Mathematical modeling of biomagnetic flow in a micropolar fluid-saturated Darcian porous medium

Bég, O. Anwar, Takhar, Harmindar S., Bhargava, Rama, Sharma, S. and Hung, Tin-Kan (2007) Mathematical modeling of biomagnetic flow in a micropolar fluid-saturated Darcian porous medium. International journal of fluid mechanics research, 34 (5). pp. 403-424. ISSN 1064-2277

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Abstract

In this paper a mathematical model of the two-dimensional fully developed steady, viscous flow of a non-conducting biomagnetic micropolar fluid through a Darcian porous medium model of tissue is presented. The momentum conservation equations with zero pressure gradient are extended to incorporate the biomagnetic body force terms along the X and Y axes and also the Darcian linear drag in the X and Y directions, with appropriate boundary conditions. An angular momentum equation is also included for the spin of the microelements. The equations are non-dimensionalized using a set of transformations following Tzirtzilakis et al. (2004). A finite element solution is generated to the resulting non-dimensional model and the effects of biomagnetic number (NH), Darcy number (Da) and micropolar viscosity ratio parameter (R) on the X- and Y-direction velocity profiles is studied in detail. A number of special cases of the flow model are also discussed. The numerical solution is compared with a finite difference solution using central differencing and found to be in excellent agreement The model finds applications in biomedical device technology, blood transport in tumors, brain tissue and soft connective tissue zones as well as in fundamental hydrodynamics of ferrofluids in porous materials.