Present study examines the numerical analysis of MHD flow of Maxwell fluid with thermal radiation and Joule heating by considering the recently developed Cattaneo-Christov heat flux model which explains the time relaxation characteristics for the heat flux. The objective is to analyze the governing parameters such as viscoelastic fluid parameter, Magnetic parameter, Eckert and Prandtl number’s impact on the velocity and temperature profiles through graphs and tables. Suitable similarity transformations have been used to reduce the formulated PDEs into a system of coupled non-linear ODEs. Shooting technique has been invoked for finding the numerical solutions of the dimensionless velocity and temperature profiles. Additionally, the MATLAB built-in routine bvp4c has also been used to verify and strengthen the results obtained by shooting method. From some special cases of the present work, a comparison with the previously published results has been presented.

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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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