I wish to manually calculate the flow rate of water required to cool a cylindrical cup shaped object which is being heated by 10kW beam? Can anyone tell the equations or methods to calculate the flow rate.The geometry is attached in the figures.I need to put cooling pipes around it.But for an estimate I need a theoretical calculation.
Please look at this interesting Book it can help you.Good luck
Introduction to Heat Transfer, Sixth Edition
Theodore L. Bergman, Adrienne S. Lavine, David P. DeWitt, Frank P. Incropera
http://bookzz.org/book/1181859/cee99a
You need to extract the 10 kW of energy by the water. The water in the pipes will be heated up by the 10 kW in steady state, so you can already calculate the temperature rise of the water equating the energy influx. dT=10 Kw/(water mass flux*specific heat).
You need also to transfer the energy to the water in the pipe. The heat transfer coefficient can be calculated for turbulent flow from correlations given in heat transfer books (see comment from Zoubair) and the heat flux / area is the heat transfer coefficient times the temperature difference.
Please note that the water temperature along the tubes will rise, so either the heat flux will drop or the wall temperature will increase. From your drawing I do not fully understand the heat flux distribution from the beam. Is it on the inside, what is the distribution of heat flux to the walls of the cylinder?
Hello Bharat
As well said Michael Pfitzner, this procedure is correct, Only I suggest you calculate water flow rate, as follow:
water flow rate = required beam/(Cp*DT)
where
required beam = 10 kW
Cp = 4.181 kJ/kg K (fluid specific heat, in this case for water)
DT = 2 or 10 °C (depend of the cooling medium, for example a cooling tower)
Best regards
Alejandro
Hello Bharat
As suggested by Zoubair Boulahia, it is explained in the book that the cylinderical body can be regarded as a vertical flat plate (provided it satisfies some conditions). It is well explained in this book. Heat transfer will not take place only through conduction, convection will also surely play its role. So you better refer the mentioned book.
If it doesn't help, let me know. I have another book to suggest.
Regards
Harmanpreet
Hello,
I agree with the suggestions above.
But, looking to the images attached, I see that it is a rather small device (30 mm of length?). So I'm wondering what diameter are you expecting for the refrigerating pipe. Very small diameter will probably lead to laminar flux (low convection) or high operation pressure... May be, there could be another design options for the refrigeration?
Hello Joaquin,
I have added an update.I have simulated it using a pipe of 6mm diameter.The water from the chiller is at 15 degrees C.
Fine; if you do not want the water to boil in your pipes you can now easily calculate the
minimum mass flow within the pipes using alejandros formula and with that using standard correlations the corresponding pressure drop in the pipes. Using correlations for the heat transfer coefficient (laminar or turbulent depending on the Reynolds number), you can calculate the necessary temperature difference. You will then see, how hot the pipes will be. If large temperature difference emerges, then large temperature gradients will probably form within the configuration.
A conjugate heat transfer analysis using CFD with your configuration can estimate those material temperatures.
Will the water boil even if it is at low pressure since the dimensions are small will the water reach the boiling temperature immediately?
it will boil at even lower temperature at lower pressure. Boiling temperature =100°C is only accurate at p=1bar (see boiling curve). If wall temperature is above boiling temperature the water will boil locally, the pressure drop will increase, so you need more delta p to drive the flow.
I suggest you calculate mass flow, Reynolds number, velocity, delta T and post the results.
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