The investigations presented in the thesis are theoretical studies of magnetohydrodynamic flows, heat and mass transfer in Newtonian/non-Newtonian cooling liquids, due to horizontal/vertical stretching sheet. The theoretical studies include the effect of magnetic field, uniform and non-uniform heat source/sink (flow and temperature dependent heat source/sink) effects. The considered problems include flow of viscous fluids in the presence of applied magnetic field and electric field with first order chemical reactions. The viscous incompressible Newtonian fluid flow in porous medium with Darcy-Forchheimmer model, electrically conducting fluid and nanofluid is studied. We introduce innovative techniques for finding solutions of highly nonlinear coupled boundary value problems such as Runge-Kutta method, Perturbation method and Differential Transform Method (DTM).   Chapter 1-2 gives a brief introduction. Chapter 3 focuses on Lie group analysis of MHD flow and heat transfer over a stretching sheet. The effects of viscous dissipation, uniform heat source/sink and MHD on heat transfer are addressed. In Chapter 4-6 we examined the laminar flow, thermocapillary flow of a nanoliquid thin film over an unsteady stretching sheet in presence of MHD and thermal Radiation in different situations. An effective medium theory (EMT) based model is used for the thermal conductivity of the nanoliquid.  Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) - water base liquid. In Chapter 7-9 we analyzed, heat and mass transfer in MHD, mixed convection, viscoelastic fluid flow, non-Darcian flow due to stretching sheet in presence of viscous dissipation, non-uniform heat source/sink and porous media have been investigated in different situations.  MHD and viscous dissipation have a significant influence on controlling of the dynamics.    In Chapter 10 the linear stability of Maxwell fluid-nanofluid flow in a saturated porous layer is examined theoretically when the walls of the porous layers are subjected to time-periodic temperature modulations. A modified Darcy-Maxwell model is used to describe the fluid motion, and the nanofluid model used includes the effects of the Brownian motion. The thermal conductivity and viscosity are considered to be dependent on the nanoparticle volume fraction. In Chapter 11 we studied MHD flow in a vertical double passage channel taking into account the presence of the first order chemical reactions. The governing equations are solved by using a regular perturbation technique valid for small values of the Brinkman number and a DTM valid for all values of the Brinkman number.