Heat transfer through a higher grade Forchheimer porous CuO–H2O-nano-medium confined between non-isothermal moving plates

Abstract

In this study, the aim is to analyze numerically heat transfer through a higher grade Forchheimer porous CuO–H2O-nano-medium in an unsteady magneto-hydrodynamic (MHD) porous flow. The nano-medium is confined between two non-isothermal moving infinite parallel plates. The flow governing equations are developed through variational calculus approach and are resulted in partial differential equations. The temperature of both the plates are taken to be variable. The governing flow PDEs along with the prescribed boundary conditions are solved using finite difference approach for time discretization and finite element approach for discretizing the spatial coordinate. The algorithm used is described here in detail for the numerical simulations and calculations of results. The proposed algorithm is implemented through MATLAB and simulations are performed for parameters of interest which includes: Nusselt number, skin friction coefficients, Forchheimer constant, volume fraction, Prandtl number, Grashhoff number, Hartmann number, and convection and porosity parameters. Effective implementation of the proposed algorithm is demonstrated through plots of time profiles of non-dimensionalized thermodynamic velocity and temperature against these parameters. It is observed that the larger the porosity of the nanomedium leads to the larger skin friction at both the plates. The plate's temperature gets increased with the increase in the Forchhiemer number. However, the hydrodynamic velocities get smaller as the porosity gets elevated. Forchheimer constant and skin friction coefficients are related with direct proportionality. Whereas the skin friction coefficient is observed behaving monotone in relation to the Hartman constant. The Nusselt number at both the plates get increase in its value as the nanoparticles concentration increases. By increasing the velocity ratio between the two moving plates shows opposite trend. However, the Nusselt number decreases if the porosity of the nano-fluidic medium is increased. It is pertinent to mention that the present modeling approach can be used to analyze the Forchheimer medium flows involving catalytic converters and gas turbine dynamics.