This is the master level research problem of mathematical model which publish in reputable European research journal, you may read online or download completely from DOI as mentioned at the top of the post.

You should read the introduction as well.

Every matter that can flow, is the fluid. Every fluid flow has its a unique equation and they can be written in the form of system of Partial Differential Equations (PDEs).

Every system of PDEs has several methods to solve them. All are authentic but graphical solution may be unique, that represents the fluid flow.

For the solution, there are some integral transforms, as we applied firstly Laplace transform, which convert the system of PDEs into simple system of algebraic equations. Then we used the Hankel transform which convert the problem from cylindrical domain into rectangular domain, and we can get the general solution in to the any form like convolution theorem of Laplace form.

At the end, graphical representations show the nature of flow, which may interesting for you, if you have some mathematical background.

I shall welcome all serious queries.

Thanks.