Gas liquefaction utilizing the entropy transport by flux lines (FLs) in the mixed state of type-II superconductors has been proposed. Refrigerating power and the Joulian heat generated by FL current are proportional to and to the square of the superconducting (super-) current, respectively. The optimum super-current, the corresponding field strength, and the net refrigerating power (q(n)) are expressed by the elemental parameters. Introducing the well-defined FL-flow viscosity coefficient, we show that the maximum q(n) appears at the field with 1/9 of the upper critical field under the corresponding super-current density, and we expect the optimum refrigeration power density of about 15.8j(0)* and 4.49j(0)* W/m(2) (where j(0)* is the critical super-current density) for Nb3Ge (T-0 = 23.2K, B-C2 = 14.5 T at T-0) and MgB2 (T-0 = 40.0K, B-C2 = 16T, at T-0), respectively. (C) 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.