Look at this link it may be helpful for your topic. Good luck.

http://mathematica.stackexchange.com/questions/78439/4th-order-runge-kutta-method-to-solve-a-system-of-coupled-odes

Aren't the (Navier-Stokes) equations for fluid flow partial differential equations? If so, you need to have a way to do spatial as well as temporal discretization. How are you planning on doing that? Also, the resulting system of ordinary differential equations is usually stiff, which means explicit methods like RK4 will probably fail unless the time step is unusually small. So you will need an implicit Runge-Kutta method. Is your aim high accuracy? If so, you will need to be careful in your selection of a method. If not, then maybe implicit Euler is the best thing to use, at least to start with.

Dear Ajaz Ahmad,

the equations, which govern fluid flow (the Navier-Stokes equations) are partial differential equations and are usually solved by the finite volume method. Other methods have been used as well by many researchers. 

Many commercial (Ansys), open-source (OpenFOAM) or in-house research codes are available online. 

If I remember correctly, micropolar fluids are modelled by introducing an addtional term in the momentum equations. We have done this using our in-house code, email me if you need addtional info.

In my opinion Mathematica and the Runge-Kutta method are not the way to go. Firstly the governing equations are not ODE and secondly due to the nonlineary of the flow, the discretization has to be able the capture the flow phenomena, i.e. the grid size and time step must be small and Mathematica is perhaps not the best choise.

I would recommend using C/Fortran or Matlab/Scilab plus the finite volume method.

Use the package ode45 in matlab

Runge Kutta for the fluid flow equations? Generally the RK methods are only used for systems of ODEs, so are you solving a self-similar boundary layer problem or a channel flow problem? It is sometimes possible to use it for time-stepping when the flow is parabolic in time.

If, as I suspect, you do have a system of ODEs, then Dr Wakif''s suggestion of using ode45 in matlab is very good, although for a channel flow the classical RK4 method will work well and it will be easier to use grid refinement to reduce numerical errors systematically.

Dear Ajaz, in his book The Essence of Chaos (see attached file), Edward Lorenz explains use of fourth-order Runge-Kutta method for solving a non linear system of ODEs from usual PDE fluid flow equations. Note the use of very small time steps. But this system is numerically integrable using tools like Mathematica or Matlab.

If you want another example of how to solve ODEs for fluid flows using Mathematica, see Reza Malek-Madani paper about swirling flow and Rayleigh-Benard flow.

Gianluca