•The mathematical model is useful for analyzing the heat exchanger performance.•The most probable variant of heat exchanger operation is established.•There is a risk of frost accumulation within the fixed-bed regenerator. The paper describes an original mathematical model of heat and mass transfer for a fixed bed regenerator used to determine the effect of internal airflow leakage on heat exchanger efficiency. First, the build and operating principles of a fixed-bed heat exchanger were discussed. The presence of internal leakage was shown along with a proposed solution for its elimination. Then, a mathematical model based on a modified ε-NTU method for numerical simulation and analysis of coupled heat and mass transfer in a fixed-bed heat exchanger was presented. The model was supplemented with an additional detailed submodel designed to determine frost surface temperature and frost growth analysis. Initial numerical simulations of the operation of the model were performed for low outdoor air temperature conditions. Different zones of heat and mass transfer within the regenerator matrix were distinguished. The presence of accumulated frost area and its influence on the course of heat and mass transfer processes was revealed. In addition, the presence of a relative humidity limit curve associated with a mass balance deficiency conditioning the occurrence of frost accumulation was established.