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

• MHD flow and heat transfer of non-Newtonian fluids through a microchannel are studied.
• Effects of viscous dissipation and joule heating on Nusselt number are investigated.
• The modified power-law model is used to describe the non-Newtonian fluids.
• With the increase of Ha, Nu increases for low value of Br and decreases for high values of Br.
• Increasing Br leads to reduction in Nu for all values of Ha.

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.