Effect of Prandtl Number on Mixed Convective Heat Transfer from a Porous Cylinder in the Steady Flow Regime

Abstract

The effect of the Prandtl number (Pr) on the flow and heat transfer from a porous circular cylinder with internal heat generation in the mixed convection regime is numerically investigated. The steady flow regime is considered over the ranges of the Reynolds number (Re), Darcy number (Da), and Richardson number (Ri), varying from 5 to 40, 10−6 to 10−2, and 0 to 2, respectively. The wake structure, the temperature distribution, and the heat transfer rate are discussed. Besides precipitating the growth of the recirculating wake, the Prandtl number is found to have a significant impact on the thermal characteristics. The concave isotherms, resembling a saddle-shaped structure, occur behind the cylinder at larger Pr, resulting in swells of the isotherms pairing off at the lateral sides. These swells are found to have a negative effect on heat transfer owing to a relatively smaller temperature gradient there. Then, the heat transfer rate in terms of the local Nusselt number (Nu) and enhancement ratio (Er) is calculated, which is closely related to Pr, Re, Da, and Ri. The local minimum heat transfer rate along the cylinder surface is found at the position where the swells of the isotherms form.