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The numerical solutions of the upper‐convected Maxwell (UCM) nanofluid flow under the magnetic field effects over an inclined stretching sheet has been worked out. This model has the tendency to elaborate on the characteristics of “relaxation time” for the fluid flow. Special consideration has been given to the impact of nonlinear velocity slip, thermal radiation and heat generation. To study the heat transfer, the modified Fourier and Fick's laws are incorporated in the modeling process. The mass transfer phenomenon is investigated under the effects of chemical reaction, Brownian motion and thermophoresis. With the aid of the similarity transformations, the governing equations in the ordinary differential form are determined and then solved through the MATLAB's package “bvp4c” numerically. This study also brings into the spotlight such crucial physical parameters, which are inevitable for describing the flow and heat transfer behavior. This has been done through graphs and tables with as much precision and exactitude as is possible. The ascending values of the magnetic parameter, the Maxwell parameter and the angle of the inclined stretching sheet cause decay in the dimensionless velocity while an assisting behavior of the thermal and concentration buoyancy parameters is noticed.

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Background: In this article mixed convection boundary layer flow of MHD fluid on permeable stretching surface is investigated under the effects of velocity and thermal slip. The physical unsteady problem is examined by considering thermal radiation effects on momentum and thermal boundary-layer flow. Different from available literature, in the present study we consider mix convective flow, thermal radiation, transverse applied magnetic field, velocity, and thermal slip. Methodology: The transform non-linear system of differential equation is tackled numerically by the aid of finite difference scheme named as Keller-Box. Stable solution is correct up to six decimal places and special cases overlaps with the existing results in literature validating the present analysis. Conclusion: It is concluded that mixed convection leads to accelerate fluid-flow and reduce temperature profile. Injection contributes in rising magnitude of velocity and temperature when compared with suction effects. Velocity and thermal slip parameter influence in lowering fluid-flow while temperature profile decrease for velocity slip parameter and opposite trend is witness corresponding to thermal slip parameter. Both velocity and temperature are increasing function of thermal radiation. In addition, the skin friction coefficient and the local Nusselt number are tabulated and analyzed. Novelty: Present study is concerned with fluid-flow applications in plastic films, polymer extrusion, glass fiber, metallurgical processes, and metal spinning.