This study examines the effects of super-hydrophobicity, thermal radiation, and porous media on buoyancy-induced flow of an electrically conducting fluid across a vertical microchannel with alternately heated plates. The theory of simultaneous equations has been employed to determine the closed-form solutions of the stated ordinary differential equations. The computational research revealed that in both cases—Case I (heating the super-hydrophobic surface, or SHS) and Case II (heating the no-slip surface, or NSS)—the heat gradient and fluid motion are significantly enhanced as the values of thermal radiation and Darcy porous parameters increase. However, because of the heat flow channel, increasing the thermal radiation impact decreased the fluid temperature at the NSS. On the other hand, when the magnetic field factor increases, the velocity decreases due to the Lorentz force dragging the molecules, triggering fluid retardation. Our comparison of current research to previously published literature for the limiting scenario reveals a superb relationship that confirms the precision and validity of this work.