Natural convection flow in a fluid-saturated non-Darcy porous medium within a complex wavy wall reactor

Abstract

This study elucidates a numerical simulation of natural convective flow inside a confined 2D reactor containing a fluid-saturated non-Darcy porous medium. The lower wall of the reactor is wavy, while all other walls are plane surfaces. All walls of the reactor are kept at surrounding temperature. A chemically reacting fluid produces flow within the reactor by a heat generating exothermic reaction. A coordinate transform is dispensed to turn the waviness of walls into the plane surface, and then, the flow governing equations in transformed coordinates are solved using the finite difference scheme. Streamlines and isotherms that describe, respectively, the flow patterns and temperature distributions within the reactor are displayed varying the dimensionless numbers, namely the Darcy number (10−4 ≤ Da ≤ 10−2), the Rayleigh number (103 ≤ Ra ≤ 105), the Frank-Kamenetskii number (0.5 ≤ Kf ≤ 3.0) and the Forchheimer drag parameter (0 ≤ F ≤ 1). Also local Nusselt numbers at the upper and lower walls are plotted to observe the heat transfer characteristics. The remarkable results reveal that the strength of vorticity and the highest temperature within the reactor increase with increasing the Frank-Kamenetskii number and the amplitude of waves. Because of increasing the Darcy number and Rayleigh number, the strength of vorticity enhances but the highest temperature diminishes. Opposite characteristics are observed due to an increase in the Forchheimer drag parameter. Heat transfer is relatively stronger in plane wall than in wavy wall in every case of dimensionless number. Moreover, maximum heat transfer is noticed at the points on the upper wall that are exactly above the peaks of the wave.