Fluid flow and heat transfer characteristics of Williamson fluids flowing in saturated porous media

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Abstract
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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