Numerical solution of the partial differential equations that model the steady three‐dimensional flow and heat transfer of Carreau fluid between two stretchable rotatory disks

Abstract

AbstractNon‐Newtonian fluids are significantly better on the heat transfer phenomenon than from Newtonian fluids, so they are helpful in air conditioner and heating and cooling devices. Blood, toothpaste, ketchup, paint, and so on are common non‐Newtonian fluids in our daily lives. Among other non‐Newtonian fluid models, Carreau fluid has gained much acceptance because of its unique features of shear thinning and shear thickening for various power‐law index ranges. Owing to the significance of Carreau fluid, a theoretical analysis has been performed here to investigate the steady three‐dimensional flow of Carreau fluid between two coaxially rotatory and stretching disks. The fluid is electrically conducting, and a uniform magnetic field is applied perpendicularly to the circulating disks. The heat transfer phenomenon is also analyzed in the presence of nonlinear thermal radiation, viscous dissipation, joule heating, and nonuniform heat source/sink subject to convective boundary conditions. With specific similarity transformation, the leading partial differential equations are diminished to ordinary differential equations and then tackled numerically through the Keller–Box scheme. It is concluded that with the increase in the disks rotation rate, the fluid velocities enhances whereas plummets for the magnetic parameter and predicts two diverse behaviors for Weissenberg number. The temperature escalates for the magnetic parameter, radiation parameter, temperature ratio parameter, Eckert number, heat source/sink parameters, and lower disk Biot number, but the temperature decays for rotation parameter, Prandtl number, and upper disk Biot number.