GANITA, Vol.70(1), 2020, 41-52 41 A Class Of Exact Solution Of Equations Governing Aligned Plane Rotating Magnetohydrodynamic Flows by Martin’s Method Sayantan Sil 1 , Mantu Prajapati 2 & Manoj Kumar 3 1 Department of Physics, P.K. Roy Memorial College, Dhanbad-826004, Jharkhand, India. sayan12350@gmail.com 2 University Department of Physics, Ranchi University, Ranchi-834008, Jharkhand, India. mantuprajapati15@gmail.com 3 Department of Physics, Ram Lakhan Singh Yadav College, Ranchi-834001, Jharkhand, India. profmanoj@rediffmail.com Abstract In this paper an approach has been made to determine the exact so- lution of steady, plane, aligned, MHD fluid flow having infinite electrical conductivity in a rotating frame by the application of Martin’s method. The non-linear governing equations of the fluid flow are converted into a new form called Martin’s form by employing differential geometry where in the curvilinear coordinates (φ, ψ) in the plane of flow the co-ordinate lines ψ =constant are the streamlines of flow and the co-ordinate lines φ = constant, are left arbitrary. Also von Mises co-ordinates (x, ψ) that require the use of φ =x in Martin’s co-ordinates (φ, ψ) are taken. Fi- nally the value of magnetic field vector, velocity vector, pressure function, vorticity and the current density function are found out. Keywords: MHD, Martin’s method, exact solution, rotating frame, aligned flow, stream function. 1 Introduction Martin [1] introduced a new method to study steady plane flows of viscous fluid. The study of fluids having infinite electrical conductivity is done for the mathematical idealization for completeness and to include super conducting liquid metal of the future. The theory of rotating fluid is very important because of its appearance in many natural phenomena and its application in various areas like oceanography, meteorology, atmospheric science and limnology. Various transformation techniques are applied to convert the non-linear partial differ- ential equations into linear differential equations. The Navier-Stokes equations and the basic equations governing the flow of magnetohydrodynamic (MHD) fluid are inherently non-linear partial differential equations and have no general solution. Only a small number