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This study examines the magnetic effect on Darcy Brinkman convection in a Bidispersive horizontal porous layer, considering the importance of convective motions of electrically conducting porous media accompanying a magnetic field in real-life applications such as geophysics, metallurgical field and solidification structures. In order to conduct a thorough study, the boundaries are classified as free-free, rigid-free, and rigid-rigid. The fluid motion is described using the Brinkman-Darcy equation with a single temperature in the macropores and micropores. The eigenvalue problem is solved analytically for the free-free case by employing linear stability theory. A non-linear analysis using the energy method is undertaken to prove that linear instability and global non-linear stability thresholds are the same. The eigenvalue problem for rigid-free and rigid-rigid boundaries is numerically solved with the bvp4c routine in MATLAB R2020 with the Rayleigh number as the eigenvalue. It is found that the Hartmann number M 2 , Darcy number Da, permeability ratio κ r , and momentum transfer coefficient γ stabilize the system. Rigid-rigid boundaries are found to be the most stable ones, followed by rigid-free and free-free, which are the least stable boundaries. [ABSTRACT FROM AUTHOR]

This article investigates the visualizations of heatlines in a natural convection magnetohydrodynamic flow from a vertical cylinder via heat function concept. Fluid is electrically conducting in the existence of an applied magnetic field. The constitutive equations of time-dependent, coupled and highly nonlinear Jeffrey fluid model are evaluated mathematically by utilizing well-organized unconditionally stable finite-difference Crank–Nicolson method. Simulated results are given for several values of Deborah number and Hartmann number to present interesting aspects of the solution of the flow variables, friction factor and heat transfer rate. Results specify that required time to achieve time-independent state rapidly rises with the boosting values of Hartmann number. Boundary-layer flow visualization has been made using heatlines, isotherms and streamlines to perceive the understanding of heat and fluid flow. It is noticed that heat function value reduces for augmenting Hartmann number and also for all smaller physical parameter values and these heatlines become closer to the hot wall. It is also remarked that the hydromagnetic flow-field profiles concerning the Newtonian fluid show a different pattern from that of non-Newtonian Jeffrey fluid. [ABSTRACT FROM AUTHOR]