Convective Heating From Vertical Surface to Horizontal Surface 1

[joedvo]

I am trying to find a way to calculate the heat (Btu's) transferred from a vertical surface to a horizontal surface via convection currents. This is a difficult scenario to explain in words, so I took a moment to create a picture showing the details.

Basically I have a tank with a shell surface temperature of 216 degF that is losing heat via convection. Because heat rises in convection currents, these currents are expected to rise in the dry air; adding heat to the bottom of structural tubing next to the shell. This structural tubing can be as close as 2 inches from the shell surface to more than 10 inches, as shown in the top view diagram. The ambient air is 40 degF beyond the convection current. Is there a way to calculate the amount of heat received on the bottom surface of the structural tubing due to the convection currents?

I have already calculated the conductive and radiative heat in the structural tubing, these Btu's from convection would be the final piece I need to add to the energy balance and find the surface temperature. I have really baked on this and it seems to be more than just the convective heat transfer equation of q=hA(Ts-Ta) because there should be losses in Btu's due to turbulence. I feel like there is a distance component missing. Can someone please steer me in the right direction.

Thank you for your time!

 

[IRstuff]

There are diffusion and continuity equations that model the behavior, but they cannot be easily done by hand. You need a decent CFD program to model your problem.

TTFN

FAQ731-376

 

[Dave41A]

I write this assuming that I interpreted your drawing properly.

First, a question: What's the temperature of the tubing? If these too are at 40F, then there is no heat lost to the tubing, since there would be no temperature difference between them and the ambient environment.

I suspect you think the tubes are cooler than the 40F air. You should verify this with a surface thermometer, and then treat the tubes as horizontal tubes in free convection. There are numerous correlations for this calculation: Morgan or Churchill and Chu have published these results (see Incropera or another heat transfer text). These will estimate Nu which is used to compute the heat transfer coefficient h.

Another way is to measure the temperature inside the tubes (if possible) and also the temperature on the outside of the tubes. This will give you a temperature difference across the tubes' wall, which (assuming you know the tube material) could be used to compute the heat rate through the tube (radial resistance problem). This temperature difference is likely small, so the former method will probably give you better results.

Good luck,

Dave

 

[joedvo]

Dave41A,

I have already calculated the approximate temperature of the tubing to be 45 degF at the bottom of the tubing where the 10" space location and 53 degF at the 2" space location (on drawing, top view). These temperatures are a result of a calculated temperature distrubution via conduction through the frame and radiation from the shell. So this tubing is not and would not be at an ambient temperature of 40 degF.

The convection currents caused by the 216 degF shell (below the tubing) and the 40 deg ambient air should cause heat to rise, heating up the bottom surface of the tubing even more.

I have attempted to calculate the Rayleigh number to identify if the distance is in a laminar area or a turbulent area. I got 17,630 which indicates that it occurs in a laminar area. I have also attempted to calculated the Nusselt number and got 6.6, giving me a heat transfer coefficient of 0.201 Btu/hr*ft^2*degF. This is much lower than I expected since many references indicate a range of 1 to 5 Btu/hr*ft^2*degF for free convection in air . Even with this calculated "h" value, how is it applied if there are three temperatures involved; the shell, the ambient air, and the convection current air temperature? I am ultimately trying to calculate the heat (Btu's/hr) in the convection current acting on the bottom surface of the tubing.

IRStuff, I am looking into CFD software, but what I have read up on does not (at least) advertise a way to calculate all three forms of heat transfer, to include the heat generated by a convection current. Most of what I see is a way to model the fluid dynamics aspects of conduction. Nothing I saw modeled anything outside of the part or object, it seemed to be all internal.

I am still interested in a calculated method if anyone can assist.

 

[IRstuff]

Your calculated value does appear to be low, by a factor of at least 5, particularly given the high temperature difference between the source and the ambient air. You might want to compare your calculations to some online calculators, like:

http://www.efunda.com/formulae/heat_transfer/convection_forced/calc_lamflow_isothermalplate.cfm#calc

but there are numerous other ones.

I'm unclear about your statement about CFD. I personally don't use it, but most complex convection and airflow problems can only be done by CFD; see

http://www.mentor.com/products/mechanical/products/flotherm

as a reference

TTFN

FAQ731-376

 

[prex]

If I understand correctly your figure, the structural tubing is in open air outside the vessel. This means that a tiny, practically negligible, fraction of the air heated along the vessel will efficiently impact and transfer heat to the tubing. Almost all the hot air will flow past the tubing in the space between it and the vessel, as even a 2" space should be sufficient to let it go past (and if it wasn't, then the air flow would deviate, going where the gap is larger).
So my conclusion is that you are looking after a quantity that cannot be reliably modeled, even by using a sophisticated software.
Anyway you should start by studying the correlations for the natural convection from vertical surfaces in a book on heat transfer.
As an example of what I was stating above, my McAdams's Heat Transmission gives a graph on page 167 that shows that the air temperature in the flow near a vertical plate drops to ambient in a few millimeters and the velocity profile also has a peak at 2-3 mm distance from the plate and rapidly drops down. This would indicate that your structural tubing would not see any hot air.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes and launchers for fun rides

http://www.levitans.com

: Air bearing pads

 

[Dave41A]

joedvo:

If the tubing is in fact between 45 and 53 F, it will lose heat to the 40F ambient environment.

This assumes, of course, that the tubing is not within the boundary layer that will form on the tank surface. I have not done any computations on this, but prex seems to be on the right track: the boundary layer around the tank is most likely very thin (and very close to the tank), in which case the tubing would essentially be surrounded by 40F air.

So the sitation that you have is as follows: Heat is transmitted from the tank to the tubing via radiation, and then also from the tank to the air via free convection, and from the tubing to the air via free convection. Heat is also lost in the tubes via conduction: i.e. the tubes transmit heat along their length to whatever is holding them up. There would be no convective heat transfer from the tank to the tubes.

Also, on the size of "h," typical values are between 1 and 5 W/m^2K for free convection. I don't work in English units too often (so am bound to mess this up), but I get between about 0.18 and 0.9 BTU/hr ft^2 F as the equivalent values in English units.

Hope this helps,

Dave