Entransy method is developed for the analyses of thermal processes with variable thermophysical properties. The entransy and enthalpy entransy balance equations for thermal processes with variable thermophysical properties are derived based on the definitions of differential entransy and enthalpy entransy. The definitions of the entransy and enthalpy entransy for an object are presented. The optimization principles for heat transfer and heat-work conversion processes with variable thermophysical properties are discussed with the concept of entransy. Entransy analyses for a two-stream heat exchanger and a closed Brayton cycle with variable thermophysical properties are conducted and compared with the entropy generation analyses. For the heat exchanger, the results show that both the minimum entransy-dissipation-based thermal resistance and the minimum revised entropy generation number correspond to the maximum heat exchanger effectiveness when the inlet condition of the heat exchanger is prescribed, but the minimum entropy generation rate and the minimum entropy generation number do not. For the closed Brayton cycle, the results show that both the maximum entransy loss rate and the minimum entropy generation rate correspond to the maximum output power and both the maximum entransy loss coefficient and the minimum entropy generation number correspond to the maximum heat-work conversion efficiency when the inlet conditions of the streams and the environmental temperature are prescribed. When the inlet temperature of the hot stream increases, larger entransy loss rate and larger entransy loss coefficient still correspond to larger output power and larger heat-work conversion efficiency respectively. (C) 2015 Elsevier Ltd. All rights reserved.