Laminar MHD flow and heat transfer of power-law fluids in square microchannels

The steady fully developed laminar flow and heat transfer of electrically conducting non-Newtonian fluids through square microchannels at the presence of transverse magnetic field are investigated with emphasis on viscous dissipation and joule heating effects. The governing continuity, momentum and energy equations are being discretized using a finite difference approach using Modified Power-Law (MPL) model and have been solved iteratively, through Alternating Direction Implicit (ADI) scheme with successive over-relaxation under the classical boundary conditions of no-slip velocity and uniform constant heat flux for flow and thermal fields. The velocity, temperature profiles, product of friction factor-Reynolds number and Nusselt number are computed for various values of flow index and dimensionless shear rate parameter of modified power-law fluids. Also, the effect of Hartmann number and Brinkman number on velocity, temperature distributions and Nusselt number are discussed. It is shown that the results are in good agreement with the previous studies. (C) 2015 Elsevier Masson SAS. All rights reserved.