I'm a bit lost getting started analyzing the following system, a pump of sorts: http://i.imgur.com/P82vtZ1.png It consists of a vertically-orientated tube submerged in water with heating elements around the middle. Heat energy goes in, causing a temperature difference which drives a buoyant flow. I reckon at first, there won't be much flow and the water in the tube will heat up. But once the temperature difference is high enough, the steady flow energy equation will be satisfied (the temperature and flow rate will be high enough that the enthalpy of the water leaving equals the heat energy and enthalpy coming in), What I'm failing at completely is figuring out the flow rate through the system. I would be happy finding the body force on a block of warm fluid, but don't know how it will work with a control volume. Could someone please help me write down the equations governing this system? I am happy to make every simplifying instruction, and am aiming to find what flow rate the system will settle at for a given heat input (assuming the tank is sufficiently large that ALL the water heating up is not a factor).