The proposed model offers a wide range of practical use, including nuclear energy plants, oil recovery, geothermal extraction, solar systems, dispersing fog, electrical power generation, hydro-metallurgical industry and advancements in medical sciences. The article explores the impact of radiative-convective heat transfer(HT) and magneto-hydrodynamic flow of a viscous fluid in a vertical porous channel with varying thermal conductivity and viscosity. The developing mathematical model analyses fluid flow and temperature distribution profiles. The nonlinear coupled differential equations (DEs) have been solved analytically and numerically. The numerical solution has been obtained from the Chebyshev spectral collocation method and a significant agreement is found with the analytical solution in the special case. The obtained solution offers a graphical representation of velocity, and temperature profiles have been found with respect to involving various parameters. The authors also study the behaviour of fluid flow near the surface and heat transfer from high to low temperatures at the walls. Correlations have been established for skin friction and Nusselt number in relation to involving parameters. The study reveals that the velocity profile is more pronounced when thermal conductivity changes compared to variable viscosity. The purpose of the study is to enhance the efficiency of oil recovery, geothermal extraction, etc., models.
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