This article investigates the physical interpretation of the magnetic field on the free convection of hyperbolic tangent fluid within a microchannel. The radiating heat through the permeable surface, dissipative heat and the additional heat source experience an important role. The interaction of magnetic dissipation and Darcy-dissipation can be neglected as the flow is supposed to be affected by including a magnetic field and the medium’s permeability. The dimensional form of the designed model is converted to its corresponding non-dimensional form for the use of the similarity variables. Further, these are handled using an approximate analytical technique known as the Adomian decomposition method. The physical behaviour of certain characterizing parameters on the non-Newtonian flow phenomena is exhibited and displayed graphically, and the tabular form is used for the numerical simulation of the rate coefficients.