Numerical analysis of thermal characteristics for micropolar fluid flux close to an isothermal vertical plate inward porous region

The merit of this manuscript is to examine numerically a heated vertical plate with uniform temperature subjected to a steady, viscous, incompressible micro-polar fluid flow that is situated inside a saturated porous medium with permeability and porosity. Similarity variables have been applied to convert coupled of constrained partial differential equations that describe physical problem into coupled of constrained nonlinear ordinary differential equations, which in turn allows for the reliable numerical solution of the problems. Finite difference and shooting methods coupled with Runge-Kutta scheme have been implemented by Matlab function bvp4c to solve equations numerically. The graphical findings showed the impact of emerging dimensionless physical parameters for micro- polar liquid on non-dimensional velocity, temperature, and micro-rotation distributions. The latest findings exhibit a high degree of agreement with the findings from earlier research. Elevating parameter values drive to an increase in the velocity profile values, but a decrease in the temperature distribution values. The benchmarks parameters of this research are modified vortex viscosity and micro-inertia density. The high porosity in the range of 0.7–0.9 is considered the noteworthy limitation of the current study. Furthermore, increasing the material's physical characteristics cause the micro-rotation vorticity profile's curvature to flip.