mathematical models for biomagnetic fluid flow and applications

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In all the above cases the magnetization M o is dependent on the temperature T of the fluid. In such a case (non-isothermal case), it is also necessary to consider in the mathematical model, describing the problem under consideration, the energy equation containing the temperature T of the fluid. This equation can be written as [8] DT ∂M o 2 ρ Cp +µ oT ⎡V⋅( ∇ H) ⎤ = k∇ T+ ηΦ (12) Dt ∂T ⎣ ⎦ where k is the coefficient of thermal conductivity of the fluid, C p the specific heat and Φ the dissipation function. 4. APPLICATIONS Biomagnetic fluid flow in a Channel As a simple, but representative, application of biomagnetic fluid flow we consider the steady two-dimensional laminar flow of an incompressible viscous biomagnetic fluid (blood) in a space between two parallel flat plates (channel). The length of the plates is L and the distance between them is h (h
of the magnetic source the friction coefficient is increased substantially due to the action of the magnetic field. The contours of the stream function, for various magnetic numbers, are shown in Figures 4-6. The magnet affects the fluid flow and two vortices are created near the magnetic pole, as the magnetic field strength is increased. The contours of vorticity function are shown in Figures 7-9 and of temperature function in Figures 10-12. Near the pole we observe a slight increase of the temperature as a result of additional energy from the magnetic field of the pole. It should be remarked that in the absence of the magnetic field straight lines represent temperature, stream as well as the vorticity function. Thus, the formation of these contours is the result of the action of the applied magnetic field on the flow field. These results show that in the presence of the magnetic field, the flow field is changing drastically, and especially the skin friction coefficient, which is affected near the area of the magnetic pole. These conclusions suggest that a careful choice of the imposed magnetic field will affect the flow characteristics and hence can be utilized for medical and engineering applications. Figure 4. Contours for stream function for Mn=2000 Figure 5. Contours for stream function for Mn=4000 Figure 6. Contours for stream function for Mn=6000 Figure 7. Contours for vorticity function for Mn=2000 Figure 8. Contours for vorticity function for Mn=4000 Figure 9. Contours for vorticity function for Mn=6000
Page 1 and 2: MATHEMATICAL MODELS FOR BIOMAGNETIC
Page 3: for medium shear rates, like blood

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