The present work investigates the impact of the Maxwell-Cattaneo effect (or hyperbolic heat flow) on the flow and heat transfer dynamics of a porous medium in a local thermal non-equilibrium (LTNE) state. The study focuses on the quantitative investigation of natural convection in a square porous cavity filled with water and crude oil. The thermal conditions in the square porous cavity are such that the temperature is fixed on the vertical surfaces with the temperature on the left higher than that on the right, and the top and bottom horizontal surfaces are thermally adiabatic. The Darcy-Brinkman model for the fluid flow is utilized, taking into account the Maxwell-Cattaneo (MC) relation of temperature and heat flux for the fluid and solid. We investigate the role of the pertinent parameters such as the Rayleigh number (103 ≤ Ra ≤ 105), Darcy number (10−4 ≤ Da ≤ 10−1), Brinkman number (0 ≤ Br ≤ 20), interface heat transfer parameter (0 ≤ H ≤ 150), MC parameter in fluid (0 ≤ Cf ≤ 10−4), MC parameter in solid (0 ≤ Cs ≤ 0.5), and porosity parameter (0.4 ≤ φf ≤ 0.8) on streamlines, isotherms, and the average Nusselt numbers of fluid and solid. The numerically simulated results through the finite element method show that the MC effect is active in reducing fluid friction and increasing the heat transfer rate in both fluid and solid. It has more impact on the water sandstone than the crude oil sandstone. The influence of the Rayleigh number, Darcy number, and the Brinkman on the thermal state of the medium is discussed in detail.
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