Mathematical Analysis of Unsteady MHD Blood Flow through Parallel Plate Channel with Heat Source

In the present study, a mathematical model of unsteady blood flow through parallel plate channel under the action of an applied constant transverse magnetic field is proposed. The model is subjected to heat source. Analytical expressions are obtained by choosing the axial velocity;temperature distribution and the normal velocity of the blood depend on y and t only to convert the system of partial differential equations into system of ordinary differential equations under the conditions defined in our model. The model has been analyzed to find the effects of various parameters such as, Hartmann number, heat source parameter and Prandtl number on the axial velocity, temperature distribution and the normal velocity. The numerical solutions of axial velocity, temperature distributions and normal velocity are shown graphically for better understanding of the problem. Hence, the present mathematical model gives a simple form of axial velocity, temperature distribution and normal velocity of the blood flow so that it will help not only people working in the field of Physiological fluid dynamics but also to the medical practitioners.

Numerical Study of Slip Effect of Unsteady MHD Pulsatile Flow through Porous Medium in an Artery Using Generalized Differential Quadrature Method (Comparative Study)

The unsteady pulsatile flow of blood through porous medium in an artery has been studied under the influence of periodic body acceleration and slip condition by considering blood as incompressible Newtonian electrically conducting fluid in the presence of magnetic field. In this paper, a new technique of differential quadrature method is introduced to find numerical solution of non-linear partial differential equations such as the equation of motion of this problem “Navier-Stokes equation”. The presence of the nonlinearity in the problem leads to severe difficulties in the solution approximation. In construction of the numerical scheme “a new algorithm” a generalized differential quadrature method (GDQM) is to use for derivatives with respect to space variables of differential equations and for the time derivative applying fourth order RungeKutta Method (RKM). The GDQM changed the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The obtained system of ODEs is solved by 4th order RKM. This combination of DQM and 4th order RKM gives a very good numerical technique for solving time dependent problems. The algorithm is coded in Matlab 7.14.0.739 and the simulations are run on a Pentium 4 CPU 900 MHz with 1 GB memory capacity. The effects of slip condition, magnetic field, porous medium, and body acceleration have been discussed. The numerical results show that the proposed method is more accurate and convergent than other numerical methods in literature. The method is illustrated and compared with the exact and analytical solutions and it is found that the proposed method gives a better accuracy and is quite easy to implement.