The present investigation reveals the non-Newtonian flow characteristics for the Williamson nanofluid through a parallel channel due to the conjunction of thermal buoyancy. As a good conductor of heat, the metal like Copper is treated as the nanoparticles submerged into the base fluids water and kerosene to perform the flow phenomena within the channel embedding with the porous medium. For the involvement of the applied magnetic field and permeability it is not wise to neglect the impact of dissipative heat energy. Therefore, both the Joule and the Darcy dissipations are also considered those are affecting the thermal properties. The model is developed considering the Mintsa model thermophysical properties of conductivity and the Gharesim model viscosity for the enhancement of heat transport properties. In various industrial as well as engineering applications nanofluids are used as a best coolant. The use of suitable similarity variables and stream function helps to transform the governing nonlinear differential equations into nonlinear ordinary. Further, an approximate analytical approach such as Adomian Decomposition Method is used to handle those transformed equations. The current outcomes obtained from the behavior of various flow characteristics are presented via graphs and table to validate the results. The observation shows that with an augmentation in the particle concentration, fluid velocity retards however the retardation in case of water-based nanofluid overrides the case of kerosene-based nanofluid. Further, particle concentration enriches the nanofluid temperature greatly in comparison to pure fluid.
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