Impact of mode of application of magnetic field on rate of heat transfer of rarefied gas flows in a microtube

This paper examines theoretically the impact of transverse and radial mode of application of magnetic field on rate of heat transfer of rarefied gas in a micro tube. The momentum and energy governing equations are solved analytically with a uniform wall heat flux (H2 boundary conditions) applied on the heated perimeter of the cross section while the remaining arc length is assumed to be adiabatic. The velocity, temperature and Nusselt number are presented as a function of Knudsen number, azimuth angle and Hartmann number. During the course of numerical and graphical representations, results indicate that the role of magnetic field is to increase rate of heat transfer for both modes of application, while the impact of Knudsen number is to decrease rate of heat transfer for both cases. Furthermore, rate of heat transfer is higher in case of radial magnetic field in comparison with transverse magnetic field for both continuum flow and slip flow regimes.