Abstract
Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1－αt)1/2 and a magnetic field proportional to B0(1－αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, BO denotes a representative magnetic field and α-1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.
Highlights
The quest for similar solutions is important with respect to the mathematical character of the solution
Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H 1 t 1 2 and a magnetic field proportional to B0 1 t 1 2 is applied perpendicular to the disks where H denotes a representative length, B0 denotes a representative magnetic field and 1 denotes a representative time
Guria et al [6] obtained exact solution of hyderomagnetic flow between two porous disks rotating with same angular velocity about two non coincident axes in the presence of a uniform transverse magnetic field
Summary
The quest for similar solutions is important with respect to the mathematical character of the solution. Bhupendra et al [4] considered the problem of forced flow of an electrically conducting viscous incompressible fluid due to an infinite rotating disk under the influence of uniform magnetic field, applied normal to the flow. Pavlov [5] found an exact similarity solution of MHD boundary layer equations for the steady two dimensional flow of an electrically conducting incompressible fluid due to rotation of a plane elastic surface in the presence of a uniform transverse magnetic field. Usha and Vasudevan [10] studied a similar flow between two rotating disks in the presence of a magnetic field and obtained rather expensive solution of the problem to observe the effect of flow parameters on the velocity fluid
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