The effect of a magnetic source of variable strength was studied on ferro-nanofluid incorporating nanoparticles of cobalt ferrite (CoFe2O4) and water as a base fluid. Group method was used to remodel the mathematical model to a system of ordinary differential equations. The recent study was motivated by inspecting the effect of four parameters including nano-particles volume fraction (𝜙), Prandtl number (𝑃𝑟), magnetic field strength of the source ( 𝛾), and temperature difference ratio with respect to ambient temperature ( 𝛾𝑇). The results showed that the nanofluid velocity and shear stress increased as long as 𝛾 and 𝛾𝑇 increase. On the other hand, both are inversely related to the increment in Pr and 𝜙. Temperature distribution inside the boundary layer was noticed to increase due to the increment in Pr values and decrease due to the increment 𝜙 ratios. Contrarily, the heat flux throughout the boundary layer decreased and increased due to increasing Pr 𝜙, respectively.