Heat gain in buried chilled water pipes 1

[amer015]

As per 2008 ASHRAE HANDBOOK CHAPTER 11, to determinate annual heat gain for a buried system the STEADY-STATE CALCULATIONS are appropriate.
can anybody tell me why in that formula it's not present the heat transfer by convention from the pipe to the chilled water? what they mean with this steady-state?

Rs={ln{(d/r0)+[(d/r0)^2 - 1]^1/2 } }/2 pi Ks

Rs = thermal resistence of soil
Ks = thermal conductivity of soil = 2.6 W/m K (as per ashrae for saturated soil)
d = burial depth to centerline of pipe= 1.87 m
r0 = outer radius of pipe = 0.62 m

Rp = {ln(r0/r1)}}/ 2 pi Kp (negligible)
Ri = {ln(r2/r0)}}/2 pi Ki

Rp = thermal resistence of pipe (negligible)
Ri = thermal resistence of insulation
r1 = internal radius of pipe = 0.6 m
r2 = outer radius of insulation = 0.67 m
Kp = thermal conductivity of pipe (negligible)
Ki = thermal conductivity of insulation = = 0.026 W/m K (polyurethane foam)

Rt = total thermal resistence = Ri + Rs

q = (Ts-Tf)/Rt

q = total heat gain W/m
Ts = average annual soil Temp. = 30 deg. Celsius
Tf = fluid Temp. = 5 deg. Celsius


any help please

 

[KiwiMace]

The text states that this is a close (1%) approximation. I take this to mean that the convective resistance at the inner pipe/water boundary is so low (forced convection with water) that the higher resistance of the soil dominates. Likewise the steel pipe wall. Try adding these in to the calc and see what difference it makes.

Steady state means that the flow, water, soil and ambient temps are considered fixed for the basis of the calculation. c.f. transient calc, where something is changing.

 

[IRstuff]

Please do not double post and red flag your other posting, if the above answer is sufficient

TTFN
faq731-376

 

[urgross]

I would guess it is because they are using the conduction shape factor, which includes consideration of depth of burial, length of run, and pipe radius.