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In this analysis, the Jeffrey fluid flow over boundary layer magnetohydrodynamic exponentially enlarged sheet with thermally stratified medium in existence of suction is studied. The equations of governing flow together with boundary conditions are renewed into a non-similar arrangement with appropriate similarity transformations and are computed with the aid of MATLAB solver bvp4c. The things of several constraints on velocity and temperature are studied graphically. The computational outcomes of skin-friction and the heat transfer rate are studied pictorially. This article describes that the rate of heat transfer on the surface rises with effect of thermal stratification. The fluid velocity diminishes through growing in magnetic and Jeffrey parameters.