The major objective of this work is to investigate the magnetic effect on heat-fluid and entropy generation interactions in a porous medium for a laminar, incompressible, non-Dracy model flow in an inclined channel. The flow field considered is composed of porous and clear viscous layers. The constant magnetic force is assumed to be acting parallel to the y-axis perpendicular to the walls. The governing equations related to flow and thermal fields, which are coupled and nonlinear, are solved for both clear fluid and porous regions by implementing the semi numerical-analytical techniques differential transform method (DTM) and generalized differential quadrature method (GDQM). While keeping the channel walls at different constant temperatures (isothermal walls), the influence of the applied magnetic field on velocity, temperature, and entropy generation are investigated and presented graphically with the corresponding physical interpretations. Additionally, the effect of dimensionless parameters such as the Hartmann number (Ha), formation factor (F), porous parameter (sigma), Brinkman number (Br), and the angle of inclination (phi) on velocity and temperature fields are examined. The entropy generation (N-s) number for the physical system is derived and plotted using velocity and temperature profiles and dimensionless quantities. One of the main advantages of this study compared to similar studies is to give a straightforward open form solution by using DTM and GDQM. By applying these techniques it is possible to obtain a tractable and easily applicable recurative form of nonlinear field equations. In many similar studies it is said that the equations have been solved; however, neither solution procedure provides neither accuracy nor, even more important than these, clarity of applicability cases and limits of using the technique to the reader. In this work, these are presented in a simple way.