Effects of Viscosity and Magnetic Field on a Non-Isothermal Cylindrical Channel Flow
Roseline Ize. Ndu *
Department of Mathematics, Rivers State University, Port Harcourt, Nigeria.
Chinedu Nwaigwe
Department of Mathematics, Rivers State University, Port Harcourt, Nigeria.
Amos Emeka
Department of Mathematics, Rivers State University, Port Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study examines the effect of viscosity and magnetic field on a non-isothermal cylindrical channel flow. This work considered a model of convective-thermal-diffusion with constant viscosity and magnetic field. The governing model equations are nondimensionalized using the dimensionless quantities and then solved analytically using power series method of Frobenius type so as to tackle the singularity in the model equations. Furthermore, the analytical solutions are displayed via graphs to show the effects of the flow parameters on the flow velocity, temperature and concentration profiles. The graphical results show that increase in viscosity, magnetic field and solutal Grashof number parameters retard the fluid flow. While increase in thermal Grashof number enhances the flow velocity. Thermal conductivity and solute injection parameters increase the fluid temperature and concentration respectively while the cooling and diffusive parameters decrease the fluid temperature and concentration respectively. Further studies can be carried out for a multi-directional flow as against the unidirectional flow and in a vertical channel in place of horizontal channel as studied in this paper.
Keywords: Cylindrical channel, thermal Grashof, Solutal Grashof, fluid velocity, viscosity, magnetic field, temperature and concentration