MHD free convection in a vertical slit micro-channel with super-hydrophobic slip and temperature jump: non-linear Boussinesq approximation approach

Abstract

An exact solution is obtained for natural convection flow of electrically conducting fluid in a vertical slit micro-channel with super-hydrophobic slip and temperature jump using non-linear Boussinesq approximation approach. The inner surface of one of the micro-channel surfaces is structurally changed so that it exhibited super-hydrophobic velocity slip and jump in temperature. A transverse magnetic field is applied to the flow direction. A unified solution is derived for two different physical situations. Case I, represents a physical situation when super-hydrophobic surface is heated and no-slip surface is unheated while case II represents a physical situation when no-slip surface is heated and super-hydrophobic surface is unheated. The velocity slip lowers the Nusselt number in Case I and raises it in Case II while the temperature jump co-efficient does the opposite. Velocity and flow rate are higher in case of non-linear density variation with temperature in comparison to linear density variation with temperature.