Development length of laminar magnetohydrodynamics pipe flows

In this article, a laminar magnetohydrodynamics (MHD) developing flow of an incompressible electrically conducting fluid subjected to an external magnetic field is considered. The aim of the study is to propose a correlation for computing the development length of the laminar MHD developing flow in a pipe. A numerical approach is considered to solve the problem. In the first step, the numerical Finite Volume Method (FVM) is conducted to analyze the problem. Hereafter, the artificial neural network (ANN) is used to develop the datasets and in the last step, the curve fitting is applied to find a correlation for prediction of the development length as a function of the Reynolds and Hartmann numbers. In addition, the effect of the problem parameters on the development length are studied. It is found that the development length declines with the increase of the Hartmann number and grows with the rising of the Reynolds number.