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# Natural Convection Heat Transfer Coefficient Inside Storage Tanks

heat transfer natural convection floating roof storage tank roof underside floor topside roof toside

12 replies to this topic
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### #1 smrastgou

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Posted 05 December 2018 - 06:44 AM

Hi everyone,

I’ve got a query about calculation of heat transfer coefficient for natural convection inside floating roof storage tanks. Could you please help me to resolve this conflict?

In order to determine the overall heat loss of a single deck floating roof, I’m trying to calculate the heat transfer coefficients for natural convection of inside surface of the roof (hvr) and inside surface of the floor (hLB) as per article, “Predict Storage Tank Heat Transfer Precisely - By J.Kumana and S.Kothari”.

The article suggests applying equation 20 for facing down horizontal surfaces (Roof Inside), Nnu = 0.27 x (NGr NPr)0.25 and equation 19 for facing up horizontal surfaces (Floor Inside and Roof Outside), Nnu =  0.14 x (NGr NPr)0.33. However, comparing these formulas and their applications with other heat transfer books like “Heat Transfer by Holman” – Refer table 7-1, P. 334, it is understood the application should be reversed. i.e. apply equation 20 to upper surface of a cooled plate (floor inside and top side of roof) and apply equation 19 to lower surface of cooled plate (roof inside). As the fluid temperature is always higher than roof and floor plate temperatures, the roof and floor plates are considered as cooled plate when calculating the heat transfer for inside of the tank, however roof plate could be considered as hot plate when we calculate roof outside coefficient as surface temperature higher than air temperature.

Since the single floating roof fully contacts the product, the heat loss through roof is significant and misunderstanding of application of these formulas obviously has an outstanding effect on total heat loss estimation.

Could you guys please clarify to me which formulation should be applied to roof underside and which should be applied to floor top side?

Many thanks,

smrastgou

### #2 Art Montemayor

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Posted 05 December 2018 - 06:51 PM

Smrastgou:

The Kumana/Kothari article you have uploaded is one that I transcribed from the old, original magazine article to Word for Windows back around 9-1/2 years ago.  I did this in order to avoid losing the valuable information I thought it contained.  I shared it with our Forum members then and it generated a very profitable Forum topic that involved an experienced and very charitable member, Enrico Lammers, who took it upon himself to convert the contents of the article into an engineering calculation sheet for the heat loss of a vertical, fixed roof storage tank.  As I recall, both the Kumana/Kothari article and Lammers’ calculations were based on determining the heat loss incurred in a vertical, fixed roof storage tank.  What does these calculations have to do with what you call a “floating roof storage tanks”?

The two are very different types of storage tanks and you fail to identify exactly and specifically what type of floating roof storage tank you are referring to.  There are basically two different types of floating roof storage tanks - as you probably know (or don’t know): an external floating roof type and an internal floating roof type.  We probably are safe in guessing that you are referring to an internal floating roof type - but you should definitely state ALL the correct and specific basic data if we are to understand what you are writing and requesting.  It isn’t fair to our members to feed them crumbs of information and expect a reasonable, helpful, and correct response.  The quality of the responses will be in accordance with the quality of the basic data supplied.

Please furnish a detailed sketch of the heat transfer you are trying to describe inside the (internal?) floating roof storage tank so our members can fully identify the type of heat transfer and areas of what you call “natural convection”.  For example, if we are dealing with an internal floating roof storage tank, the construction could be a closed floating roof storage tank (CFRT) - a design variation similar to the basic internal design.  It uses an internal floating roof but eliminates natural ventilation of the tank vapor space.  Instead, the CFRT is equipped with a pressure-vacuum (PV) vent and may even include a gas blanketing system such as that used with fixed roof tanks.

An internal floating roof storage tank further reduces roof and partial wall heat transfer losses due to the gas phase layer between the fixed roof and the internal floating roof deck that has an inherent heat insulation effect to the heat transfer expected through the floating deck inside the tank.  Are you referring to potential natural convection currents over the floating roof?  Kindly dedicate some work to being specific and detailed in your explanation(s) and always furnish a sketch to further explain exactly what areas you are alluding to inside the tank.  Engineering drawings are the common language of all engineers and need no translations or explanations when done properly and in detail.

If you supply our members with applicable, detailed, and specific information you will find that they will reward you with applicable, detailed, and specific responses.

### #3 smrastgou

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Posted 05 December 2018 - 08:35 PM

Hi,

The type of storage tank that I'm dealing with is external single deck floating roof (there is no fixed roof above the floating roof and the deck plate is only 6mm steel plate contacts the content fluid). The only difference between this tank with the one is solved as an example in the article is I'm dealing with fluid under the roof and the example is dealing with vapor under the roof.

