This study reports the flow of Williamson fluid in a microchannel, considering the effect of thermal radiation, heat source, slip regime, and convective boundary. The physical phenomenon is demonstrated by employing the Williamson model. The mathematical expressions are made dimensionless by using nondimensional quantities. The numerical approach called Runge–Kutta–Fehlberg scheme is hired to get the solution. The upshots of the pertinent flow parameter on physical features are visualized through graphs. It is established that the augmentation of Nusselt number has been achieved by increasing Weissenberg number and Reynolds number. In addition to this, it is emphasized that the reduction in the wall velocity gradient is obtained for a higher Weissenberg number.

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The current examination delves into the Casson nanofluid flow in the vertical microchannel. The model employed in this investigation is Buongiorno model which emphasizes the light on Brownian motion and thermophoresis effects occurring during the fluid flow. The microchannel walls are constructed in such a way so that they facilitate the suction and injection of the fluid simultaneously. Porous media is incorporated using Darcy-Forchheimer model. Involving these effects governing equations are modeled which is solved using Runge-Kutta Fehlberg 4 th -5 th order method. Entropy generation and Bejan number are also obtained for the concerned flow to record irreversibilities in the microchannel. The findings of this examination depict that rise in Casson parameter augments the flow velocity but causes depletion in Bejan number. On packing the microchannel with high porosity, the velocity magnifies. Both Brownian motion and thermophoresis parameter magnifies the temperature.

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