heat rate calculation

[adamjt]

I have a pipe in which the internal water flow heats up at 20 deg C per hr. The pipe is 3" thick carbon steel, with 3" of insulation in a 22 deg C room, with known thermal conductivities. How do you go about finding much the carbon steel pipe lags behind the water in heating up?

 

[MintJulep]

The delta-T between the water and the pipe will not be a constant, it will vary with time and position in both the length and radial dimensions.

The solution requires a 2-dimensional transient analysis. Not a particulary easy thing to do. It might be possible to to a 1-dimensional approximation by descritizing the length dimension into small slices (this is essentially what an FEA program would do).

In a nut-shell, the how-to is "conservation of energy equations". Energy in = Energy out + Temperature Gain x specific heat.

 

[sailoday28]

It seems that the heat up rate of 20C per hour is a bulk rate. If there is a negligible water temp gradient, axially and radially, then dependent on other considerations in the outside boundary conditions, there should be negligible axial gradients in the steel and insulation.
Then the problem can be reduced to a one dimensional transient. Closed form solutions with the steel and insulation will be difficult to solve.
I therefore recommend numerical solutions.

 

[reena1957]

Dear adamjt,
Is there flow in the pipe or stagnant liquid or well mixed liquid?How is the temperature increased uniformly and is it the bulk temperature? give some details.

 

[adamjt]

The liquid is flowing very fast, very turbulent and is a 36" diameter pipe. The temp increase is the bulk temperature of the water going up 20 C/hr.