Numerical solution of unsteady boundary layer flow over a stretching sheet in a porous medium using BVP4C

The movement of fluid within a porous medium plays a pivotal role in various industrial applications including water circulation in geothermal reservoirs, nuclear waste storage, food processing and others. Nonetheless, examining unsteady boundary layer flow in a stretching sheet over a porous medium presents a complex interplay of nonlinear differential equations influenced by multiple external factors. This study also incorporates the effects of velocity and thermal slip to provide deeper insights. By applying similarity transformation, the governing nonlinear partial differential equations were transformed into a system of nonlinear ordinary differential equations. Subsequently, the ordinary differential equations were numerically solved using the BVP4C method within MATLAB software. Numerical results are presented for the dimensionless velocity profile, temperature profile, skin friction coefficients and the local Nusselt number under varying parameter conditions. Following that, the results were validated by comparing the BVP4C method with other established numerical methods ensuring the reliability of the findings. The findings indicate that an increase in the permeability parameter leads to a decreased velocity profile and skin friction coefficient while simultaneously enhancing the temperature profile and the local Nusselt number.