The purpose of this study is to validate whether the local thermal equilibrium for unsteady state is an appropriate assumption for the porous media with closed pores. It also compares the transient temperatures between the pore scale and volume averaged approaches to prove that the volume averaged method is an appropriate technique for the heat transfer in closed-cell porous media. The interfacial heat transfer coefficient for the closed-cell porous media is also discussed in details.
The governing equations for the pore scale and continuum domains are given. They are solved numerically for the pore scale and volume-averaged domains. The results are compared and discussion was done. The performed discussions and explanations are supported with figure and graphics.
A local thermal non-equilibrium exits for the closed-cell porous media in which voids are filled with water during the unsteady heat transfer process. Local thermal non-equilibrium condition exists in the cells under high temperature gradient and it disappears when the heat transfer process becomes steady-state. Although a local thermal equilibrium exists in the porous media in which the voids are filled with air, a finite value for heat transfer coefficient is found. The thermal diffusivity of air and solid phase are close to each other and hence a local thermal equilibrium exists.
The study is done only for the closed-cell porous media and for Rayleigh number till 105. Two common working fluids as water and air are considered.
There are many applications of porous media with closed pores particularly in the industry, such as the closed-cell metal foam or the closed cells in porous materials such as foods and plastic-based insulation material. The obtained results are important for transient heat transfer in closed-cell porous materials.
The obtained results are important from the transient application of heat transfer in the closed-cell material existing in nature and industry.
The authors’ literature survey shows that it is the first time the closed-cell porous media is discussed from local thermal non-equilibrium point of view and it is proved that the local thermal non-equilibrium can exist in the closed-cell porous media. Hence, two equations as solid and fluid equations should be used for unsteady heat transfer in a closed-cell porous medium.
The first author gratefully acknowledges the financial support from China Scholarship Council (No. 201808050059), which has sponsored his PhD study at the Shizuoka University in Japan.
Wang, C., Mobedi, M. and Kuwahara, F. (2019), "Simulation of heat transfer in a closed-cell porous media under local thermal non-equilibrium condition", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 8, pp. 2478-2500. https://doi.org/10.1108/HFF-01-2019-0081
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