Forced convection in a self heating porous channel: Local thermal nonequilibium model

Abstract

Laminar forced convection flow through a parallel plates channel completely filled with a saturated porous medium where occurs a uniform heat generation per unit volume with volumetric heat generation is investigated numerically. The Darcy-Brinkman model is used to describe the fluid flow. The energy transport mathematical model is based on the two equations model which assumes that there is no local thermal non-equilibrium between the fluid and the solid phases. The dimensionless governing equations with the appropriate boundary conditions are solved by direct numerical simulation. The effect of the controlling parameters, Biot number, thermal conductivities ratio, heat generation rate, and the Reynolds number on the local thermal equilibrium needed and sufficient condition is analyzed. The results reveal essentially that the local thermal equilibrium condition is unfavorably affected by the increase in the heat generation rate, the thermal conductivities ratio, and the decrease in the Biot number. In addition, for a given heat generation rate, the effect of Reynolds number on the local thermal equilibrium condition is reversed depending on the conductivities ratio threshold.

Numerical Investigation of Metal Foam Pore Density Effect on Sensible and Latent Heats Storage through an Enthalpy-Based REV-Scale Lattice Boltzmann Method

“…The U-profiles at X = 0.5, for Re = 50 and Pr = 0.7 set for different Darcy numbers, can be observed in Figure 2 for a quantitative comparison between our TLBM results and those of Kim et al [48]. The good qualitative and quantitative agreement is also apparent by presenting the LTNE intensity in Figure 3 along the dimensionless transverse distance Y at two axial positions X = 0.5 and X = 0.14, thereby strengthening the comparison with Abdedou et al [49]. Finally, as shown in Figure 4, the evolution of dimensionless fluid (Θ f ) and solid (Θ s ) temperatures is consistent with the results of Krishnan et al [50], thereby confirming both the implemented model validity and our code reliability.…”

“…The results show that this parameter has a significant effect, especially at Re 400. As can be seen (Figure 6), the LTE assumption could be adopted during the charging process for case 1, since LTNE 0.05 < [49,51], 0.05 being the limit value allowed so that the LTNE can be conjectured. This obviously cannot be for case 2 ( LTNE 0.05 > ) whatever PPI The effects of the pores' density ω (PPI = 10, 30 and 60) and the Re number (200 and 400) will be investigated in the following sections whereas the Prandtl, Stephan, and Eckert numbers are kept fixed throughout this study.…”

“…The results show that this parameter has a significant effect, especially at Re 400. As can be seen (Figure 6), the LTE assumption could be adopted during the charging process for case 1, since LTNE < 0.05 [49,51], 0.05 being the limit value allowed so that the LTNE can be conjectured. This obviously cannot be for case 2 (LTNE > 0.05) whatever PPI and Re.…”

Numerical investigation of porosity effect on a PCM's thermal performance in a porous rectangular channel via thermal lattice Boltzmann method

“…Such a number is a key parameter to secure the LTE and/or LTNE assumptions in porous media. Previous studies dealt with LTNE and LTE conditions [29,30,31]. From these studies, it appeared that, to satisfy the LTNE condition, Bi must be low ( 0.1 Bi  ) while filling the condition /1 Bi Kr , which takes place in our study.…”

Advanced thermal lattice Boltzmann method for the simulation of latent heat thermal energy in a porous storage unit

“…To validate our in-house code, figure . 3 presents the comparison of the difference between temperatures with results of Abdedou et al [11] at two axial positions 0.14 X and 0.5 X .…”