Investigation of transient conduction–radiation heat transfer in a square cavity using combination of LBM and FVM

Abstract

In this paper, the effect of surface radiation in a square cavity containing an absorbing, emitting and scattering medium with four heated boundaries is investigated, numerically. Lattice Boltzmann method (LBM) is used to solve the energy equation of a transient conduction-radiation heat transfer problem and the radiative heat transfer equation is solved using finite-volume method (FVM). In this work, two different heat flux boundary conditions are considered for the east wall: a uniform and a sinusoidally varying heat flux profile. The results show that as the value of conduction-radiation decreases, the dimensionless temperature in the medium increases. Also, it is clarified that, for an arbitrary value of the conduction-radiation parameter, the temperature decreases with decreasing scattering albedo. It is observed that when the boundaries reflect more, a higher temperature is achieved in the medium and on boundaries.

Conductive-radiative heat transfer in a 2D semi-transparent medium with a square centered obstacle

“…These proposed numerical simulations also approve the behavior of the 1D numerical results presented in Fig. 13 The behavior of the simulations here is not far from those presented on Fig. 16, but the obstacle is smaller and enables more rays travel from south to north boundaries.…”

“…Once is calculated for all the grid's cells including the boundary surfaces, Eqs. (12)(13) are used to compute the radiative heat flux vector ⃗ and the radiative source = −∇. ⃗⃗⃗⃗ ⃗ .…”

“…It was observed that the LBM converged faster than FVM in case of coupled radiation-diffusion. In fact, researchers such as Sakami et al [7], Rousse et al [8], Mahapatra et al [9], Luo and Shen [10], Lazard [11], Ghattassi et al [12], Keshtkar [13], have developed similar analysis with excellent results compared to benchmarks solutions, when the size of the obstacle is set to be zero.…”

Application of a new single staggered grid method to the heat transfer problems

“…However, in practical engineering, the heat transfer problems are difficult to be solved analytically due to the irregular and complex boundary conditions of different models. The finite volume method (FVM) as an effective numerical method has been widely applied to obtain numerical solutions of complex heat transfer problems [4,5]. For the FVM, it is important to choose a reasonable grid system for improving the accuracy of numerical solution and reducing the computation time.…”