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This book comprises of six chapters and discusses the heat and mass transfer effects on a laminar, two dimensional, steady/unsteady, free/mixed convection flow of a viscous incompressible electrically conducting and radiating fluid past a semi-infinite vertical porous moving plate / stretching sheet / stretching cylinder/ horizontal circular cylinder bounded by a porous (or non-porous) medium, in the presence of various effects such as MHD, chemical reaction, viscous dissipation, thermophoresis, Brownian motion, thermally stratified medium, variable thermal conductivity and partial slip. The book is divided into six chapters. The first chapter deals with unsteady case, whereas the later five chapters deal with steady case. The governing equations of the flow under consideration were solved with the associated boundary conditions by using a traditional perturbation method or Runge - Kutta fourth order scheme along with shooting technique or Crank-Nicolson finite difference scheme.