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Computer ME Assisted Design of Thermal Systems
Heat Exchanger Calculations Effectiveness-Ntu Method Two Types of Problem: Rating Problem or Sizing Problem Rating Problem: The heat transfer surface area is known. Exit temperatures are unknown. This is like using a heat exchanger given to you off the shelf, where you know everything about it except for how it works. That is, what exit temperatures it will produce. You will be able to calculate the Ntu from information given, but will have to calculate or determine the effectiveness from an -Ntu relationship or graph. Sizing Problem: All of the operating conditions are known or can be calculated from the first law of thermodynamics. The heat transfer surface area is unknown. This is like being told what temperature requirements the heat exchanger must have and then calculating how large it must be. You will be able to calculate the effectiveness from the information given, but will have to calculate or determine the Ntu from an -Ntu relationship or graph. When working a heat exchanger problem several questions need to be answered up front. Among them are: 1. Is the problem a rating problem or a sizing problem? 2. What type of heat exchanger are we using? What are the appropriate effectivenessNtu equations or graph? 3. Is the overall heat transfer coefficient specified or are we going to calculate from: (1) the effectiveness-Ntu calculations (like a sizing problem except the area is specified) or (2) employ a thermal circuit model and Nusselt number correlations for the convective heat transfer coefficients? 4. How are we going to handle the cP evaluation? Once these questions are addressed the problem can be set up in the format shown below and the given conditions can be entered on the table.
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ME 416 CAD of Thermal Systems
Solution Problem Table Type: (Rating or Sizing) Heat Exchanger Type: (crossflow, tube & shell, etc.) Fluid #1 (Water) Hot TH,in = TH,out = TH,avg = cP,H = & mH = CH = = Cmax or Cmin mixed or unmixed U= A= = Ntu = Then depending on whether we have a sizing problem or a rating problem two different solution methodologies can be used. Fluid #2 (Air) Cold TC,in = TC,out = TC,avg = cP,C = & mC = CC = = Cmax or Cmin mixed or unmixed
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ME 416 CAD of Thermal Systems
Rating problem methodology 1. Evaluate specific heats at inlet temperatures 2. Calculate CH and CC. Determine Cmin and Cmax and calculate
Cr = C min C max
3. Calculate U. 4. Calculate
Ntu = UA C min
5. Use appropriate effectiveness-Ntu equation or graph to determine the effectiveness. 6. Calculate the actual heat transfer
& & q act = q max = C min (TH,in - Tc,in )
7. Use the first law to calculate the exit temperatures
TH,out = TH,in TC,out = TC,in & q act CH & q + act CC
8. Re-evaluate the specific heats at the average temperatures and repeat steps 2-7 as needed.
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ME 416 CAD of ...