Jeffrey fluid flow in the presence of magnetic field through porous medium in tubes of small diameters is studied. It is assumed that the core region consists of a Jeffrey fluid and the peripheral region of a Newtonian fluid. Making the assumptions as in the work of Chaturani and Upadhya, the linearised equations of motion have been solved and analytical solution has been obtained. The influence of various pertinent parameters on the flow characteristics such as effective viscosity, core hematocrit, and mean hematocrit has been studied and discussed through graphs. It is found that the effective viscosity and mean hematocrit decrease with Jeffrey parameter and Darcy number but increase with tube hematocrit and tube radius. Also, the core hematocrit decreases with Jeffrey parameter, Darcy number, tube hematocrit, and tube radius. Further, it is noticed that the flow exhibits the anomalous Fahraeus-Lindquist effect.
In this paper, the effects of porous medium on a two-fluid model for the flow of Jeffrey fluid in tubes of small diameters are studied. It is assumed that the core region consists of Jeffrey fluid and Newtonian fluid in the peripheral region. The analytical solutions for velocity, flow flux, effective viscosity, core hematocrit and mean hematocrit have been derived and the effects of various relevant parameters on these flow variables have been studied. It is noticed that the flow exhibits the anomalous Fahraeus-Lindqvist effect.
A two-fluid model of Herschel-Bulkley fluid flow through tubes of small diameters and slip at the wall is studied. It is assumed that the core region consists of Herschel-Bulkley fluid and Newtonian fluid in the peripheral region. Following the analysis of Chaturani and Upadhya, the equations of motion have been linearized and analytical solution for velocity, flow flux, effective viscosity, core hematocrit and mean hematocrit has been obtained. The expressions for all these flow relevant quantities have been numerically computed by using Mathematica software and the effects of various relevant parameters on these flow variables have been studied. It is found that effective viscosity, core hematocrit and mean hematocrit of Newtonian fluid are less than those for Bingham fluid, power-law fluid and Herschel-Bulkley fluid. Effective viscosity increases with the yield stress, power-law index, slip and tube hematocrit but decreases with Darcy number. It is observed that the effective viscosity and mean hematocrit increase with tube radius but the core hematocrit decreases with tube radius. Further, it is noticed that the flow exhibits the anomalous Fahraeus-Lindqvist effect. ª 2015 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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