Numerical investigation of heat and mass transfer of variable viscosity Casson nanofluid flow through a microchannel filled with a porous medium

Abstract

Thermal behaviours and hydrodynamics of non-Newtonian nanofluids flow through permeable microchannels have large scale utilizations in industries, engineering and bio-medicals. Therefore, this paper presents the numerical investigation of heat and mass transfer of variable viscosity Casson nanofluid flow through a porous medium microchannel with the Cattaneo-Christov heat flux theory. The highly nonlinear PDEs corresponding to the continuity, momentum, energy and concentration equations are formulated and solved numerically via the second order implicit finite difference scheme known as the Keller-Box method. Accordingly, the numerical simulations reveal that variable viscosity parameter, thermal Grashof number, solutal Grashof number, thermophoresis parameter, Schmidt number and Casson fluid parameter show increasing effects on both velocity and temperature of the nanofluid. Furthermore, the temperature profile escalates with increasing values of the Eckert number and the thermal relaxation time parameter. Thus, the Cattaneo-Christov heat flux model is beneficial in warming the transport system of microfluidics when compared to that of the classical Fourier heat conduction law. The temperature profile however, indicates a retarding behavior with increasing values of the Brownian motion parameter, Prandtl number and porous medium parameters namely Forchheimer number and porous medium shape parameter and hence, the porous medium quite effectively controls the nanofluid temperature distribution which plays substantial roles in cooling the transport system of microfluidics. Moreover, the concentration profile shows an increasing pattern with escalating values of the Prandtl number, Schmidt number and thermophoresis parameter but it demonstrates a decreasing trend with the Casson fluid, variable viscosity, thermal relaxation time and solutal relaxation time parameters. It is also observed that coefficient of the skin friction increases with increasing values of the pressure gradient parameter, Eckert number, Forchheimer number and injection/suction Reynolds number. Besides, the heat transfer rate at both walls of the microchannel enhances with rising values of the Eckert number, variable viscosity, parameter and injection/suction Reynolds number. The Casson fluid and thermal relaxation time parameters reveal opposite scenarios on the heat transfer rate at the left and right walls of the microchannel. In addition, the mass transfer rate at both walls of the microchannel shows an increasing pattern as the Eckert number, variable viscosity parameter, Schmidt number and suction/injection Reynolds number increase.