The question is am I correct to apply formula 20 of the article to roof underside heat convection coefficient as per solved example, while according to heat transfer books formulation like the one I attached, this equation is only applicable to upper surface of a cooled plate or top side of hot plate which refers to floor plate of the tank rather than roof plate?

Regards.

### #4 PingPong

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Posted 06 December 2018 - 08:58 AM

Formulas 19 and 20 from the article are taken from reference 8, which is Perry 5th edition.

There a formula like 19 is indicated for Facing Upward (FU) when 2*107 < Ra < 3*1010

and a formula like 20 is indicated for Facing Downward (FD) when 3*105 < Ra < 3*1010

Perry 5th edition does however not indicate whether that is for hot or cold surfaces.

In view of other publications, including later edition of Perry,  it must however be for hot surfaces.

Perry 8th edition is clearer and gives for hot surfaces facing upward, or cold surfaces facing downward:

Nu = 0.54Ra1/4 for 104 < Ra < 107

Nu = 0.15Ra1/3 for 107 < Ra < 1010

and for hot surfaces facing downward, or cold surfaces facing upward:

Nu = 0.27Ra1/4 for 105 < Ra < 1010

There are many sources that give formulas in the form Nu = a.Rab for natural convection,

often with different values for a and b and for different ranges for Ra.

It's not an exact science.

### #5 smrastgou

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Posted 06 December 2018 - 05:42 PM

Thanks a lot PingPong for guides.

Your explanations confirms my understanding of the application of the formulas. This means to me comparing to current books and references, these formulas are misapplied in the worked example of the article.

My calculated Ra is about 1.2e15 which is much higher than recommended range of application of these formulas. I used characteristic dimension rather than diameter to reduce the value, but it didn't help much. In all references that I've got, the formulas only cover up to 1e11. Do you know of any reference books or article that stretch the ranges to higher Ra than 1e11.

Regards.

### #6 PingPong

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Posted 07 December 2018 - 06:03 AM

Do you know of any reference books or article that stretch the ranges to higher Ra than 1e11.
Not that I remember.

But are you sure that in your case Ra is really as high as 1.2e15 ?

What values and units of measurement did you use for the parameters in the formulas ?

### #7 breizh

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Posted 07 December 2018 - 11:27 PM

Hi ,

Consider the reference attached to support your work.

Breizh

### #8 smrastgou

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Posted 08 December 2018 - 12:53 AM

Thanks Breizh for introducing the reference book.

This text book like others develops the natural convection heat transfers over horizontal flat plates up to Ra < 3E10 which is much less than my case Ra number of 1.2E15.

Regards.

### #9 smrastgou

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Posted 08 December 2018 - 01:21 AM

This is a crude storage tank with 78m dia x 19m High - single deck external floating roof. It is supposed to keep the product' temp in 40 ºC where ambient temp is 5ºC and wind velocity is 21 Km/Hr.

Crude Properties:

Density =  860 kg/m3

Volumetric Expansion = 0.00075 1/ K,

Viscosity = 0.0145 kg/m.s,

Thermal Conductivity = 0.1322 W/m K,

Specific Heat = 2030 J/kg K,

g = 9.81 m/s2

Characteristic Length = 19.5m,

Npr = 222.65,

Liquid temperature = 40 C = 313.15 K,

Wall Temperature: 1st trial =22.5 C = 295.65 K

Diff. Temperature = 17.5 K,

Ngr = 3.36e12,

Ra = 7.48e14.

Regards.

### #10 breizh

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Posted 09 December 2018 - 07:11 AM

http://www.lv-soft.c...tanks.tank..htm

Hi ,

you may consider the resource above , they offer a try option and there is an example which could help you and others.

Using your favorite engine you may find other software.

note : I did not find other correlation with extended range of Ra.

good luck.

Breizh

### #11 PingPong

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Posted 09 December 2018 - 10:13 AM

Ngr = 3.36e12

Ra = 7.48e14

That is correct for the parameters that you used.

I suggest you use the above correlations also for this high Ra number.

The fact that the researchers did not take Ra numbers higher than 1011 into account does not necessarily mean that the correlation will be less accurate at your Ra number. In any case that sort of correlations are not very accurate anyway.

If you are calculating heat loss to determine size of tank heating coils then you should apply a safety factor to the total heat loss so as to assure that it will maintain the required oil temperature not only in theory but also in the real world.

### #12 smrastgou

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Posted 09 December 2018 - 06:15 PM

Thanks Breizh and PingPong for caring and helpful guides.

I checked the software. It seems it doesn't calculate the heat transfer coefficient for inside of the roof.

Thanks anyway.

### #13 HelioMagalhaes

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Posted 10 June 2021 - 07:40 PM

Hi, I attached the original article!