I've got a project due this Friday whose objectives are no more than a single sentence: cooling tower improvements. This is for a thermal hydraulics class, so I thought I'd investigate the effects of different shapes of a hyperbolic cooling tower on heat flux q" through the walls of the tower and evaporative cooling (mass in the form of steam straight out the top). I used maple to build a few different hyperbolic shapes and I found formulas for volume and area on wolfram. I figured I could use Reynold's Transport Theorem in an energy balance to find how much energy has left the steam via conduction through the tower wall by the time it has reached the top of the tower. However, I've never solved Reynold's transport for a funny (non-uniform) area crosssection before and frankly don't have much confidence in my ability to do so. I have this next week to mess around with it and the professor will probably give me a hand if I need some help. Is this the best way to go about assessing performance of a cooling tower? Does anyone know of a better method? I'm not adverse to doing a long derivation with Reynold's, but I want to make sure that it will be meaningful to the end to figuring out what shapes are best for cooling.