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The study of the MHD flow with heat transfer is a new offshoot of mathematics currently receiving considerable interest.It has wide applications in Geophysics,Astrophysics,Engineering,Aeronautics. The essence of MHD comprises models which help to arrive at optimum decisions. These models constitute the subject of this book.The book considers the problems of the MHD flow with heat transfer.It is written for postgraduate students of Mathematics, Physics,& Engineering. Chapter1 is a General Introduction which gives i)A brief history of MHD.ii)Some fundamentals of the subject.Chapter2 consists of important parameters, definitions and basic equations governing the MHD flow with heat transfer.Chapter3 contains a discussion of the impact of heat transfer in the MHD flow past an infinite vertical plate with time- dependent suction.Chapter4 deals with the heat transfer aspect in a three dimensional MHD flow along a porous infinite flat plate in the presence of viscous dissipative heat anda transverse magnetic field.Chapter5 is an investigation into the effect of an electromagnetic field on generalized Couette flow with heat transfer.