The equations governing the flow of couple stress and modified second grade non-Newtonian fluid flows for systems of non-linear ordinary differential equations are formed and thus these systems have no general solutions. The general solutions become more rare if we study these flows together with heat transfer analysis and even more harder if we introduce the variable viscosity instead of constant viscosity. In the first part of the thesis we study the steady incompressible couple stress channel fluid flows together with the energy equations taking variable viscosity into account. The Reynolds and Vogel’s viscosity models have been used for the temperature dependent viscosity. Depending on the relative motion of the plates, four different problems are considered, viz plane Couette flow, plug flow, plane Poiseuille flow and Couette- Poiseuille flow. Approximate analytical and numerical approaches have been used to solve the nonlinear developed equations arising during the mathematical modeling of these problems. Solutions for the velocity profiles, temperature distributions, volumetric flow rates, average velocities Nusselt number and shear stresses are obtained. The influence of different emerging parameters on the flow pattern has been discussed and presented with the help of graphs. A study of thin film flows for the Generalized (modified) second grade fluid together with the energy equation is carried out in the next part of the analytical investigation. Two different problems have been investigated, (i) when a wide belt is moving vertically upward through a container with a constant speed V0 and (ii) when fluid is falling on the stationary infinite vertical belt under the influence of gravity. For the above stated problems the governing equations are converted into ordinary differential equations and then solved exactly for the velocity profile and temperature distribution. Expressions for the volume flux, average velocity and shear stress are obtained in both these problems. Effects of different parameters on velocity and temperature are presented graphically. Furthermore approximate solutions have been developed for the Generalized second grade fluid in cylindrical coordinates.