A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of viscous dissipation and stress work on MHD forced convection flow adjacent to a non-isothermal wedge. The velocity and temperature distributions inside the boundary layer are considered as simple polynomial functions and the variational principle is formulated. The Euler-Lagrange equations are reduced to simple polynomial equations in terms of boundary layer thicknesses. The values of skin friction coefficient and the Nusselt number are presented for various values of wedge angle parameter $m$, wall temperature exponent $2m$, magnetic parameter $\xi$, Prandtl number (Pr) and Eckert number (Ec). The present results are compared with known available results and the comparison is found to be satisfactory and the present study establishes the fact that the accuracy is remarkable.