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The problem of a micropolar fluid about an accelerated disk rotating with angular velocity Ω proportional to time has been studied. By means of the usual similarity transformations, the governing equations are reduced to ordinary non-linear differential equations and then solved numerically, using SOR method and Simpson’s (1/3) rule for s ≥ 0, where s is non-dimensional parameter which measures unsteadiness. The calculations have been carried out using three different grid sizes to check the accuracy of the results. The results have been improved by using Richardson’s extrapolation.

Eringen [1,2] introduced and formulated the theory of micropolar fluids. These fluids exhibit certain microscopic effects due to the local structure and micro motion of the fluid elements. Unsteady flows of micropolar fluid have been considered by a number of authors. Chawla [

The flow of an incompressible viscous fluid past an infinitely rotating disk was first studied by Von Karman [

In this paper, we examined the problem of Watson and Wang [

The fluid flow is non-steady, laminar and incompressible. The cylindrical coordinates (r, q, z) are used, r being the radial distance from the axis, q the polar angle and z the normal distance from the disk. We assume that there is no body force and body couple. With these assumptions the governing equations of motion for micropolar fluids become:

By using the following similarity transformations:

where

where primes denote differentiation with respect to _{, },

The boundary conditions are:

The governing third order ordinary differential equations are reduced to second order ODE’s.

let

Then, Equations (5)-(9) become

The boundary conditions (11) become

In order to obtain the numerical solution of nonlinear ordinary differential Equations (13) to (17), these equations are approximated by central difference approximation at a typical point _{ }of the interval [0,¥) and then solved by using SOR method. The first order ordinary differential equation (12) is solved by Simpson’s (1/3) rule with the formula given in Milne [^{6}) is achieved, on the basis of above solutions by using Richardson’s extrapolation.

The numerical results have been computed for three different grid sizes namely h = 0.5, 0.025, 0.0125 for the comparison purpose. The results are obtained for several values of the parameter s in the range

The numerical results of the velocity components namely f the axial component, g the circumferential component and

Graphically, the results have also been demonstrated.

The unsteady flow of micropolar fluids about an accelerated rotating disk is discussed in detail. The set of difficult non-linear ODE’s is solved by using a very easy and efficient numerical scheme. The accuracy of the results is checked by comparing the results for three different grid sizes. The constants “C’s” affect the micro rotation of micropolar fluids flow. If one of these constants