A thermal nonequilibrium model to natural convection inside non‐Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

Abstract

This article displays a numerical investigation on natural convection within non‐Darcy porous layer surrounded by two horizontal surfaces having sinusoidal temperature profiles with difference in phase and wave number. The Darcy–Brinkman–Forchheimer model and local thermal nonequilibrium condition have been employed. Simulations have been performed for wide ranges of inertia coefficient (10–4 ≤ Fs/Pr* ≤ 10–2), thermal conductivity ratio (0.1 ≤ K r ≤ 100), phase difference (0 ≤ β ≤ π), modified Rayleigh number (200 ≤ Ra* ≤ 1000), wavelength (3 ≤ k ≤ 12), and nondimensional heat transfer coefficient (0.1 ≤ H ≤ 100). Results demonstrate that Nusselt number highly relies on Fs/Pr*, K r, β, Ra*, and k as compared to H. A considerable enhancement in fluid, solid, and overall Nusselt numbers has been observed with diminishing Fs/Pr* and β and increasing k, K r, and H. The raising in β has a significant impact on Nu for smaller k and this effect is almost ignored when k > 12. The increase in Ra*, K r, β, and H and decrease in Fs/Pr* and k acts to reduce the severity of nonequilibrium zone and increase the size of thermal equilibrium zone. The influence of H on nonequilibrium area is more evident than K r.

Conjugate local thermal nonequilibrium and non‐Darcy flow inside porous enclosure: Analysis of localized heating and cooling arrangements

“…For porous medium region 58–60 : $$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0,$$$ $$${(\rho {C}_{p})}_{f}\left[u\frac{\partial {T}_{f}}{\partial x}+v\frac{\partial {T}_{f}}{\partial y}\right]=\phi {k}_{f}\left[\frac{{\partial }^{2}{T}_{f}}{\partial {x}^{2}}+\frac{{\partial }^{2}{T}_{f}}{\partial {y}^{2}}\right]+h({T}_{S}-{T}_{f}),$$$ $$$(1-\phi ){k}_{S}\left[\frac{{\partial }^{2}{T}_{S}}{\partial {x}^{2}}+\frac{{\partial }^{2}{T}_{S}}{\partial {y}^{2}}\right]+h({T}_{f}-{T}_{S})=0,$$$ …”