Calculating water flow rate to achieve lower skin temperature

[Afterword]

Hi! I need some help with the following -

I have a square oven that has an outer shell of stainless steel (10mm thick) that has a skin temperature of 180degC. Outer shell size of each side is 800mm x 800mm. This has to be water cooled to bring down the skin temperature to 50degC. We need to provide a square stainless steel pipe (square coil size - 40mm length x 40mm breadth x 5 mm thick) of roughly 4000 mm overall length (per face, water cooling to be provided on all faces) through which water will pass. I need to calculate how much water / rate of flow in liters per minute to be passed to achieve desired skin temperature per face. We can consider temperature of water at inlet to be 25degC.

If any other details are required please let me know. Velocity of water (if required) can be considered as 1m/s.

 

[edgepflow]

I am note sure I can totally visualize your arrangement. Do you have a simple sketch?

 

[Afterword]

Sure, here you go -

http://img854.imageshack.us/img854/5831/coolingcoils.jpg


According to drawing, please find the edited query -

I have a square oven that has an outer shell of stainless steel (10mm thick) that has a skin temperature of 180degC. Outer shell size of each side is 800mm x 800mm. This has to be water cooled to bring down the skin temperature to 50degC. We need to provide a square stainless steel pipe (square coil size - 50mm length x 50mm breadth x 5 mm thick) of roughly 4500 mm overall length (per face, water cooling to be provided on all faces) through which water will pass. I need to calculate how much water / rate of flow in liters per minute to be passed to achieve desired skin temperature per face. We can consider temperature of water at inlet to be 25degC.

If any other details are required please let me know. Velocity of water (if required) can be considered as 1m/s.

 

[edgepflow]

OK, here is a simplified and approximate approach.

First, figure the amount of heat released by the hot oven plate without cooling.

Q-Total = h A (Ts - Tamb)

h = natural circulation heat transfer coefficent for flat plate. See any heat transfer text for this.

A = surface area = 800 mm X 800 mm
Ts = surface temperature = 180 degC
Tamb = temperature in room outside oven (maybe 30 C or so).

With Q-total, we can now "size" the cooling coils:

Q-total = U A (Tluid-avg - Ts)

Note: You could (and should) use a log mean temperature difference (LMTD). But for simplicity I just used an average temperature difference)

U = overall heat transfer coefficient. This will be controlled by the internal convection)

so,

Q-total = h A (T-fluid-avg - Ts)

You can figure h from an internal forced convection correlation such as the Dittus Boelter. They depend on the Reynolds Number: Re^n. This will let you figure out the flow rate.

A = area of pipe in contact with oven door.

T-fluid-avg = (Tin + Tout) / 2

And also an energy balance for the water in the pipe:

Q-total = mdot * cp * (Tin - Tout)

mdot = mass flow rate in pipe.
Of course, Tout should be less than 50 C.

You will have to iterate to solve all the equations at same time.

Sorry, I have to hurry to type this. Give it a try!

 

[Afterword]

Thanks edgepflow, this is a new topic for me so I'll have to start with the basics first.

However coming to the problem, when you say "natural circulation heat transfer coefficent for flat plate. See any heat transfer text for this. " - is there any source online where I can get this? If I get this I can follow through the problem and begin solving it.

 

[edgepflow]

Thanks edgepflow, this is a new topic for me so I'll have to start with the basics first.

However coming to the problem, when you say "natural circulation heat transfer coefficent for flat plate. See any heat transfer text for this. " - is there any source online where I can get this? If I get this I can follow through the problem and begin solving it.

The Churchill and Chu correlation is often used for this. This link:

http://en.wikipedia.org/wiki/Nusselt_number

Has a form of it under the section

Empirical Correlations / Free convection / Free convection at a vertical wall.

This link also has the Dittus Boelter correlation I mentioned that you can use for the water inside the tube.