An analysis of the two-dimensional flow of an incompressible, viscous fluid past an infinite porous plate is presented under the following conditions: (i) the suction velocity normal to the plate is constant, (ii) the free stream velocity oscillates in time about a constant mean, (iii) the plate temperature is constant, (iv) the difference between the temperature of the plate and the free stream is moderately large causing the free convection currents. Approximate solutions for the coupled nonlinear equations are obtained for velocity and temperature field. Expressions for the mean velocity, the mean temperature and the mean skin-friction are derived in part I. The mean velocity, the mean temperature are shown on graphs and the numerical values of the skin friction are entered in table 1. The effects of $G$ (the Grashof number), $P$ (the Prandtl number) and $E$ (the Eckert number), on the mean motion of air and water are described during the course of discussion. Some of the important observations are as follows. There is a reverse flow of the mean velocity profile of fluids, with small Prandtl number, in the boundary layer close to a plate which is being heated by the free convection currents. The mean skin friction increases with more cooling of the plate and decreases with more heating of the plate. In part II of the paper, the fluctuating flow is described.