The Effect of Boundary Conditions on the Wall Ends on Temperature Conditions and Effectiveness of Heat Exchangers with Parallel Flow of Heat Carriers

The effect of heat conduction through the wall along the flow of heat carriers on the effectiveness of heat exchangers (HEs) when the wall ends are not thermally insulated from the environment has been investigated. An analytical solution of the problem for cocurrent flow of heat carriers was obtained for the same ratios of thermal equivalents of the heat carriers beta and heat-transfer coefficients alpha on both sides of the wall separating hot and cold heat carriers and for a counter flow at beta = alpha = 1. The solution to the problem depends on the number of heat-transfer units Ntu, parameter C(A )describing the axial wall heat conduction, the Biot number Bi, which determines relative heat transfer from the wall ends to the environment, and temperatures of the fluid in contact with the wall ends. The effect of axial wall heat conduction becomes more pronounced with decreasing parameter C-A. Two cases are examined: case I with surrounding fluid temperatures assumed as equal to the inlet and outlet temperatures of the hot heat carrier and case II with surrounding fluid temperatures assumed as equal to the inlet and outlet temperatures of the cold heat carrier. The results obtained demonstrate that, at low Biot numbers (Bi < 10(-3)), the effectiveness of a heat exchanger epsilon for any values of CA in a cocurrent HE hardly differs at all from the effectiveness of the HE in the absence of the axial wall heat conduction effect, epsilon(0), and for a counter flow at low C-A the HE effectiveness is noticeably less than epsilon(0) and decreases by two times at Ntu >> 1. At high Biot numbers (Bi > 1), the effect of axial wall conduction can increase the effectiveness of either heat carrier, while the temperature of the other heat carrier will change slightly during its flow through the heat exchanger. The predictions indicate that the best way for increasing the HE effectiveness is to employ the same thermal equivalents of two heat carriers and heat-transfer coefficients on both sides of the wall separating the hot and the heat carriers (beta = alpha = 1).