This paper proposes a novel method to quantify the synergy of bubble swarm patterns and heat transfer performance in a direct-contact heat exchanger (DCHE) by using computational homology. Betti numbers are used to estimate the number of bubbles aggregating in flow patterns and to obtain the pseudo-homogeneous time. A simple linear model of a bubble swarm and the heat transfer performance of a DCHE is constructed on the basis of experimental analysis, in which a new index (beta(t)) is defined by the Betti number average as well as the pseudo-homogeneous time. A good fitting curve between beta(t) and the volumetric heat transfer coefficient average is obtained with a correlation coefficient of 0.95. A paradigm is established on the basis of this novel method for the study of flow patterns and heat transfer performance, and it offers an alternative route to explore the relationship of flow patterns and heat transfer in other heat transfer processes such as convection, multiphase flow, and turbulent flow. (C) 2014 Elsevier Ltd. All rights reserved.