Abstract: Based on the boundary layer theory, the rules of the formation of both velocity and thermal boundary layers of an incompressible fluid flowing at zero initial velocity along a vertical plane under the action of gravity are discussed, of which the fluid is featured with a big Prandtl number and constant thermal property. Computing formulas of thickness of both velocity and thermal boundary layers are given. Then, based on these formulas the calculation method on the convective heat coefficient is discussed further with a mathematical expression derived in detail. Compared with the model that the fluid flows along a horizontal plane, both the velocity boundary layer and thermal layer become thicker and the convection heat transfer is less turbulent in short distance flow. Many problems of heat transfer in actual engineering can be simplified as the models that fluid flows along vertical plane under the action of gravity. Applying these formulas in the thermal analysis of the gearbox attached to an aeroengine, an accurate result was obtained.