Performance of a counterflow heat exchanger with heat loss through the wall at the cold end

The performance of high effectiveness heat exchangers used in cryogenic systems is strongly controlled by irreversibilities such as longitudinal heat conduction and heat leak from ambient. In all heat exchanger analyses, it is assumed that no heat is lost through the heat exchanger walls. In the case of small J-T refrigerators such as microminiature refrigerators, the heat exchanger cold end is almost directly connected to the evaporator, which may result in a large amount of heat loss through the heat exchanger wall at the cold end. The rate of heat loss through the wall at the cold end is also strongly dependent on the longitudinal thermal resistance of the wall. In this paper, we present the relationship between the effectiveness of a heat exchanger losing heat at the cold end and other resistances such as number of transfer units (NTU), longitudinal thermal resistance etc. The performance of such heat exchangers under different operating conditions is also discussed.