Mixed Convection Flow Behaviour in Existence of Lorentz Forces in a Vertical Micro Circular Duct having Time Periodic Boundary Conditions: Steady Periodic Regime

Abstract

The purpose of this research is to study mixed convection flow behaviour in existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface. Effects of velocity slip and temperature jump are also taken into consideration. The research analysis is carried out by considering fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations with arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically. Numerical procedures are examined for various active parameters namely; fluid wall interaction, rarefaction, Hartmann number, Prandtl number, the dimensionless frequency. The results of the research revealed that, magnetic field plays a damping impact in flow and results in decreases in fluid velocity for both air and water. Further, increases the rarefaction parameter and fluid-wall interaction parameter reduces the oscillation amplitude of the dimensionless velocity.