Effects of internal heat generation and partial heating on transient natural convection in an inclined porous cavity using LTNE model

The aim of the present study is to analyze the effects of internal heat generation and partial heating on transient natural convection in an inclined porous cavity using a local thermal non-equilibrium (LTNE) model. An isothermal heater is placed on the bottom horizontal wall with length d, while the remainder of the wall is adiabatic. The left and right vertical walls are maintained at constant cold temperature T_c and the top horizontal wall is adiabatic. The Darcy law is used along with the Boussinesq approximation for the flow. The dimensionless governing equations subject to the selective boundary conditions are solved numerically using the finite difference method. The governing parameters of this study are the Darcy-Rayleigh number, heat source length, cavity inclination angle, heat generation parameter, modified conductivity ratio, and dimensionless time. The developed computational code is validated comprehensively using the grid independency test and numerical and experimental data of other studies. The obtained results reveal that the nonequilibrium effects are very strong at the cold walls and at the center of the cavity. In addition, increasing the inclination angle has the effect of reducing the heat transfer rate.