الملخص

In this paper, we studied a flow of fluid in a pipe under the effect of electromagnetic field in a polar coordinate, be done build a mathematical model which  represented by system of  two dimensional non-linear partial differential equations and we solved it by using  Alternating Directions Implicit method (ADI) which is one of the finite differences method, and from the numerical solution indicated the behavior of  temperature distribution inside the pipe, be done explication the influence of  Rayleigh number and Prandtl number as well as the influence of Eckert number upon the behavior of  temperature distribution are also done through the energy equation  in polar coordinate, we arrived to steady state from unsteady state, we find the behavior of fluid flow inside the pipe  and also we studied the influence of  Hartmann  number  upon the behavior of  fluid flow in pipe and all this done through the motion equation in polar coordinate.