Two-phase flow of couple stress fluid thermally effected slip boundary conditions: Numerical analysis with variable liquids properties

The study of multiphase flows has earned much attention from researchers due to its numerous applications in mechanics and industry such as sewage management, synthetic fabrication, electricity generation, and medication processes. In the present work, we examined the Poiseuille flow of a couple stress fluid between parallel plates in presence of velocity and temperature slip boundary conditions. The effects of thermal conductivity and thermal radiations, variable viscosity, and non-uniform magnetic field on velocity and temperature fields in the existence of hafnium nanoparticles are also investigated. The temperature-dependent viscosity model, namely, Vogel’s model is utilized. The non-linear system of equations is solved numerically by using the shooting technique due to its fast convergence and prosperity to initial approximation. It is examined that the velocity slip parameter speeds up the flow rate of fluid but decelerated the temperature field while the temperature slip parameter upsurges the temperature of the fluid. It is also investigated that the concentration of nanoparticles enhanced both the velocity and temperature of the fluid. Further, the comparison of Newtonian and non-Newtonian (Couple stress fluid) is expressed with the help of graphs. To check the validation of results, a comparison with previous literature is also presented.