Cooling down a storage tank with commodity 1

[daviddor]

Hii everyone,
since the last post was gone, don't know why actually, i have some more issues so i will ask here.
So we have a storage tank with a ton of fruits, i know all the data inside and outside including materials . Besides the respiration heat, that i know already, if i want to keep the tank in let's say 10c , the outside temperature and the fruits temperature are 30c , obviously the fruits temperature will change with the time. How much power do i need to keep it 10c for 2 hours. Note that i don't want to change the temperature of the fruits completely but just keep the environment at a certain temperature .
Thank you very much

 

[LittleInch]

The thing I'm not understanding here is how the fruits are laid out in this mysterious box and where and how the air flow is going. A drawing or sketch would help enormously.

There is a vast difference between a whole bunch of fruit randomly filling a box with only small air gaps around them and say a small grill in one corner of the box with an exit at the other corner and something like a commercial chiller cabinet with fruit laid out on trays allowing cold air to circulate around all the individual fruits.

So which is it?

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

 

[daviddor]

At the moment its a bunch of fruit randomly filling a box with only small air gaps around them as the worst case scenario. That is why i am gonna do the calculation few times assuming different spheres sizes as like the mangoes are connected. but the first calculation for one mango ...

 

[FMJalink]

Hi daviddor,
Now I see two errors in my previous posting:
- Addressed it to pierreick, as I was in the meantime reading his posting, and
- made an error in the heat convection formula, which should have been Nu = f(Pr, Re, mu).

Re-evaluating the matter, I think following points are important to your problem:
- The formula used for heat convection on the outside of the sphere is for a “free” sphere in a homogenous (air) flow. Having here a packed bed with “spheres”, the opening between the spheres will be more characteristic.
- With the spheres packed in the tank, only a part of the sphere outside will be in contact with the air.
- The method used for the heat conduction inside the sphere is for low Biot numbers. With higher Biot numbers, the approximation of a homogene internal sphere temperature is no longer valid. This is quite important for your heat convection on the outside of the sphere.
- A packed bed of spheres has a substantial pressure drop. I think the remark made above on the 2 m/s air velocity is quite spot on.
- In case you change the method, keep in mind that temperature and heat flow on the outer surface of the sphere are not free, but have a relationship.

I hope this will help you.

 

[georgeverghese]

300-400w/m2/degK for ho on the surface of the mango with air as the cooling agent? That must be way too high.

 

[daviddor]

Yeah so i think this is exactly what makes the h convective so high, high velocity means high Re means High Nu means High h. Maybe in a fridge especially when the fruits are arranged in a big pile i can assume natural convection like 30[W/m2*s] . the air goes out from the fan at 2[m/s] maybe but doesn't reach the fruits at that intensity .

FMJalink and georgeverghese what do you think?

 

[georgeverghese]

Agreed, most of the surface of each of the mangoes will be in "dead ends", not in the direct path of cooling air flow, so ho derived from natural convection correlations may be a safer assumption.

 

[FMJalink]

Hi daviddor,

Appears you have used the thermal conductivity of the mangoes, instead of that of the surrounding air, in the convective heat transfer calculation of the sphere. You will get than a more realistic heat transfer coefficient. The Biot number will still be high, which means that the outside of the sphere cools faster than the inside of the sphere. The heat conduction inside in the sphere is limiting.

I wish I could help you more, but that is at this moment quite difficult, as I am on my holiday location and do not have access to the means I normally have available.

For a good approach a numerical modelling appears required. There the blinded outside surface parts and not symmetric heat flow should be somehow taken into account. I did try to start with a symmetrical approach, but one finger typing on this tablet appeared already a real challenge.

Kind regards,
FMJalink

 

[daviddor]

FMJalink no worries, every help is appreciated. I will come up with my final results and post them here, thank you very much

 

[daviddor]

Characteristic length of a sphere is not D/6? means V/A. Don't know why they are using r here for Bi and also for Fourier number.

Also after i found the temperature in the center , how can i find the distribution inside the fruit?, Since at the end i want calculate the total heat transfer from the apples Q=mCp(t2-t1). And the temperature t2 is not uniform inside.
**For this i found "Heisler charts" i think its good

Thank you very much

 

[FMJalink]

Hi daviddor,
There is an analytical method to determine the temperature development inside a sphere:

http://demonstrations.wolfram.com/TransientCoolingOfASphere/

If you calculate heat flow on the outside of the sphere you get an impression of the heat released by the sphere. Due to the higher Biot number it takes a substantial time for the sphere center to cool down, where as the shell is already on a low temperature. The shell temperature will determine the heat release to the surrounding air and touching spheres.

Do not know your starting points, budget available and means available, but your earlier question formulation having fruits packed stapled in a tank seems to me not a good idea.

A thermally insulated container or room with entrance doors is much easier for the fruit handling e.g. on trolleys, and allows the fruits to be spread out in boxes or trays allowing the cooled breeze to get to the fruit surface. You can find on the internet a lot of examples searching for blast cooling / freezing. Also can such rooms/containers and blast chillers be purchased as a unit.

Keep in mind that different types of fruit have different minimally allowed low temperatures and that you will have to know the desired cooling down temperatures at the start of your engineering.

 

[daviddor]

Hii everyone,
So after finishing with the calculation I mostly realized that if i put for example mango in an atmosphere of 10c for 2 hour , it's whole body will change also to 10c so then , calculation of heat transfer would be simple Q=mCp(T2-T1).
for 1 ton of mangoes for example 60 [megajoul] or 57000 btu. Not including leakage and respiration which are a quite small amount.

i want to discuss now about the setting of the cooling system. So our cooling system consists of a vessel that mixes air with Co2 and discharges a cold air( with extra co2) . The maximum power of this system would be discharging air at -20c at a flow rate of 300[liter/min] .Of course in the future we can change the size and the power of the system . So first of all my idea is to use the air from inside the tank to mix it with the co2, because it's cooler so I'll need less energy for that. Then how to locate the pipes coming out from the vessel, whether from the side or from the bottom .And installing a fan with the same amount of flow rate on the opposite side. I can also stretch pipe lines inside the tank in between the fruits packages. I will draw the 2 sketches :

Any other thought on the system would be appreciated , thank you very much.
And btw the fruits eventually going to be arranged in boxes with small gaps in between .