Conduction along length of copper water filled pipe

dfru

I am looking for assistance in doing some calculations to determine certain factors associated with an uninsulated water filled pipe. The pipe is 1" copper pipe. It starts off at ambient temperature. Say 60 degrees F. 3 feet away, along the length of the pipe is a tee connection which delivers 140 degree water to the piping system. Assume that 100% of the 140 degree water flows along the other run of the tee, away from the cold water leg, and that there is no flow through the cold water leg. The 3 ft pipe run is horizontal.



How do I calculate the rate of heat transfer to the cold water pipe?

What will the maximum temperature become at the piping along the cold water pipe, 3 ft from the tee?

How long will it take to reach this temperature?



Any assistance would be much appreciated  

Gordy

Missing information

How long is the 1" cu pipe with 60* water? No flow in this pipe? If not how is it maintaining 60* ambient?



T connection from the 140* water pipe to the 60* water pipe?



I think some sort of piping diagram referencing pipe sizes, and fitting locations, flow rate of 140* pipe.



Only partially visualizing what you have let alone function.... Heat exchanger?

dfru

Missing Information

The 1" pipe goes to a water softener, then continues on the the building water supply. Cold water will periodically flow through the pipe, but I am analyzing the system during off hours when there will not be any flow in the system.



The pipe is connected to a domestic water heater, and provides cold water to it. Just upstream from the connection is a recirculating hot water pipe which tees into the cold water line. I am assuming as a worst case that the recirculating water back to the heater is at 140 degrees F.



I will put together a diagram if it still does not make sense.

JeffM

calculus

This seems like it could be determined with a fairly straightforward differential equation (you have a starting condition, and want to understand the changes with time), but my calculus skills are so rusty that I'm not going to go near this one! If you've got a buddy with a college calculus text around you might get somewhere.