Effect of spatio-temporal internal heat source on the thermal convection in a porous layer using a thermal non-equilibrium model

Convection induced by internal heating and adverse temperature gradient in a porous medium has various real-world applications, such as solar energy collectors, solar-based drying and cooking. Thus, it is crucial to analyze such flows to understand the physics behind the flow and analyze heat transfer through the system. We assume that volumetric heating occurs within the fluid phase due to radiation exposure from an overhead source or a stratified arrangement of heat-generating materials. For modeling convenience, we further assume that internal heating diminishes exponentially with the depth of the porous layer and fluctuates sinusoidally over time, affecting the mean value. Solid and fluid phases of the porous layer are considered out of thermal equilibrium. Floquet theory is employed to determine the linear instability bound of the system. By analyzing the eigenvalue spectrum, we identify the critical Rayleigh number that marks the onset of instability. Subsequently, a weakly nonlinear analysis is carried out using a truncated Fourier series expansion of the physical quantities to analyze the heat transfer within the system. The effect of governing nondimensional parameters on the system’s stability and heat transport is graphically illustrated and thoroughly discussed. The effect of modulation amplitude and volumetric heat is to enhance heat transfer, whereas depth coefficient and modulation frequency suppress heat transfer.