A sticky question of heat transfer
A sticky question of heat transfer
(OP)
I have a configuration like this.
- ambient air at -36°C (still)
- 38 mm insulation (foamglass K=0.045 W/m°C)
- electric heat tracing
- 25 mm steel wall
- 100 mm nitrogen wall (tank 2nd jacket, K=0.026 W/m°C)
- 25 mm steel wall
- glycol at 20°C
The question is: how much is the heat introduced with the electric tracing to maintain the glycol at 20°C ?
Thank you in advance.
- ambient air at -36°C (still)
- 38 mm insulation (foamglass K=0.045 W/m°C)
- electric heat tracing
- 25 mm steel wall
- 100 mm nitrogen wall (tank 2nd jacket, K=0.026 W/m°C)
- 25 mm steel wall
- glycol at 20°C
The question is: how much is the heat introduced with the electric tracing to maintain the glycol at 20°C ?
Thank you in advance.





RE: A sticky question of heat transfer
Thus one needs to estimate U, the overall heat transfer coefficient (OHTC) composed by conduction across the foamglass plus the convection and radiation effects on the surroundings. For a delta T of 20+36=56oC, the heat load Q, per unit area A, would be fixed by the equation:
Please correct me if I'm wrong.
RE: A sticky question of heat transfer
Additionally, the deltaT applies primarily to the top surface of the glycol, while the transfer equation to the sides of the tank is more likely to have a positive heat flow from the heater with a smaller negative deltaT, while the heater has a larger positive deltaT to the environment.
For a 1ft square top surface and assuming h=4 W/m^2*K, I swag about 20 W each for convection and radiation.
TTFN
RE: A sticky question of heat transfer
A clarification: the steel wall in contact with the glycol is the enclosure of a rectangular tank of approx 120 cum capacity. The second steel wall is the outside enclosure of the tank jacket in which nitrogen is used as buffer fluid. All tank (jacket included, is installed inside another steel enclosure and not subject to sun radiation.
RE: A sticky question of heat transfer
Is construction identical on the top?
Is the tank filled?
TTFN
RE: A sticky question of heat transfer
Tank dimensions are approx 9.5 x 4 x 4 m (LxWxH).
Top of the tank is identical to the bottom; all wall surfaces are subject to a small internal pressure, approx 0.2 barg plus liquid head where applicable.
The tank jacket is under higher pressure, approx 0.8 barg.
The tank is normally filled with glycol.
Thanks for your cooperation.
RE: A sticky question of heat transfer
TTFN
RE: A sticky question of heat transfer
The heater needs to be at a minimum of 20ºC, so you've got the maximum deltaT across the foam glass and your heater is primarily heating the foam glass.
TTFN
RE: A sticky question of heat transfer
1. The interface between the glycol and the steel is at 20 degrees C
2. The interface between the air and the insulation is at -36 degrees C. Normally, I would calculate the heat transfer coefficient for natural convection. However, you can assume the outer wall is at -36 degrees C for the worst case scenario.
3. No contact resistance around the heater.
4. No radiation heat transfer
Design Optimization
Now all you have to do is determine the cost of the heater. Then determine the cost increase by manipulating the design. For instance, how much does it cost to increase the thickness of the insulation or the N2 wall? This added cost to the overall design might lower your monthly electrical bill in the long run.
RE: A sticky question of heat transfer
1. the tank is inside a housing such as a hangar
2. all tank surfaces are insulated and heated in the
same manner
3. there is some measure of moisture or ice intensification
factor by deposition on the external foamglass at
-36oC
4. disregarding the fact that for the same surface-to-air
temperature differences, walls would lose heat by
natural convection in a different rate: top
face=1.3*vertical walls=2*bottom face
5. radiation effects to the surrounding air are small but
not negligible
I'd say that your estimate of 12 W/m2 is on the low side. A ballpark estimate would bring the heat loss to 10 times as much.
RE: A sticky question of heat transfer
(0.045 W/mK)/38mm = 1.184W/m^2K
with 56°C delta, that results in 66 W/m^2
TTFN
RE: A sticky question of heat transfer
RE: A sticky question of heat transfer
I get heat through foam of 57 W/m^2 with the outer surface of the foam at -28°C. This results in convective loss of 31 W/m^2 and radiative loss of 25 W/m^2.
This is obviously very rough, using ideal emissivities, etc., and applies only to the vertical sides. This also assumes that the glycol is essentially in an isothermal region, since it's surrounded by heaters on all sides and therefore, there is no loss from the glycol itself.
I need to get a life...
TTFN
RE: A sticky question of heat transfer
Seems to me that the convective losses should be much greater than the radiative losses.
RE: A sticky question of heat transfer
But that's a very gross model, since neither the foam nor the ambient are perfect blackbodies, hence my caveat of "ideal emissivities, etc."
Obviously, there are lots of factors involved that are not modeled well by the Stefan-Boltzmann radiation model, particularly, subtleties such as the high atmospheric absorption between 5 and 8 micrometers.
As a zero-order model, it's nearly a wash anyway because if you assume no radiation you get 66 W/m^2, while the perfect blackbody model gives you 57 W/m^2.
From a practical design perspective, you'd have to design with some margin and then run the thermal control with one or more temperature monitors in the glycol itself.
TTFN
RE: A sticky question of heat transfer
RE: A sticky question of heat transfer
TTFN
RE: A sticky question of heat transfer
RE: A sticky question of heat transfer
On the basis of info had from you and others from my knowledge and library, I have reached the following conclusion.
Disregarding the terms relevant to steel walls and glycol side, only three are partecipating to the heat transfer:
- convection+radiation on still air side, coeff. 4 W/sqm°C
- conductivity of foamglass, coeff. 1.18 W/sqm°C
- conductivity+radiation+convection, coeff. 2.22 W/sqm°C
Based on above, the overall heat transfer coefficient becames 0.646 W/sqm°C and heat loss through 1 sqm surface 36.2 W/sqm.
The critical point of this evaluation is the coefficient through the nitrogen filled double wall. In the coefficient assumed (calculated according to an engineeering manual), 14% is by conductivity, 58% by radiation and remaining by convection. Somebody knows a specific procedure and/or formula to evaluate this?
Again, thank for your help and partecipation.
Roal