New way for simulation of transient natural convection heat transfer

A method for improving numerical solution of transient natural convection heat transfer in enclosures is proposed, where temperature, a stream function, and vorticity are decomposed into Fourier components of a body-fitted curvilinear coordinate. Using addition formulas of trigonometric functions, the equations of motion, energy, and continuity can also be separated into Fourier series. This reduces the number of variables by one and leads to reduction of the numerical computation time.As an example, given is a seven-terms numerical solution for a Grashof number of 19,600 in case of air in a circular cylinder.