Effect of viscous dissipative fluid in a slit micro-channel with heated super-hydrophobic surface

Abstract

The analytical solution of heat transfer and hydro magnetic flow for an incompressible, electrically-conducting, and viscous dissipative fluid traveling vertically through an isothermally heated parallel plate in a slit micro-channel is performed. One channel surface was super-hydrophobic slip and temperature jump, whereas the other did not. This study also examined the effects of super-hydrophobic slip and a temperature jump on characteristic flow of magneto-hydrodynamics (MHD) free convection flow with viscous dissipative fluid. The perturbation technique was used to solve the coupled nonlinear and coupled equations analytically. With the aid of illustrative graphs, the results were presented, and the effects of the relevant controlling parameters namely Brinkman number, magnetic field, velocity slip condition and temperature jump effects were analysed for temperature, velocity, skin friction and Nusselt number distributions when either wall is heated by constant wall temperature. The result demonstrated that the activities of Brinkman number, Br, substantially increase fluid velocity, whereas growing levels of magnetic field effect was seen to slow down the flow movement. In addition, the fluid velocity is higher for greater values of temperature jump and velocity slip effects respectively. Furthermore, this research can prove very useful for designers in improving the performances of mechanical systems when viscous dissipation is involved, as well as heat transfer in micro-channels, as it is in combustion.