In the present study, a suitable composition of parameters has been obtained to provide an efficient process of cooling flue gas with complete condensation of water vapour from air-water vapour mixture on a water film in co-current upward flow in the tube of the direct contact heat and mass exchanger. The results showed that the value of the irrigation density depends on the velocity of the air-water vapour mixture and the initial vapour content and should be calculated from an empirical equation. The active pipe height depends on the velocity of the air-water vapour mixture and the initial vapour content and should also be calculated from an empirical equation. For example, if the initial vapour content of the air-water vapour mixture is 11%, the velocity of the mixture is 20.8 m/s the height of the channel should not exceed 0.460 m. The value of the water heating limit temperature increases from 46◦C to 62◦C with a change in the initial vapour content from 11% to 30%. The present experimental results could be helpful in the design of direct contact heat and mass exchangers for waste heat recovery.

In the paper the practical stability problem for the discrete, non-integer order model of one dimmensional heat transfer process is discussed. The conditions associating the practical stability to sample time and maximal size of finite-dimensional approximation of heat transfer model are proposed. These conditions are formulated with the use of spectrum decoposition property and practical stability conditions for scalar, positive, fractional order systems. Results are illustrated by a numerical example.