In this paper, we inaugurate the exact solutions for rotational and oscillations of Maxwell fluid through a cylindrical region. Maxwell fluid model has abundant significance in engineering and industrial applications Due to its considerable interest in the technical field such as glass-fiber, paper production, application of paint, food processing and biological transportation. This thesis is trying to scrutinize the heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating cylinder with the impact of magnetic field and constant well temperature. The problem is modelled in term of partial differential eq. with initial and boundary condition. Non-dimensional variables are used to transform the governing problem into dimensionless from. The dimensionless form is fixed via the process of transformation of Laplace and Hankel to determine the proper solution for velocity, shear stress, and temperature. The solution for MHD and porous, Newtonian and Non-Newtonian fluid is also obtained as a special case and some visual descriptions are addressed at the end.

Keywords- Maxwell fluid, oscillating flows, velocity field, shear stresses, Laplace and Hankel transforms.