Mixed convection with heating effects through a vertical pipe in the presence of magnetic field

This manuscript addresses the impact of magnetic field in the mixed convective flow through a vertical pipe in a porous medium along with heat source effect. We have used the non-Darcy-Brinkman-Forchheimer (NDBF) extended model to describe the flow in porous medium. The solutions for the coupled differential equations have been obtained using the Chebyshev spectral-collocation approach. It is demonstrated that under the limiting conditions the present numerical results agree well with the existing numerical data. The primary aim of this study is to investigate the influence of multiple parameters, including heat source effect, magnetic field, Forchheimer number and Darcy number on both velocity and temperature profiles. Key findings show that increasing the magnetic field strength results in a reduced fluid velocity profile up to a certain value. After this point, the velocity profile is nearly flat in the domain, but an enhanced temperature profile is observed within the pipe. Furthermore, the maximum temperature increases as the heat source intensity increases. Additionally, higher values of the heat source lead to a point of inflection and flow separation in the velocity profile. The velocity profile becomes smooth as well as flat when elevated drag force values are exerted in the medium.