MHD natural convection flow in a vertical micro-concentric-annuli in the presence of radial magnetic field: An exact solution

This paper deals with a theoretical investigation of steady fully developed MHD natural convection flow of viscous, incompressible, electrically conducting fluid in micro-concntric-annuli in the presence of radial magnetic field. The velocity slip and temperature jump at the micro-concentric annuli surface are taken into account. Exact solutions are derived for energy and momentum equations under relevant boundary conditions. The solution obtained is graphically represented and the effects of various controlling parameters such as the radius ratio (η), Hartmann number (M), rarefaction parameter (βvKn), and fluid-wall interaction parameter (F) on the flow formation are discussed. The significant result from the study is that as rarefaction parameter (βvKn) increases the velocity slip on the surface of cylinders increases while fluid wall interaction parameter (F) decreases the velocity inside the micro-concntric-annuli. Furthermore, it is found that increase in radius ratio leads to increase in the volume flow rate.