Magnetogasdynamic flow and heat transfer in a microchannel with isothermally heated walls

The presence of ionized gas flow in an applied electric and magnetic field could result in an electromagnetic driving force and a joule heating. It is desirable to understand the causes of the two mechanisms and their roles on ionized gas microflow and heat transfer. In this study, a mathematical model is developed of the pressure-driven gas flow through a long isothermally heated horizontal planar microchannel under an applied electric and magnetic field. The fully developed solutions of the flow and thermal field distributions as well as the corresponding characteristics are derived analytically and presented in terms of dimensionless parameters. It is found that an electromagnetic driving force can be produced by a combined non-zero electric field and negative magnetic field and results in an additional velocity slip and an additional flow drag. Also, a joule heating can be produced only by an electric field and enhanced by a positive magnetic field and results in an additional temperature jump and an additional heat transfer. The effects of electromagnetic driving force and joule heating on velocity slip and temperature jump can be magnified by increasing the Knudsen number; however, the force and heating effects on flow drag and heat transfer rate are found to be diminished.