# Calculating Temp Difference in a hot water tank

I want to calculate the difference in temp between the bottom & top of a hot water tank,
Presumably the height of the tank, the diameter, the actual temp and time would be the variables. I will assume no heat loss. The heat input would be at the base of the tank.

## Answers and Replies

Redbelly98
Staff Emeritus
Homework Helper
More information is needed to answer the question. Is this a homework or a self-study problem? Is it from a textbook, and if so what subject does this section of the book deal with (i.e., heat transfer by conduction? Convection? Other?)

I have a central heating system which passes hot water in through a copper coil pipe to heat water in a sealed tank. The warm water rises naturally with no mechanical agigitation. My question is if the coil is at the bottom of the tank what is the approx difference between the temp at the bottom of the tank and that at the top. The tank is approx 50cm diam and 1.3 m high. Lets assume no heat loss for the tank. Obviously time will be a factor

It seems to me if there is no heat loss from the system, all the water would have to be at the same temperature as the coil. It is only if there is a heat loss that there would be a temperature difference. Am I missing something here?

Thank you for your reply. I really dont know very much but imagine that if you circulate hot water through a coil at the bottom of a tank that heat will be passed to the surrounding water and will rise to the top. Only when the system has reached a steady state will both temperatures be the same at the top & bottom of the tank. The application is if I have a temperature probe at athe the bottom of the tank what will be he temp difference at the top?
Thanks

Can one assume that before water is circulated through the coil, the water is uniformly at ambient temperature? Then at the instant hot water is first circulated through the coil, presumably warmer water would begin rising from the coil. Without any heat loss I don't know if there would be any convection currents or how they would flow. My guess is that they would be chaotic. It sounds like you are asking what the temperature difference would be at some time after heat is applied to the coil. To deduce the temperature at the top of the tank solely from a sensor at the bottom of the tank I think would be next to impossible.