Forced or Natural Convection?(Storage Tank) 1

[ONEPOINT]

Hi

I am doing heat transfer calculations for a 71'-0" height and 250'-0" diameter oil storage tank.The tank is not insulated and the roof of the tank is a floating type one that moves up and down with the level of the fluid in the tank. The peak velocity of the air outside the tank is 14 m/s. For the cooling stage, I have considered free convection inside the tank due to the buyonacy forces and turbulent forced convection outside of the tank due to the wind velocity. I have also calculated heat transfer(conduction mode) through the shell,roof and the bottom walls as well as the conduction from the bottom through the soil(conduction through a semi infinite solid)...

In the second stage(heating and mixing process),the oil is pumped out of the tank, heated with a heater until reaches 0C and then pumped back into the tank. The ambient temperature is -35C. The whole process takes about 5 days.

There are also jet mixers attached at the nozzle.The velocity of the oil in the middle of the tank(centre volume averaged velocity) is 0.18 m/s and the flow rate is 1000 m^3/h.

I am not sure if for the above mentioned conditions, there is a forced convection or natural convection in the tank? If there is forced convection, how could I calculate the convective heat transfer coefficient inside the tank?

Kindly Regards,

One Point

 

[torpen]

Hello,
For your first question, you can calculate the following ratio Gr/Re^2.
Free convection is negligible if Gr/Re^2 << 1
Forced convection is negligible if Gr/Re^2 >> 1
Mixed convection for Gr/Re^2 ~ 1

Regards,

Torpen

 

[Montemayor]

Torpen:

There are so many Numbers in Fluid Flow and Fluid Mechanics .... Do you mean the Grashof Number (Gr) and the Reynolds Number (Re)?

If so, where are these relationships in convection found or referenced to? In a specific Fluid Mechanics text book?

Thanks.

 

[torpen]

Montemayor,

Yes, these numbers (and the Prandtl Number Pr) are used to calculate the Nusselt number Nu by mean of empirical correlations.

NuL = f(L, ReL, Pr) for forced convection
NuL = f(L, RaL, Pr) for free convection
with,
L : characteristic length
k : thermal conductivity
RaL : Rayleigh number (by definition RaL = GrL * Pr)

With the Nussel number Nu you then obtain the convection heat transfer coefficient h [W/(m2.K)].

NuL = (h * L) / k
L : characteristic length
k : thermal conductivity of the fluid

The numbers ReL, RaL, GrL, Nul are based on the characteristic length L of the geometry.

You can find a definition of these numbers in the following book :
"Introduction to Heat Transfer", Franck P. Incropera, David P. De Witt, 4th Edition, John Wiley & Sons, 2002.

Regards,

Torpen

 

[ONEPOINT]

Hi Torpen,

In your reply you have mentioned about the following ratios:

Gr/Re^2 << 1
Gr/Re^2 >> 1

In the Gr and Reynolds formulas, there are a couple of terms regarding the properties of the fluid. Where are those properties taken? Are they considered in the bulk of the fluid or at the wall?

Through a process of iterative method I have got the temperatures of the fluid at the wall. These wall temperatures(or film temperatures) are not known initially, so one has to resort to an iterative method in order to get the values from them.

The Nuselt number expression that you mentioned(NuL = (h * L) / k) is used in for natural convection only or it is also used for forced turbulent convection situations?

When you say characteristic length Lc, what do you mean by this length? In this regard(as what Lc should be))is there any difference between the vertical wall(shell) and the floating flat cylindrical roof of the tank?

When I have calculated the heat loss for the shell,I have used the height of the tank as L in the Gr. expression, but when I have calculated the heatloss for the roof of the tank and at the bottom of the tank, I have considered the characteristic length Lc in the Gr.expression(Lc=D/4)...That was for the inside of the tank.

As for the outside of the tank(wind velocity =14m/s),when I did the calculations at the roof for the forced convection,I have used a completely different formula for the Nuselt number, then the one that you mentioned in your reply.That formula was for turbulent flow regime and forced convection. In that formula one of the terms was Reynold number.The roof being a circulat flat plate, I have considered again the characteristic length in the Reynolds formula. The properties considered were at the outside roof wall(film)temperature.

So considering all the above mentioned data, could you tell me, where do I have to considere those propertios in order to calculate the ratios that you have written in your reply?

Regards,

One Point

 

[quark]

Nusselt number correlation is valid for any type of convection. You have emperical correlations for Nusselt number, in convective heat transfer, and then you calculate convective coefficient value using the h and Nu equation.

Characteristic length is what you consider as a boundary for a given condition of heat transfer. For ex. if your tank is half full, then the vertical heat transfer is split into two parts. The characteristic length in the first part is liquid column height and the values are to be calculated according to the conditions of liquid section. The characteristic length of the gas phase is (total tank height - liquid column height)

All the properties are to be calculated at average of wall and bulk temperatures (i.e Tw+Tb)/2

Incase of vapor phase, Beta is to be calculated at air temperature.

