In the paper, the Reynolds transport theorem (RTT) for three phase systems is developed, in terms associated with a moving control volume. The basic tools applied to the derivation are the generalized transport theorem by Truesdell and Toupin, and generalized surface transport theorem by Aris as well as Slattery. The final results referenced to a generic extensive quantity demonstrate the theorem in the integral instantaneous form. As a further illustration of applicability of the theorem relation developed some specific forms are deduced from such as for multiphase systems in terms of fixed control volume, surface systems and homogeneous spatial systems.

The theoretical basis for the indirect measurement approach of mean heat transfer coefficient for the packed bed based on the modified single blow technique was presented and discussed in the paper. The methodology of this measurement approach dedicated to the matrix of the rotating regenerative gas heater was discussed in detail. The testing stand consisted of a dedicated experimental tunnel with auxiliary equipment and a measurement system are presented. Selected experimental results are presented and discussed for selected types of matrices of regenerative air preheaters for the wide range of Reynolds number of gas. The agreement between the theoretically predicted and measured temperature profiles was demonstrated. The exemplary dimensionless relationships between Colburn heat transfer factor, Darcy flow resistance factor and Reynolds number were presented for the investigated matrices of the regenerative gas heater.