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# Heat Loss from Large Tanks

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## Heat Loss from Large Tanks

(OP)
Hi,

I try to model a sensible stratified storage tank by use of multi-node method (splitting tank into segments in 1D). At this stage, I am in focus on the heat loss from the storage tank (in fact from each of these segments).

So two case exists: (i) one idle period without charging or discharging so the stored medium loose heat to the environment, which I modelled by natural convection, and (ii) the other period is with charging/discharging, modelled by forced convection.

IDLE PERIOD - Natural Convection
I used the formulation 9-21 (shown below) from Yunus Cengel's heat transfer book for the natural convection: which is for vertical plates but stated to be valid for large storage tanks.

DIS/CHARGING PERIOD - Forced Convection
I tried the Nusselt correlations given in Correlations for Convective Heat Transfer. It doesn't matter which correlation I tried for laminar flows through the storage tank: at low flow conditions, the heat loss during dis/charging (forced convection) results in lesser value than natural convection! This does not sound correct to me! Asking you:

Is it possible physically to obtain a higher heat loss via natural convection when compared to a forced convection situation with the extremely low flow rate in a large cylindrical storage tank?

When I increase my flow rate, the forced convection becomes larger than the natural convection! The direction of flow was not included! Please see the observation results below:

System Description:
A storage tank at a diameter of 0.450 m and at a height of 5 m. Storage water medium at 60 °C and outdoor temperature at 20 °C. The total resistance (wall material, insulation, outer casing) is 2.54 °C/W.

Natural convection at idle periods results in: Qloss_natural=132.7 W

For a maximum charging rate at 0.0819 kg/s (5 liters/minute) ~ Re=103 [-]. At this maximum flow rate (5 l/m - 0.0819 kg/s) heat loss at forced convection was found to be Qloss_forced=89.1 W

Now pushing to upper flow rates just to see how forced convection changes the overall heat loss (the maximum flow is given as 5 l/m - 0.0189 kg/s cannot be exceeded normally!):
At a flow rate of 0.05 kg/s (Re=287) Qloss_forced becomes 108.5 W.
At a flow rate of 0.5 kg/s (Re=2890) Qloss_forced becomes 111.7 W.

Another question: Can any of you correct me that if these Nusselt correlations can be used for large storage tanks?

Thanks in advance. Regards.

“In life, the truest guide is science” – Mustafa Kemal Atatürk

### RE: Heat Loss from Large Tanks

"Simulation" using two different equations that begin by making dozens of different assumptions for two different conditions inside the tank DOES NOT equal two comparable heat exchange values.

First, switch the two assumed conditions. Do both filling and stagnant heat exchange conditions using both equations. You will end up with four heat exchange calc's. Repeat using highest external temperature and wind speed (I think you are cooling down the tank's liquid - but you didn't tell us ANY actual liquid temperatures, pressures, nor external conditions!), lowest external conditions for the four results.

More important, what is the fill rate of the tank? A few centimeters per minute? (change in height of fluid per second of fill time is what matters.)

Do you really think the wall of the tank is fully turbulent compared to statically near-laminant when the overlap between the two fluid flow states is a bloody mess of of unpredictable random values in the mix between the two conditions - for both fluid flow and heat transfer?

### RE: Heat Loss from Large Tanks

Dynamic Thermal response may be more important anyway: Depending on initial and final temperature, and tank size and fluid flow rate and length of the pipe (?) from temperature 1 to temperature 2 (initial temperature of the tank, ground, pipeline, and ground/air/insulation of the tank and pipeline), the fluid may need a lot of energy just to heat up the tank walls and floor, ground under the tank, and ground around the fill pipeline.

Or maybe not. Once the bottom of the tank is covered new fluid that has begun heating up the cold (?) tank and foundation, the newly arriving fluid must heat up the now-cooled fluid in the tank. If you fail to check your thermal mass dynamics of heat loss as you fill, you will not know if this part is important, or is trivial.

I suspect the two wall flow assumptions between natural convection and forced convection during the comparably rare times of actual tank fill are also minor compared to total mass heat loss over time after the tank is filled.

### RE: Heat Loss from Large Tanks

There's something wrong with your math. You claim you got a natural convection heat loss of 132.7kW, with a surface area of about 7.2m^2, which results in 459W/m^2-K, assuming ALL the temperature difference is dropped in the air. That's basically impossible, unless you're modeling the heat loss in a windstorm. Natural convection heat loss is on the order of 7-10 W/m^2-K.

Your units for wall resistance is incorrect; it should have units of m^2-°C/W, otherwise your numbers are even more nonsensical. Assuming that it's m^2-°C/W, and the same 7.2m^2 area, your maximum wall loss is only 113 W. at a 40°C temperature delta. Since you must have some temperature drop to the air from the outer surface, your natural heat loss must be less than 113 W. Using 10 W/m^2-K, and the numbers above, your natural convection heat loss is about 110 W.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: Heat Loss from Large Tanks

Also a storage tank of 0.45m x 5m is NOT a large storage tank but simply a 5m long piece of 18" pipe. Think of a reasonable sized domestic radiator....