Top roof should be considered as flat plate and diameter should be treated as length.

There is an excellent paper titled Predict storage-tank heat transfer preciselyby Jimmy Kumana et al appeared in March' 82 volume of Chemical Engineering Magazine. The method given in the paper considers only natural convection upto 35 mph (15.6 meters/sec). I highly recommend you to have a look into it.

However, Torpen is right about the condition for natural and forced convections. Incropera and Dewitt dealt with this in detail.

 

[torpen]

Hello,

Empirical correlations indicate at which temperature are evaluated the fluid properties (often at the film temperature).

The Nusselt number is by definition equal to the dimensionless temperature gradient at the wall.
The equality NuL = (h * L / k) is valid for free, forced and mixed convection.

The characteristic length L is specified by the choosen correlation.
For average Nusselt numbers and internal flows it is equal to 4*A/P where A is the flow cross-sectional area and P is the wetted perimeter (for circular tubes L = D).
For average Nusselt numbers and external flows it is equal to A/P where A is plate surface area and P is the perimeter.
For local Nusselt numbers L is the location on the surface.

You can proceed as follows to calculate heat transfer coefficients from empirical correlations:
- Identify the flow geometry (external/internal flow, plate, cylinder ...)
- Choose between average or local heat transfer coefficient
- Find possible empirical correlations (laminar and turbulent)
- Consider the characteristic length used in the candidate correlations
- Calculate the reference temperature specified by the candidate correlations (film temperature for example)
- Calculate the fluid properties at the reference temperature
- Determine wether the flow is laminar or turbulent by comparing the Reynolds number or the Rayleigh number to a critical value
- Select the appropriate empirical correlation according the nature of the flow (laminar or turbulent)
- Calculate the Nusselt number from the choosen correlation
- Calculate the heat transfer coefficient

For the internal convective heat transfers (for all convective heat transfers) the choice of L depends on the choosen correlations.
I think that for the heat transfer between the fluid and the shell L would be equal to R.
And for the one between the fluid and the floor L would be the height of the tank.
To be confirmed with the selected correlations.


To calculate the Grashof number (ratio of the buoyancy force to the viscous force) you need :
- the difference temperature (Ttank_1 - Ttank_2)
- the characteristic length (heigth for the roof or radius for the shell)
- the fluid properties evaluated at the average temperature (Ttank_1 + Ttank_2)/2

To calculate the Reynolds number you need :
- the velocity
- the film temperature
- the characteristic length (here not easy to define
- the fluid properties evaluated at the film temperature


To determine the forced convection on the roof you apply the proposed methodology :
- external flow on a horizontal circular flat plate
- average heat transfer coefficient -> NuL
- characteristic length : L = A/P = D/4
- laminar or turbulent flow?
turbulent flow if L >> xc (ReL > Rex,c = 5E5)
where xc = viscosity * Rex,c / velocity
- if the flow is laminar : NuL = 0.664 * ReL^1/2 * Pr^1/3 (Pr > 0.6)
- if the flow is turbulent : NuL = 0.037 * ReL^/45 * Pr^1/3
- all fluid properties evaluated at the film temperature

For the shell in cross flow of air, Hilpert has proposed the following empirical correlation :
NuD = C * Re^m * Pr^1/3
where the constants C and m are listed in a table in function of ReD.
All properties are evaluated at the film temperature.


Regards,

Torpen

 

[ONEPOINT]

Hi Quark,

Thanks for your answer. Regarding the calculation of heat rate loss from or to a circular flat plate, some heat transfer text books, recommend for the Grashoff formula and convective coefficient formula, to use Lc(characteristic length) instead of the diameter. Lc being = D/4.

You have mentioned in your reply that "Top roof should be considered as flat plate and diameter should be treated as length." I have got that article that you have mentioned about, and I have noticed that the authors have used diameter instead of Lc in their calculations for Grashoff and convectice coefficient expressions.

As I have said above, some textbooks (Heat Transfer by J. Holman) recommend the use of Lc=D/4 for Grashoff and h(convective coefficient).

So which option is the most approapiate for the calculations of heat loss through a circular floating plate roof? The one with Lc=Diameter in the or one with Lc=D/4? I look forward for a reply into this matter.The results in terms of heat rate loss is quite significant...

Regards,

One Point

 

[quark]

Lc = D/4 (or A/P) would give you accurate result. However, I saw calculations using D and 0.9D also. Though, Grashoff number increases by sixty four times, if you go with L=D, Nusselt number increase by about 2.5 times and convection heat loss estimate may increase by about 25% (worst case).