Entropy Optimization in Transient Hydromagnetics Laminar Flow Through a Vertical Stream With Emission of Thermal Energy and Temperature‐Dependent Properties Governed by Newtonian Cooling

This study incorporates thermal energy, temperature‐dependent properties, thermal‐dynamic irreversibility in MHD fluid flow embedded in a porous vertical medium driven by Newtonian cooling. The study considers an incompressible, electrically conducting fluid flowing laminarly in a vertical channel bounded by two infinite parallel plates. The governing equations are developed and discretized using Crank‐Nicolson finite difference scheme (CN‐FDM) where the discretized equations are simulated using MATLAB software. The findings reveal that rising magnetic field by 2% lowers both velocity and temperature up to 0.2% with intensified entropy reduction near the walls. Amplifying permeability by 4% intensifies fluid motion while Bejan number falls by approximately 7%, stabilizing unrecovered fluid friction. Escalating the radioactive parameter by 6% improves the temperature profile while lowering Bejan number. Rising pressure gradient deteriorates the Bejan number by approximately 9% caused by stabilized fluid friction across the channel. Moreover, the temperature profile and Bejan number fall by 12% due to an increase in Prandtl number by 5%. Fluid motion deteriorates by 4% while entropy production at the central region of the channel is reduced by 13% with the increase in Eckert number. Escalating heat generation by 8% amplifies the temperature profile by 16% and reduces fluid resistance by 23%, with intensified entropy production near the walls. Fine‐tuning buoyancy forces may lower entropy production by approximately 30%. Velocity and temperature reach a steady state with buoyancy, while time increases, wall shear and heat transfer before stabilization. The findings reveal that variations of these physical quantities have a great influence to coefficient of skin friction and Nusselt number on both walls. These results inform the MHD and thermal‐fluid systems designers to ensure fine‐tuning of magnetic field parameter, Darcy number, Eckert number, internal heat generation, Prandtl number, and buoyance effects that enhance effective thermodynamic in these systems.