Two Heat-Transfer Improvements for Gas LiquefiersTwo improvements in heat-transfer design have been investigated with a view toward increasing the efficiency of refrigerators used to liquefy gases. The improvements could contribute to the development of relatively inexpensive, portable oxygen liquefiers for medical use. A description of the heat-transfer problem in a pulse-tube refrigerator is prerequisite to a meaningful description of the first improvement. In a pulse-tube refrigerator in particular, one of in-line configuration heat must be rejected from two locations: an aftercooler (where most of the heat is rejected) and a warm heat exchanger (where a small fraction of the total input power must be rejected as heat). Rejection of heat from the warm heat exchanger can be problematic because this heat exchanger is usually inside a vacuum vessel. When an acoustic-inertance tube is used to provide a phase shift needed in the pulse-tube cooling cycle, another problem arises: Inasmuch as the acoustic power in the acoustic-inertance tube is dissipated over the entire length of the tube, the gas in the tube must be warmer than the warm heat exchanger in order to reject heat at the warm heat exchanger. This is disadvantageous because the increase in viscosity with temperature causes an undesired increase in dissipation of acoustic energy and an undesired decrease in the achievable phase shift. Consequently, the overall performance of the pulse-tube refrigerator decreases with increasing temperature in the acoustic-inertance tube. In the first improvement, the acoustic-inertance tube is made to serve as the warm heat exchanger and to operate in an approximately isothermal condition at a lower temperature, thereby increasing the achievable phase shift and the overall performance of the refrigerator. This is accomplished by placing the acoustic-inertance tube inside another tube and pumping a cooling fluid (e.g., water) in the annular space between the tubes. Another benefit of this improvement is added flexibility of design to locate the warm heat-rejection components outside the vacuum vessel. The second improvement is the development of a compact radial-flow condenser characterized by a very high heat transfer coefficient and a small pressure drop.