Jeffrey Fluid Flow through Porous Medium in the Presence of Magnetic Field in Narrow Tubes

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. 1. Introduction Microcirculation is a part of human circulatory system, which consists of a complex network of blood vessels, whose diameter ranges from approximately 20？μm (microns) to 500？μm. There are several types of vessels in microcirculation such as arterioles, capillaries, and venules. Its main functions are to supply oxygen and nutrients to every part of the human body. Several anomalous effects have been observed in microcirculation. In particular, the apparent viscosity of the blood increases with tube diameter and this is referred to as the Fahraeus-Lindquist effect. This effect has been confirmed by several investigators. To explain the observed Fahraeus-Lindquist effect, Haynes [1] considered a two-fluid model with both fluids as Newtonian fluids with different viscosities. Bugliarello and Sevilla [2] have considered a two-fluid model where in the core region as well as peripheral region fluids are both Newtonian with different viscosities or both fluids are Casson’s fluid with different yield coefficients and viscosities. Sharan and Popel [3] and Srivastava [4] have reported that, for blood flowing through narrow tubes, there is a peripheral layer of plasma and a core region of suspension of all erythrocytes. Following the theoretical study of Haynes [1] and experimentally tested model of Bugliarello and Sevilla [2], two-fluid modeling of blood flow has been discussed and used by a good number of researchers. Several non-Newtonian fluid models have been considered for blood flow in small diameter tubes. Chaturani and Upadhya [5, 6] analyzed two-fluid models assuming Newtonian fluid in peripheral region and micropolar and couple