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The effect of Cattaneo-Christov heat flux model for the hydro-magnetic mixed convective flow of a non-Newtonian fluid is presented. The flow over a wall having variable thickness is anticipated under the influence of transverse magnetic field and internal heat generation/absorption effects. Mathematical formulation has been performed by making use of the suitable transformations. Convergence analysis has been performed and the optimal values are computed by employing optimal homotopy analysis method. The effects of physical parameters are elaborated in depth via graphical and numerical illustrations. Keywords: Cattaneo-Christov heat flux model, OHAM analysis, Mixed convection, Internal heat generation/absorption