The onset of Jeffreys fluid porous convection with throughflow in the presence of a heat source and electric field

The investigation delves into the examination of Jeffreys fluid flow within a porous medium, incorporating a temperature-dependent heat source and throughflow, while also taking into account the presence of an external electric field. The eigenfunction, also known as the critical Rayleigh number, is obtained to determine the initiation of convection by employing Galerkin processes during the linear stability analysis. Subsequently, the findings are scrutinized by means of graphical illustrations to explore the impacts of various factors, including the Jeffreys parameter, heat source, throughflow, and electric field. Upon careful examination of the outcomes, it becomes evident that specific parameters, such as the Jeffreys parameter, heat source, and throughflow parameters, exert an influence in stabilizing the system under consideration. The investigation evidently points toward an observation that an augmentation in the electric field parameter results in an accelerated onset of convection. This observation implies that the external electric field assumes a role as a destabilizing element within the system, thereby intensifying the convective tendencies exhibited within the medium. The results demonstrated that elevated throughflow characteristics played a significant role in the postponement of convection onset, while a rise in the heat source parameter dependent on temperature was found to enhance the overall stability of the system. Additionally, it was observed that the downward throughflow exhibited a greater stabilizing influence when juxtaposed with the upward throughflow, particularly in scenarios involving the Jeffreys term and electric fields. The implications of these findings suggest a complex interplay between throughflow parameters, temperature-dependent heat sources, and external forces, highlighting the intricate dynamics governing convection initiation and system stability in the studied environment.