An innovative engineering student has been contemplating whether or not it would be feasible to capture some of the waste heat that leaves the stack of a wood burning stove to preheat water. The proposal is to insert a 6-ft long copper coil made of ½-std type K tubing into a 4-inch (ID) stovepipe. Cold water flows at a rate of 2 gpm through the tube. The average mean temperature of the tube is estimated to be 100°F. The hot combustion gases (which can be modeled as air), flow over the outside of the copper coil in cross flow at 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,

In this equation, A_chimney is the cross-sectional area of the stove pipe, h is the total height of the stovepipe, T_gas is the free-stream combustion gas temperature, and T_amb is the outside ambient temperature. Notice that T_gas 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 8 ft.
In order to model this heat exchanger, the UA product must be determined. Let’s help the innovative engineering student by estimating the UA product for the heat exchanger under clean conditions.

V=0.68 Ad chimney. 2gh T-T gas To gas amb