Forced convection of Williamson fluid flow in porous media under constant surface heat flux conditions is investigated numerically. A model of Darcy–Forchheimer–Brinkman is used and the corresponding governing equations are expressed in dimensionless forms and solved numerically using bvp4c with MATLAB package. Boundary layer velocity, shear stress, and temperature profiles, in addition to the local Nusselt number parameter over a horizontal plate, are found. The effects of the Forchheimer parameter, Nusselt number, Darcy parameter, porous inertia, and Williamson parameter on the velocity profiles, temperature profiles, coefficient of friction, and coefficient of heat transfer are investigated. The results showed that as the Darcy parameter increases, boundary layer velocity and shear stress increase, while the temperature and Nusselt number decrease. In addition, as Williamson's parameter increases, velocity within the boundary layer, shear stress, and Nusselt number decrease while the temperature profile increases. Also, with larger values of the Forchheimer parameter, the velocity of the boundary layer, shear stress, temperature, and Nusselt number increase. Furthermore, the Nusselt number and the coefficient of friction are obtained on the surface of the horizontal plate.

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This study was conducted to mathematically evaluate the impact of forced convection of viscous dissipation on a porous media filled with Williamson fluid and exposed to fixed surface heat flux. The technique of Darcy_Forchheimer_Brinkman was employed, then the non-dimensional equations were solved numerically over a flat plate by using bvp4c through the MATLAB package. Different parameters were examined including the profiles of velocity, temperature and shear_stress in addition to Nusselt Number. Furthermore, the study evaluated the effects of several essential parameters, including Forchheimer, Darcy, porous media, Williamson, and viscous dissipation, on the temperature and velocity profiles, heat transfer and friction coefficients. The numerical solution results showed that, under high Forchheimer_parameter values, all, shear_stress, Nusselt_number parameter and temperature showed an increase in their values. Also, as Williamson_parameter increased, the shear_stress and boundary layer velocity were improved, while a decrease in Nusselt_number caused an increased in values of temperature profile. Finally, the boundary layer of velocity and shear_stress showed an increase in their values when Darcy parameter increased. On the other hand, a decrease in the temperature profile and Nusselt_number were observed.

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