The impact of internal heating on natural convection in a rectangular porous container

Abstract

This research investigates the flow of two-dimensional free convection within a porous rectangular container. In this configuration, internal heating is applied constantly throughout the layer. Linear stability analysis is accomplished numerically using the finite difference method, while weakly nonlinear analysis is carried out with a truncated Fourier series. The investigation of the impact of the height and internal heat parameters on diverse profiles of Rayleigh number, velocity, temperature, and Nusselt number are explored across a range of values for the system instability at the onset of convection, showing the novelty of our solutions. The results have been presented in terms of the Rayleigh number for different parameters, streamlines, isotherms, and Nusselt numbers for both steady and unsteady cases. The significant effect of the internal heat parameter is observed within the range [−H2H2] and is dependent on [H], and the Nusselt number for steady case is -0.20814 for ξ=0.1, -0.058134 for ξ=0.15, and 0.09186 for ξ=0.2. As the internal heat parameter and height increase, the Rayleigh number decreases, suggesting a destabilizing trend within the system and an earlier onset of convection. The Nusselt number in the unsteady state converges to a constant value over time, aligning closely with the value observed in the steady case.