Heat generation in Newtonian fluid in the porous cavity with temperature-dependent viscosity

This study describes the intricate interplay of natural convection and heat generation in a Newtonian fluid within a porous square cavity infused with heat-generating and heat-absorbing materials, where viscosity gracefully varies with temperature. A sinusoidal temperature profile adorns the left cavity wall, while the right wall remains cooler, and the upper and lower walls stand as adiabatic boundaries. The fluid flow follows the Darcy model, with governing equations elegantly derived from the fundamental principles of momentum and temperature. These equations are transformed into a dimensionless form, refining analytical clarity and insight. To capture the fluid's delicate motion with precision, a sophisticated numerical approach intertwines the Gauss-Jordan method with the alternating direction implicit (ADI) scheme. The results, brought to life through mesmerizing isotherm and streamline visualizations, alongside a meticulous analysis of Nusselt number variations and skin friction at the cavity walls, paint a compelling picture of the complex heat transfer and fluid dynamics at play.