Analysis of Heat Transfer Through Optically Participating Medium in a Concentric Spherical Enclosure: The Role of Dual-Phase-Lag Conduction and Radiation

Abstract

This paper deals with the analysis of the effects of combined dual-phase-lag (DPL) heat conduction and radiation in a concentric spherical enclosure with diffuse-gray surfaces. The enclosed medium is optically participating, i.e., it is radiatively absorbing, emitting, and scattering. Lattice Boltzmann method (LBM) is used to solve the energy equation, and finite volume method (FVM) is used to compute the radiative information. To establish the accuracy of this approach, the combined energy equation is also solved with the finite difference method. Radial temperature profiles and energy contributions by conduction and radiation at various instances and prior to steady-state are elaborated for different kind of thermal perturbations Influence of numerous conductive and radiative parameters over the heat transport process have been investigated in detail. It is observed that higher contribution of radiation to the heat transport process can destroy the thermal wave in the medium completely. Sample results for pure non-Fourier heat conduction, pure radiation, and steady-state response of combined Fourier conduction and radiation in spherical geometry are compared with the results available in literature. In all the cases, comparison shows good agreement with the reported results.

Mixed convection and activation energy impacts on MHD bioconvective flow of nanofluid with irreversibility assessment

“…Impact of radiation and dual phase lag conduction through optically participating spherical enclosure is reported by Mukherjee and Mondal [ 13 ]. Ziaei et al [ 14 ] explored MHD nanofluid flow by permeable stretching surface. Consequences of porosity and activation energy in flow of hybrid nanofluid by curved stretched is investigated by Kumar et al [ 15 ].…”

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 …”

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

“…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. The compatibility analysis involving the non-Fourier (C-V or DPL) model with the thermodynamics second law can be carried out using the theory of CIT.…”

“…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 …”