Comparison between Two Local Thermal Non Equilibrium Criteria in Forced Convection through a Porous Channel

Abstract

Two criteria are used and compared to investigate the local thermal equilibrium assumption in a forced convection through a porous channel. The first criterion is based on the maximum local temperature difference between the solid and fluid phases, while the second is based on the average of the local differences between the temperature of the solid phase and the fluid phase. For this purpose, the momentum and energy equations based on the DarcyBrinkman-Forchheimer and the local thermal non equilibrium models are solved numerically using the finite volume method. The analysis focused on searching thermophysical parameters ranges which validate local thermal equilibrium hypothesis. Thus, by using the two criteria, the obtained results mainly revealed that this local thermal equilibrium assumption is verified for low thermal conductivity ratio and Reynolds number values and for high interstitial Biot number and porosity, while it is unfavorably affected by the high values of Prandtl number. However, it is also found that the parameters ranges corresponding to the local equilibrium validity depends on the selected local thermal non equilibrium criterion.

On the Limitations and Implications of Modeling Heat Transport in Porous Aquifers by Assuming Local Thermal Equilibrium

“… Maximum and average temperature difference between the normalized temperature obtained using the LTE model and the fluid temperature obtained using the LTNE model (Hamidi et al, 2019) for each evaluated distance x ( N = number of timesteps). and Maximum and average normalized temperature difference between fluid and solid (Abdedou & Bouhadef, 2015; Al‐Sumaily et al, 2013; Khashan et al, 2006; Khashan & Al‐Nimr, 2005) obtained using the LTNE model for each distance x : and …”

“…Method 3: Maximum and average normalized temperature difference between fluid and solid (Abdedou & Bouhadef, 2015;Al-Sumaily et al, 2013;Khashan et al, 2006;Khashan & Al-Nimr, 2005) obtained using the LTNE model for each distance x:…”

“…Furthermore, it is difficult to identify and quantify the errors induced by using an LTE model with the currently available LTNE measures. Standard criteria such as the temperature difference between fluid and solid phases (Abdedou & Bouhadef, 2015; Al‐Sumaily et al, 2013; Khashan & Al‐Nimr, 2005; Khashan et al, 2006) or the difference between the local fluid temperatures of both models (Hamidi et al, 2019) have a technical meaning, and the transition to a natural environment is difficult. The implications for the heat transport modeling in the field are mostly unknown.…”

Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

“…While, for the pulsatile flow, the level of non-equilibrium might be reduced by decreasing Strouhal number or by increasing the oscillating amplitude, see Figure 25. Abdedou and Bouhadef [51] used two LTNE criteria to test the assumption of LTE for a forced convective flow during a porous canal. The first criterion was in terms of the average of the local temperature differences between the solid and fluid phases, and it can be expressed mathematically as:…”

“…Al-Sumaily et al [49] as interphase convective heat transfer parameter (H = h s f L 2 /k f ) ↑, porosity scaled fluid/solid thermal conductivity ratio (K r = εk f /(1 − ε)k s ) ↑ Wong and Saeid [50] as solid/fluid thermal conductivity ratio ↓, Pr ↓, Re ↓, Bi ↑, ε ↑ Abdedou and Bouhadef [51] when the blood perfusion rate during the tissue ↓, or the heat source intensity ↓ Hassanpour and Saboonchi [53] when k s = k f , or as the interior heat generation parameter ↓ Parhizi et al [55] higher Bi↑, Da↑, ε ↑, Ra↓ Haddad et al [56] as interfacial heat transfer parameter H = h s f L 2 / (1 − ε)k s ↑, thermal capacity ratio C = (1 − ε)ρ s c s /(ερ f c f ) ↑, thermal conductivity ratio r k = (1 − ε)k s /(εk f ) ↑, thermal diffusivity ratio (α = α s /α f ) ↑, or as the amplitude and/or the frequency of the thermal disturbance ↓ Khadrawi et al [57] as Da↓, Ra↓, or as Bi↑, effective fluid/solid thermal conductivity ratio ↑ Khashan et al [58] as magnetic field parameter (M) ↑, interphase convective heat transfer parameter h s f L 2 /(1 − ε)k s ↑, solid/fluid thermal conductivity ratio (1 − ε)k s /εk f ↑, thermal diffusivity ratio (α)↓, fluctuation amplitudes and frequencies ↓ Tahat et al [59] as interphase convective coefficient ↑, fluid/solid conductivity ratio ↑, permeability ratio ↑, and wall thickness ↑, solid/fluid heat capacity ratio ↓ Harzallah et al [60] solid/fluid conductivity ratio ↑, cylinder/particle diameter ratio ↑, Ra↓, ε ↓ Al-Sumaily et al [61] as interfacial convective heat transfer parameter (H = h s f L 2 /εk f ) ↑, porosity scaled fluid/solid thermal conductivity ratio (γ = εk f /(1 − ε)k s ) ↑, Ra↓, wall heat flux ↓ Bourouis et al [62]…”