# Calculating water flow rate to achieve lower skin temperature

• Afterword
In summary, the person needs help calculating the amount of water and rate of flow needed to cool a square oven with a stainless steel outer shell. The oven has a skin temperature of 180degC and needs to be cooled to 50degC. The solution involves providing a square stainless steel pipe with water cooling on all faces. The person will need to use heat transfer equations and correlations to solve for the necessary flow rate and mass flow rate. They may need to iterate to solve all the equations simultaneously. Additional details may be needed and a sketch of the arrangement is provided for reference.
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.

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

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.

Last edited by a moderator:
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!

Last edited:
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.

Afterword said:
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.

Last edited:

## 1. How is water flow rate related to skin temperature?

The water flow rate directly affects the skin temperature by regulating the amount of heat transfer between the skin and the surrounding environment. Higher water flow rates result in lower skin temperatures, while lower water flow rates lead to higher skin temperatures.

## 2. How do you calculate the water flow rate needed to achieve a lower skin temperature?

The water flow rate needed to achieve a lower skin temperature can be calculated using the formula Q = m*c*ΔT, where Q is the heat transfer rate, m is the mass flow rate of water, c is the specific heat of water, and ΔT is the desired change in skin temperature. This formula takes into account the amount of heat energy required to lower the skin temperature and the specific properties of water.

## 3. What factors can affect the accuracy of calculating water flow rate for lower skin temperature?

There are several factors that can affect the accuracy of calculating water flow rate for lower skin temperature, including the specific properties of the water being used, the ambient temperature and humidity, and the size and shape of the object or body part being cooled.

## 4. Is there an optimal water flow rate for achieving a lower skin temperature?

The optimal water flow rate for achieving a lower skin temperature may vary depending on the specific situation and desired results. In general, a higher water flow rate will result in a faster decrease in skin temperature, but it is important to consider other factors such as potential discomfort or safety concerns when determining the optimal flow rate.

## 5. Can calculating water flow rate for lower skin temperature be used for medical purposes?

Yes, calculating water flow rate for lower skin temperature is commonly used in medical settings for therapeutic purposes. It can be used to cool down the body in cases of fever or heatstroke, or to reduce pain and inflammation in injured or inflamed areas of the body. However, it is important to consult with a medical professional for proper guidance on the appropriate flow rate for specific medical conditions.

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