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Research Papers

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

[+] Author and Article Information
Aritra Mukherjee

Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, India
e-mail: ammaritra@gmail.com

Pranab Kumar Mondal

Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, India
e-mail: mail2pranab@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received November 24, 2017; final manuscript received April 23, 2018; published online June 22, 2018. Assoc. Editor: Sandip Mazumder.

J. Thermal Sci. Eng. Appl 10(4), 041022 (Jun 22, 2018) (13 pages) Paper No: TSEA-17-1455; doi: 10.1115/1.4040283 History: Received November 24, 2017; Revised April 23, 2018

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.

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Figures

Grahic Jump Location
Fig. 1

(a) Schematic of one-dimensional concentric spherical enclosure, (b) intensity distribution in spatial polar space, (c) control volumes with intensities at nodal points and control surfaces, and (d) D1Q3 lattice

Grahic Jump Location
Fig. 2

(a) Effect of number of grids on radial temperature distribution, (b) effect of number of lattices on radial temperature distribution, and (c) effect of number of polar space divisions on radial temperature distribution. Different conductive and radiative parameters are N=0.3,ω=0.5,β=1.0,η2/η1=2.0,ε1=ε2=1.0.

Grahic Jump Location
Fig. 3

Validation for (a) pure non-Fourier conduction and (b) pure radiation

Grahic Jump Location
Fig. 4

(a) Nondimensional energy flow rate at steady-state for N=0.3,ω=0.5,β=1.0,η2/η1=2.0, radial temperature distribution θ at different time levels for lag ratio (b) B=0.005, (c) B=0.05 and (d) B=0.5

Grahic Jump Location
Fig. 5

(a) Nondimensional energy flow rate at steady-state levels for CR parameter N=0.3,ω=0.5,β=1.0,η2/η1=2.0 radial temperature distribution θ at different time levels for lag ratio (b) B=0.005, (c) B=0.05, and (d) B=0.5

Grahic Jump Location
Fig. 6

For B=0.005 and β=1.0,ω=0.5,N=0.3,η2/η1=2.0, (a) nondimensional energy flow rate at steady-state, (b) radial temperature distribution θ at different time levels, for lag ratio B=0.005 and β=2.0,ω=0.5,N=0.3,η2/η1=2.0, (c) nondimensional energy flow rate at steady-state, and (d) radial temperature distribution θ at different time levels

Grahic Jump Location
Fig. 7

For B=0.005 and ω=0.9,β=1.0,N=0.3,η2/η1=2.0 (a) nondimensional energy flow rate at steady-state and (b) radial temperature distribution θ at different time levels, for B=0.005 and ω=0.1,β=1.0,N=0.3,η2/η1=2.0, (c) nondimensional energy flow rate at steady-state, and (d) radial temperature distribution θ at different time levels

Grahic Jump Location
Fig. 8

Radial temperature distribution θ at different time levels for N=0.3,β=1.0,ω=0.5,η2/η1=2.0 and lag ratio: (a) B=0.005, (b) B=0.05 and N=0.03, (c) B=0.005, and (d) B=0.05

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