AbstractIt is apparent that non‐Newtonian nanofluids (especially, Casson and Carreau) find their ubiquitous utilization in diverse industrial processes. The magnetohydrodynamics concept is significantly implemented in the engineering design process. Darcy–Forchheimer's effect characterized by inertia and boundary effects ameliorates the rate of heat transportation outstandingly in association with the flow of nanofluids. Entropy optimization analysis is accentuated as its minimization is the best measure to enhance the efficiency of thermal systems. In view of this, the present article is intended to investigate electromagnetic flow and thermal characteristics of Casson and Carreau nanofluids over the exponential stretched surface. Microrotation facets are entailed. Arrhenius pre‐exponential factor law and Robin's condition are implemented. The nondimensional governing equations are solved by the spectral quasi‐linearization method. The major outcomes of this study are that axial and transverse flow velocities and heat transfer rate get controlled due to strengthening Casson and microinertia density parameters. More thermal stratification augments the rate of heat transportation efficaciously. Amplification of the Weissenberg parameter intensifies the axial and transverse flow velocities and the associated boundary layer widths. Axial and transverse surface viscous drag enervate due to the rise in porosity, inertia, and magnetic parameters. The entropy generation rate is regulated by the varied Reynolds number.