Unsteady heat transfer enhancement in Williamson fluid in Darcy-Forchheimer porous medium under non-Fourier condition of heat flux

Non-Newtonian constitutive equations and models for hybrid particles are simultaneously coupled with conservation laws. The energy equation is derived under non-Fourier heat flux condition. The resulting mathematical models are numerically solved by the finite element method (FEM). The modeled problems are convertible into their special case published in the literature. The computed results are ensured to be meshed-free and convergent. The numerical results are made convergent against related rheological parameters and numerical outcomes are visualized. The results based on visualization and numerical outcomes are discussed. The velocity of Williamson fluid decreases as a function of Williamson parameter. It is also observed that the velocity of mono nano - Williamson fluid decreases faster than the hybrid nano - Williamson fluid. Darcy and Forchheimer porous media offer resistance to the flow and therefore, play a significant role in decreasing the thickness of the momentum boundary layer. Heat generation in the fluid is utilized in increasing the kinetic energy of the fluid particles. Therefore, the internal energy of the fluid particles is increased. Hence, the temperature of fluid particles increases. Numerical results have demonstrated that heat generation in hybrid nano-Williamson fluid is greater than the heat generated by the particles of mono nano - Williamson fluid. The wall shear stress (for both types of nanofluids) increases when We and F-r are increased. The wall shear stress for the case of hybrid nanofluid is greater than the wall shear stress for mono nanofluid. The rate of heat transfer in mono nanofluid is less than the rate of heat transfer in hybrid nanofluid.

Automated summary

The study focuses on coupling non-Newtonian constitutive equations and hybrid particle models with conservation laws, deriving the energy equation under non-Fourier heat flux condition. Numerical solutions are obtained using the finite element method, ensuring mesh-free and convergent results that can be visualized. The results show variations in wall shear stress and heat transfer rate under different fluid and flow conditions.