NUMERICAL INVESTIGATION OF HEAT TRANSFER IN A DEVELOPING THERMAL FIELD IN THE POROUS-FILLED DUCT UNDER LOCAL THERMAL NONEQUILIBRIUM: CONSTANT WALL HEAT FLUX

In this article, the numerical study of the laminar forced convection in a thermally developing region coming under the influence of local thermal nonequilibrium (LTNE) of parallel plate channels completely immersed in the porous material is investigated. The channel walls are kept at constant wall heat flux boundary conditions. The Darcy-Brinkman- Forchheimer equation governs the flow field in the porous region, which is unidirectional. The system is defined by certain well-known parameters, these being Darcy number (Da), thermal conductivity ratio (kappa), Forchheimer number (F), and Biot number (Bi). Numerical solutions have been obtained by applying a successive accelerated replacement (SAR) scheme. Exact solutions for dimensionless temperature and the fully developed Nusselt number in the absence of the Forchheimer number (F = 0), for the fully developed thermal field, are obtained for the Darcy model and the Darcy-Brinkman model. Plots showing velocity, skin friction coefficient, dimensionless temperature profiles, and wall temperatures in the fluid and the solid phases, as well as the local Nusselt number at the parallel plate channel, have been displayed. The effect of the thermal conductivity ratio on the local Nusselt number is significant. For a large Biot number, local thermal nonequilibrium is the same as local thermal equilibrium. As the ratio between thermal conductivities and Biot number grows, the local Nusselt number decreases.