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

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. Research Highlights Free convection inside porous layer bounded by horizontal heated walls is considered. Horizontal walls have sinusoidal temperature profiles with a phase difference and wave number. The assumptions of local thermal nonequilibrium (LTNE) and Darcy–Brinkman–Forchheimer model are included. LTNE and non‐Darcy conditions highly influences the intensity of LTNE zone and heat transfer. The peak Nusselt number is observed at high wave length and low phase difference.