The nano uids have gained tremendous signi cance due to their superior heat transfer properties. These enhanced heat transfer capabilities are promising for applications in thermal management systems and these translate into high energy e ciency, lower op- erating costs and better performance. An important mechanism of peristaltic activity for nano uid in Newtonian and non-Newtonian uids is considered. The heat transfer analysis in the absence of viscous dissipation can a ect the accurate ow simulations and measurements for the peristaltic transport. This necessitates taking the viscous dissipa- tion along with heat transfer analysis. Dissipation in return requires the viscosity to be variable being a strong function of temperature. Keeping this sequence in mind, viscous dissipation and variable properties of the uid in peristaltic transport of nano uids is discussed. Non-Newtonian uids have become a reality because the most physical u- ids are non-Newtonian in nature. These uids have very complex constitutive equations that raise the level of nonlinearity in the governing equation presenting mathematical di culty in addressing the non-linear equations. Therefore, the analysis of Newtonian uid is carried over to the non-Newtonian uid to understand the rheological properties of uid, and its use in industry. Electrically conducting uids have gained a great impor- tance and have been developed into a vast discipline of magnetohydrodynamics (MHD). MHD peristaltic ow is studied extensively with the view of its industrial and bio-medical applications, and its ability to suppress the uid velocity to avoid ow separation; how- ever, we feel that the study of magnetohydrodynamic ow of nano uids along with the temperature dependent viscosity is a missing link in the development of peristalsis that we aim to address in the present thesis. The importance of this study lies in its appli- cation in the targeted drug delivery for cancer patients, among others. In addition, we have incorporated the e ects of nonlinear thermal radiation which is generally ignored in literature or if considered; is taken as a linear approximation of radiative heat ux only. The peristaltic transport of nano uids has been the focus of this study. We start with the peristaltic ow of nano uid with temperature dependent viscosity under the e ect of x applied magneticeld. The e ects of induced magneticeld are also investigated which is a hallmark of strong magneticeld. This study in Newtonian uid is then extended to the non-Newtonian uid. The e ects of nonlinear thermal radiation are also explored. Emphasis in these studies is to incorporate the in uence of various parameters of physical importance on the peristaltic ow. Mathematical modeling of the problems is based on realistic assumptions and approximations for peristaltic transport. For nano uids, the formulation is completed in the presence of Brownian motion and thermophoresis. So- lutions are obtained by exact analytical and semi-numerical techniques. A comparative study between analytic and numerical solution is made for certainty. The results obtained are compared with existing literature wherever applicable. It is believed that this thesis will provide a profound understanding of peristaltic ows and lay a frame work for future investigations.