Evaluation of Nusselt Number for a Flow in a Parallel Plates Using Magnetohydrodynamics Second-Order Slip Model

Abstract

Abstract This study is the examination of magnetohydrodinamics (MHD) flow and heat transfer between microparallel plates with constant wall heat flux using two different boundary condition coefficients, widely known in the literature, in a second-order slip flow and temperature jump boundary condition model. The stream of incompressible viscous liquid between rigid microtwin plates with electrical conductivity was assumed to be steady, laminar, hydrodynamically and thermally fully improved. The effects of dilution, viscous dissipation, and axial transmission, which are significant at the microscale, are also contained in the analysis. Momentum and energy equations are solved analytically under second-order slip velocity and temperature jump boundary conditions. Closed type answers for the temperature field and the fully developed Nusselt number are derived as a function of the magnetic parameter (MHD), Knudsen number and modified Brinkman number. Particular attention has been paid to the effects of the magnetic field on the second-order slip flow conditions. The use of the second-order boundary condition coefficients proposed in the study varies according to the proposed boundary conditions and tends to increase and decrease the heat transfer. Otherwise, MHD increases the heat transfer for both boundary conditions.