Muhammad Sajid2025-11-262025-11-262021https://escholar.umt.edu.pk/handle/123456789/12927In this dissertation, we investigated the MHD flow of a third grade fluid through an inclined channel. The fluid is incompressible and electrically conducting with the heat transfer in the existence of a uniform magnetic field. Three different problems namely, plane Couette flow; Poiseuille flow and Couette-Poiseuille flow have been discussed. In each case, the nonlinear equations governing the flow and heat transfer are solved for velocity and temperature pro- files by employing the regular perturbation method, Homotopy perturbation method and Homotopy analysis method, and for numerical solutions bvp4c technique built-in MATLAB is used. Finally, the effects of magnetic parameter, gravitational parameters and brinkman number are analyzed for velocity and temperature profiles and the results are pre- Sented through graphs and in tabular forms. Further, we compare our obtained semi-analytical and numerical results in graphical and tabular forms.enThesis