At that volume with no movement, temperature of the water will fall and hence heat loss is not a fixed figure. Either way 130kW is way too big.

I'm not sure that the convection that was meant was the internal water circulation and yet ther eis nothing about external air movement / velocity etc.

what sort of insulation does this thing have?

How big is it really?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Heat Loss from Large Tanks

(OP)
`Thank you for your time mates.

Sorry my mistake: I fixed my typo, so all previously given heat loss values are in W level, not kW.

Description of the system: This is a storage tank used in houses for domestic hot water circuit (also known as hot water tank at the building substation at district heating systems). So the purpose is to keep the stored medium hot not to allow cooling. So the tank is insulated with PU foam and also there is an outer casing of PVC material.

Better to give results for the calculated thermal resistances:
i) idle time - stagnant water at 60 °C, outside air with no wind at 20 °C, height of tank at 5 m: inner convective part Rconv,water = 0.84345, Rcond,steel=0.00703, Rcond,PU=252.955, Rcond,PVC=1.2031, and Rconv,air=46.394 (all in °C/kW)
ii)dis/charging at a flow rate at 0.0819 kg/s, water temperature at 60 °C, air temperature (no wind) at 20°C, height of tank at 5 m: Rconv,water=40.35, and Rconv,air=47.827 (all in °C/kW) - The other conductive thermal resistences (for steel, PU, and PVC) stay same.

I think that I found an answer to my problem. Since the tank height when assumed as 5 m, the natural convection results higher than the forced convection. When I select a smaller height for the segment (reasonable with the multi-node approach, dividing tank height into segments through its height) i.e. 0.05 m; this time the forced convection becomes smaller than the natural convection. Height is a major factor on the overall heat transfer when considered for natural convection. So at long heights, the natural convection can be higher than forced convection: What is your comment on this?

“In life, the truest guide is science” – Mustafa Kemal Atatürk

### RE: Heat Loss from Large Tanks

Sorry, I think you still have mistakes elsewhere. The number quoted for your "natural" convection is already the worst case, since your water temperature is assumed to be constantly at 60C on the inside wall. Moreover, in cases where the water is moving, your volume is changing, which means that you cannot possibly at the maximum volume case for the non-moving water, which automatically means you are losing less heat, simply because you have less water.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: Heat Loss from Large Tanks

I don't think that your flowing condition can be classified as "forced convection"

A hot water tank in a domestic system normally incorporates a heating coil or element in the tank. Is this the case here?

I think you need to draw your system and then see if the correlations you're using are actually valid. E.g. if the water flow is stationary, where is the driving force coming for "natural convection"?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Heat Loss from Large Tanks

(OP)

#### Quote (IRstuff)

1)...since your water temperature is assumed to be constantly at 60C on the inside wall...
2)...your volume is changing...

1) The surface temperature both at the water and air-side changes as to the heat loss (iteration carried out)
2) I didn't consider volume change for the sake of simplicity. I will result in Nusselt correlation to avoid the implicit surface temperature calculations at a later stage. My storage model has to be quick so I can model huge amount of building substations.

#### Quote (LittleInch)

1) I don't think that your flowing condition can be classified as "forced convection"
2) A hot water tank in a domestic system normally incorporates a heating coil or element in the tank. Is this the case here?

2) We are working on a totally stratified storage tank without auxiliary heating unit so the DH water will be stored directly in this storage tank; so this is the means of storing the heat.
1) Would you please tell me why I cannot consider the forced convection during charging or discharging process? There is forced flow through the tank during charging. Do you mean that the flow is too slow that cannot be counted as forced flow?

Regards.

“In life, the truest guide is science” – Mustafa Kemal Atatürk

### RE: Heat Loss from Large Tanks

I think you are still misunderstanding my numbers. Assuming that your water is no more than 60C, the ABSOLUTE worst case heat loss is 110 W, regardless, since assuming a constant 60C inside wall temperature is as good as it gets for heat transfer; you cannot get more heat through the wall and through the air, as my previous comments indicate:
> 60C inside wall, 20C outside wall --> 113 W -- this ignores the air

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: Heat Loss from Large Tanks

"DH" water? Direct heated?

Anyway Ok your water enters at some fixed temperature (60C?)

2) In part yes, but what I interpret as forced convection is a pump which circulates the fluid from one end to the other by "forced" means.

It strikes me that if your tank is vertical and no flow you will have the hottest water at the top and the coldest at the bottom and no natural convection within the tank, no?

Something like this?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Heat Loss from Large Tanks

At 113 W loss, it'll take 8 hrs to lose 1 degC, so if the cycle time of the water is much less than that, the temperature is pretty much at 60C all the time.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: Heat Loss from Large Tanks

Fair enough. That's some decent insulation.

Therefore there won't be any natural convection in the water in that case either.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Heat Loss from Large Tanks

In my experience, if you have a decent insulation thickness, heat loss is by far dominated by insulation losses + (external convective + radiative losses at the insulation cladding surface). So it doesnt matter what happens on the inside of the tank, unless you're dealing with some viscous fluid. Assume zero resistance to heat transfer on the inside for water.

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