Heat Transfer and Natural Convection in an Internally Heated Porous Box Container With Variable Gravity Field

The study focuses on convection within a fluid-saturated porous medium, which is internally heated, with a gravitational field that changes with height across the enclosure. Four distinct configurations of gravity variation and constant volumetric internal heating are selected, and their impact on the onset of convection is analyzed across four different models. The primary aim is to examine the influence of key parameters such as the Rayleigh numbers 60, 70, 80, 100, 105, and 110, with the gravity parameter ranging from 0 to 0.06 and the internal heat parameter between 0.1 and 0.4, on the dimensionless time concerning temperature and heat transfer. The formulated differential equation is numerically solved using the Galerkin method. MATLAB's built-in solver, ode45, is used for numerical simulations to evaluate the heat transfer rate and generate two- and three-dimensional isotherms for multidimensional models under varying gravitational fields, showing the novelty of our solutions. These key parameters elevate the Nusselt number, signaling enhanced heat transfer and facilitating convection by destabilizing the system. The oscillations needed for the Nusselt number to stabilize are fewer in the vertical enclosure than in other configurations across varying gravity parameters, internal heat parameters, and Rayleigh numbers. This analysis is relevant to heat transfer and material processing applications.