Abstract: At first, the three-dimensional vector potential and vorticity function are introduced, and the vector potential and vorticity equations are obtained in the case of arbitrary variation between density and temperature of water. Then, the vector potential and vorticity equations and the method of the false transient are applied to compute the three-dimensional viscous natural convection. Finaly, the effect of the property of unusual variation between density and temperature of water on three-dimensional natural convection is analysed and discussed by use of typical examples.

Key words: three-dimensional natural convection, effect of the property of unusual variation of water, vector potential and vorticity equations, method of the false transient