In Example 5.12, the UA product for a cross flow finned tube heat exchanger was calculated. In that example, it was stated that, “… the U value of the heat exchanger will change as the flow rates and fluid temperatures change. However, if the expected change is minimal, the predicted outlet temperature using the estimated UA should be reasonably close to the expected outlet temperatures.” The purpose of this exercise is to determine the validity of this statement using manufacturer’s data for a finned tube air heating coil for residential applications. The manufacturer’s data for this cross flow, finned tube coil is given in Table P5.73. Air flows through the fins and water flows through the tubes of the heat exchanger. Given this data determine the

a. UA product for each of the three air flow rates. Can a simple relationship be developed for the UA product as a function of the air flow rate? If so, determine this relationship.
If the manufacturer only provided data for the 1,200-cfm air flow case, determine the

b. Percent error in the UA product that would occur at 1,000 cfm and 1,400 cfm compared to the UA product calculated at 1,200 cfm. Is the variation in the UA product for this heat exchanger significant over the range of air flows given for the application?

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TABLE P5.73 Manufacturer's Performance Data for a Cross Flow Finned Tube Air Heating Coil Water Flow Entering Coil (gpm) 6 6 6 Entering air temperature = 68F, entering water temperature = 180F. Air Flow Entering Coil (cfm) 1000 1200 1400 a Heat Transfer Dutya (Btu/h) 66,000 72,000 77,500