A Solution To The Simple Momentum Equation For Bouyant Flow In Glass Tanks

The one-dimensional equation for flow in a glass tank is solved analytically for a general case. An expression is developed which reveals a simple dependence of the velocity in a channel on the Grashof number, the aspect ratio and the variation in depth of the temperature gradient along the length of the channel. The expression provides a means for quickly comparing systems and conditions without resorting to elaborate numerical analysis. A comparison of the numerical solution of the one-dimensional case is also given.