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This article presents, for the first time, a comparative analysis of two different solution methodologies for the numerical investigation of flow and thermal behavior of Casson fluid through a channel having linearly extending lower wall while the upper wall is kept at rest. MHD Casson fluid boundary layer flow is supposed to be steady, laminar, viscous, and incompressible. We have taken into account the mixed convection effects, whereas the usual no slip condition has been imposed on both walls. The Navier–Stokes equations for the proposed model have been converted into nonlinear and coupled system of ordinary differential equations (ODEs) by employing similarity variables, which are then solved by using the differential transform method (DTM) and the quasi‐linearization method (QLM). We note that the quasi‐linearization approach is better than the DTM, as the latter becomes inappropriate for the increasing values of the parameters involved. Moreover, the variation of the different parameters for velocity and temperature profiles has been analyzed graphically. [ABSTRACT FROM AUTHOR]