# Stainless steel cooling container, need some help with the maths

1. Apr 15, 2013

### si-83

Hi guys, i'm designing a cooling device as part of a project and need a little help with the maths.

OK, so the scenario is this, take boiling water, put it in a stainless steel container with Thermal Conductivity of 8.7 Btu/h ft °F and dimensions of 15.811cm x 15.811cm x 1 cm to store 250ml of water with a wall depth of 4.7625mm.

What i'm struggling to find out right now is how long it will take to cool the water to 20c.

I'm looking to cool the water as quick as possible so i'm looking at a passive system as described above and then to implement a forced system and add fins to both sides to improve heat transfer rate. I've got to cool the water to room temperature in around 7 minutes and the maths is killing me even to figure out the passive system so i guess with a heat sink type design and implement a forced air flow it's going to get even worse but i'm hoping you guys are in the mood to be helpful if you can.

2. Apr 15, 2013

### Travis_King

3. Apr 15, 2013

### si-83

Thanks i've tried this equation but end up with a figure that seems too large.

heres my workings

energy difference of 250ml of water between 20 and 100 degrees= 83600 J

8.7 Btu/h ft. °F - watt/meter/K [W/(m·c)]= 15.47

area of container = 563.219cm^2

depth 4.7625mm

A = 5.63219m^2

k = 15.47 w/(m*c)

dT = 80

s = 0.0047625m

Q=1424590.431 watts?

So that means that i'm transfering 1424kj/per second? which means that the water will cool in 0.059 seconds?

4. Apr 15, 2013

### Travis_King

Well, first off, check your surface area calculation. You are finding the area of the material contacting the water. If it's a box, you have 4 sides plus a top and bottom. Keep units consistent.

5. Apr 15, 2013

### si-83

ahhhhhh, thats quite a big typo..... thanks so now i'm down to .0563244m^2 i'm getting 14245.904 watts which makes takes me up to 5.868 seconds. still seems pretty low.

The surface area i found by taking the two larger sides 250cm^2 each and then the other 4 sides 15.811cm^2. 563cm^2.

6. Apr 15, 2013

### Travis_King

Plus, as I said, that's just a starting point. Here's another couple:

Heat Transfer Look at the insulated box example.
HTC You'll need to figure out the Heat Transfer Coefficient, too.

7. Apr 15, 2013

### Travis_King

It should also be noted that just filling a box with water isn't exactly the best way to transfer heat. Typically you want the fluid to be flowing over the contact surface for good heat transfer.

8. Apr 16, 2013

### SteamKing

Staff Emeritus
And here's another tip: 1 m^2 = 10000 cm^2, not 100 cm^2.

9. Apr 17, 2013

### si-83

Thanks guys so i've got down that if i use it in a well ventilated container it will take around 12 minutes and if i use a fan to help with forced convection it will take around 3, thats using fouriers law and a heat transfer coefficient of 21 and 100 for the air respectively and a heat transfer co-efficient of 0 on the water side. sound about right?