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Engineering, 05.05.2020 16:03 bryce860
Air passing through an array of thin copper tubes submerged in a large ice/water bath is used for air conditioning in the summer. Each tube has diameter D = 50 mm, and the ice bath maintains its inner surface temperature at a uniform, constant 0oC. Air enters each tube at a mean temperature of Tmi 32oC and a flow rate of m 0.01 kg/s, and it is required for the mean temperature of the air to be at or belovw Tmo-22°C by the end of the tube. a) At what temperature do you want to calculate all the air properties (like viscosity and density)? b) Calculate the minimum tube length required to provide an exit temperature of Tmo 22°C. c) Sketch the mean temperature along the pipe, Tmx). d) Calculate the log-mean temperature difference ΔTlm between the pipe surface and the mean air temperature, and use it to determine the total heat transfer rate conv out of the air into the ice bath. I am assuming that you are ignoring the entry region, and assuming the air profile is fully-developed throughout the length of the pipe to complete your analysis. Let's now challenge that assumption e) What is the length of the entry region before the flow is thermally fully-developed? What percentage is that of the total length of pipe you calculated in (a)? Because of the entry region, is your result for the design length of pipe in (a) conservative or not? That is, if your analysis were to account for the entry region, do you expect that the actual temperature of air by the exit would be below 22oC, or would you have to make your pipe longer than what you calculated in (a)? Explain
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