6 also shows that the value of equilibrium and nonequilibrium EPRs corresponding to the Fourier model-based heat transfer is positive and identical. Therefore, equilibrium and nonequilibrium EPRs profile overlap with each other, which is also evident from Equation (22) after substituting the value of τ τ = = 0 q T into Equation ( 22); the expression of the nonequilibrium EPR obtained is the same as that of the equilibrium EPR (Equation 14).…”

“…where q denotes the heat flux, T is temperature, k is thermal conductivity, and τ q and τ T represent the thermal relaxation time concerning the heat flux and temperature gradient. Few researchers coupled the DPL heat conduction model with the steady radiative transfer equation (which is obtained by neglecting the first term on the left-hand side of Equation 1) to determine the temperature distribution inside the concentric cylindrical 22 and concentric spherical enclosure. 23 Although various researchers have used the DPL model from the perspective of thermal energy diffusion in living tissue, 7,[24][25][26] very few have addressed its compatibility with thermodynamics second law.…”

“…This heat conduction model can be represented by the following equation: $$$\vec{q}+\,{\tau }_{q}\frac{\partial \vec{q}}{\partial t}=-\left\{k\nabla T+{\tau }_{T}\frac{\partial (k\nabla T)}{\partial t}\right\},$$$where $$q$$ denotes the heat flux, $$T$$ is temperature, $$k$$ is thermal conductivity, and $${\tau }_{q}$$ and $${\tau }_{T}$$ represent the thermal relaxation time concerning the heat flux and temperature gradient. Few researchers coupled the DPL heat conduction model with the steady radiative transfer equation (which is obtained by neglecting the first term on the left‐hand side of Equation 1) to determine the temperature distribution inside the concentric cylindrical 22 and concentric spherical enclosure 23 …”

An axisymmetric bioheat transfer analysis through a unified model

“…[27][28][29][30][31][32][33] In processed meat, Antaki 27 evaluated the values of biological tissue for τ q as 16 s and τ T as 0.06 s, by fitting DPL predictions over the experiments conducted by Mitra et al 18 In the combined radiation and non-Fourier modeling, the energy balance equation comprises of radiative nonlinear term and non-Fourier instability, which makes the equation quite difficult to solve and analyze. [34][35][36][37][38][39] Many numerical schemes are available to solve the RTE while solving the coupled conduction-radiation equation such as the Monte Carlo method (MCM), 40 the spherical harmonic method, 41 the discrete transfer method (DTM), 42 the discrete ordinate method (DOM), 43 the finite volume method (FVM), 44 the lattice Boltzmann method (LBM), 45 the collapsed dimension method (CDM), 46 the integral equation solution, 47 and the radiation element solution. 48 There are a few articles available on coupled conduction-radiation model and bioheat heat transfer equation (with non-Fourier models).…”

“…In the combined radiation and non‐Fourier modeling, the energy balance equation comprises of radiative nonlinear term and non‐Fourier instability, which makes the equation quite difficult to solve and analyze 34–39 . Many numerical schemes are available to solve the RTE while solving the coupled conduction‐radiation equation such as the Monte Carlo method (MCM), 40 the spherical harmonic method, 41 the discrete transfer method (DTM), 42 the discrete ordinate method (DOM), 43 the finite volume method (FVM), 44 the lattice Boltzmann method (LBM), 45 the collapsed dimension method (CDM), 46 the integral equation solution, 47 and the radiation element solution 48 …”