Convection heat transfer from cylinders in a porous medium using the two-equation energy model

Abstract

This numerical study is directed at exploring the flow characteristics and thermal response for the flow over a circular cylinder(s) embedded in a horizontal packed bed under steady or unsteady forced convection. The analysis is made for an incompressible fluid flow through a two-dimensional bed, which consists of spherical particles that are packed randomly. The subproblems that are considered in the present study are: First, forced convective steady and pulsatile cross flows over a single cylinder placed in a porous bed. Where, for steady flow, the effects of the thermal and structural properties of the porous medium on the convective and conductive heat transfer to the fluid and solid phases, are examined. While, for pulsatile flow, the flow and heat transfer is investigated subject to a sinusoidally varying inlet flow, for both a non-filled and porous material filled channels. The effects of pulsation frequency and amplitude on heat transfer are quantified. Second, forced convective steady cross flow over multiple cylinders arranged in two staggered or in-line configurations, embedded in a porous bed. The focus is directed on how the spacing parameter between the cylinders affects heat transfer from each, at different thermal conductivity ratios and Reynolds numbers for both configurations. Specifically, the generalised momentum model, i.e., the Darcy-Brinkmann-Forchheimer (DBF) model, is employed to model the flow field. This takes into consideration the non-Darcian terms, such as inertial and viscous effects. Moreover, the energy transport within the solid and fluid phases is modelled using separate energy equations for each phase. This is sometimes called the Local Thermal Non-Equilibrium (LTNE) model, in that it makes no assumptions about local thermal equilibrium between phases. The additional convective heat transfer term between the fluid and solid phases, which emerges when using the two-phase model, is formulated using a documented empirical correlation. Furthermore, the thermal dispersion phenomenon due to the complex path of local fluid elements through the solid matrix, causing mixing and recirculation in both the longitudinal and the transverse directions, is incorporated in the modelling of the fluid phase energy equation