Abstract: In order to study natural convection effects on fluid flows under low-gravity in space, we have expanded variables into a power series of Grashof number by using perturbation theory to reduce the Navier-Stokes equations to the Poisson equation for temperature T and biharmonic equation for stream function Φ.Suppose that a square infinite closed cylinder horizontally imposes a specified temperature of linear distribution on the boundaries, we investigate the two dimensional steady flows in detail.The results for stream function Φ, velocity u and temperature T are gained.The analysis of the influences of some parameters such as Grashof number G_r and Prandtl number P_r on the fluid motion lead to several interesting conclusions.At last, we make a comparison between two results, one from approximate equations, the other from the original version.It shows that the approximate theory correctly simplifies the physical problem, so that we can expect the theory will be applied to unsteady or three-dimensional cases in the future.