Interesting heat transfer Problem

[JLooch]

Wondering if anyone has modelled this common heat transfer problem? Basically it is a Dead Zone at the end of a pipe run, as shown,

Pipe run & branch is say, 20" pipe, 35C water flows from A thru the pipe branch C and all is good on those runs, flow is continuous and assume stays at 35C.
The downstream zone B is dead head and many times if its only a few feet long, ~ 1-3 pipe dia long, it doesn't freeze but of course after a certain length it does freeze,

I modelled it as a complex "Fin", Q into dead zone = Q out of dead zone etc,
Qin is not much, water is a poor conductor, there is some turbulence at the junction so get some mixing, convection, but still poor transfer here,
Q out is simpler, but water temp varies along dead zone length,

Has any one modelled it differently?
Ideas?

^ C
| -30C ambient
A | B
---->-----------------------||
pipe tee

 

[IRstuff]

A real picture might be useful

TTFN
faq731-376

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[JLooch]

the sketch link is here

 

[chicopee]

Establish nodes spaced evenly in the dead leg. The first node will start somewhere near the "T" dead leg and the last node near the end cap. All nodes will be within the center of elemental strips, each of which will be an elemental length. Starting on the first elemental node heat transfer (conduction only) minus heat transfer to the second elemental strip (conduction only) minus heat transfer thru elemental strip wall thickness( conduction thru wall and convection from wall to ambient) equals zero. At the end cap there should be heat transfer thru it (conduction and convection). This Time step procedure for steady state condition. I am assuming that the water in the dead leg is not disturbed by water movement thru the 90 degree turn in the "T" and therefore there is no convection between the water movement thru the 90 degree turn and the start of the first elemental strip

 

[JLooch]

Thanks Chicopee, I did set my initial model up that way but I didn't want to ignore convection heat loss thru the wall along the length. I used the "stepped" temperature found in the 1st step for calculating the convection loss for each element. This will be close and I might iterate a few times to get a better value but I did it once and it shows it will freeze, my actual application has a 5' dead leg on a 20" pipe.

Will look at insulation and see, otherwise will need tracing, I agree with you that we should ignore any other gain in heat at the tee other than straight conduction.

Thanks again, Hope all is well,

JL

 

[prex]

The contribution of water conductivity is very low: in a 20" pipe heat removal from the outer surface is more than 100 times the heat conducted through water over the same length. Convection, if any, will primarily be from bottom to top, not axial (assuming your tee is horizontal), so it would not contribute. I would entirely neglect the contribution of water to heat flow, obtaining a fairly safe result for your check of freezing conditions.

prex
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[JLooch]

yes, I find the convection transfer from the outer surface of the pipe to be huge compared to the little conduction at the tee area(element). The dead water area freezes unless the dead leg length is very short. The 5' is too long, even with 2" insulation, this will need to traced.

It was hard to calculate the steady-state equilibrium condition in one step. I used various water temps, then repeat till heat gain (conduction) equaled heat loss (outer surface) and doesn't equal above 0C at wall.

Thx,

 

[FredRosse]

I have done similar problems, and the dominant phenomenon is physical circulation within the pipe, high density fluid travels along the bottom, lower density moves along the top. A reasonable first approximation is to consider the horizontal pipe as divided into three zones, each with a height of Dia/3. Consider the center zone as a stagnant (solid) entity, with circulation in the upper and lower zones. The upper and lower zones are considered connected at the pipe ends. All circulation is driven by boyancy changes (density = a function of temp) caused by the conventional heat transfer equations.