This communication studies the flow and heat transfer characteristics over a continuously moving surface in the presence of a free stream velocity. The Jeffrey fluid is treated as a rheological model. The series expressions of velocity and temperature fields are constructed by applying the homotopy analysis method (HAM). The influence of emerging parameters such as local Deborah number (β), the ratio of relaxation and retardation times (λ2), the Prandtl number (Pr), and the Eckert number (Ec) on the velocity and temperature profiles are presented in the form of graphical and tabulated results for different values of λ. It is found that the boundary layer thickness is an increasing function of local Deborah number (β). However, the temperature and thermal boundary layer thickness decreases with the increasing values of local Deborah number (β).