5.7 A copper coil heat exchanger is inserted in a 4-in. (ID) stovepipe to capture some of the energy normally rejected to the atmosphere from a wood-burning stove for preheating domestic hot water. The copper coil is made of 6 ft of

½-std type K tubing. Cold water flows at a rate of 5 gpm through the tube. The average mean temperature of the tube is found to be 88°F. The hot combustion gases (which can be modeled as air) flow over the outside of the copper coil in cross flow at a free stream temperature of 450°F.

The flow rate of the combustion gases through the stovepipe is the result of an induced draft effect. This volumetric flow rate can be estimated using the following expression:

V A gh T T T



 



 

=

−

gas 0.68 chimney 2 gas amb gas In this equation, Achimney is the cross-sectional area of the stovepipe, h the total height of the stovepipe, Tgas the free-stream combustion gas temperature, and Tamb the outside ambient temperature. Notice that Tamb in the denominator of the term in the square root must be on the absolute temperature scale. Consider the situation where the outdoor temperature is −5°F and the total height of the stovepipe is 10 ft. Estimate the UA product for the heat exchanger if it is clean

(i.e., no fouling).