In this paper a mathematical model enabling the analysis of the heat-flow phenomena occurring in the waterwalls of the combustion chambers of the boilers for supercritical parameters is proposed. It is a one-dimensional model with distributed parameters based on the solution of equations describing the conservation laws of mass, momentum, and energy. The purpose of the numerical calculations is to determine the distributions of the fluid enthalpy and the temperature of the waterwall pipes. This temperature should not exceed the calculation temperature for particular category of steel. The derived differential equations are solved using two methods: with the use of the implicit difference scheme, in which the mesh with regular nodes was applied, and using the Runge-Kutta method. The temperature distribution of the waterwall pipes is determined using the CFD. All thermophysical properties of the fluid and waterwall pipes are computed in real-time. The time-spatial heat transfer coefficient distribution is also computed in the on-line mode. The heat calculations for the combustion chamber are carried out with the use of the zone method, thus the thermal load distribution of the waterwalls is known. The time needed for the computations is of great importance when taking into consideration calculations carried out in the on-line mode. A correctly solved one-dimensional model ensures the appropriately short computational time.

The paper analyses the possibilities of treating the ignition cable in the internal combustion engine as a distributed parameter system. It presents the experimental verification of computer simulations of signal propagation generated by ignition systems in the ignition cables, modelled by the distributed parameter system. The tests conducted to determine the wave parameters of ignition cables, as well as the results of numerical simulations and their experimental verifications, are presented. It is concluded that the modelling of the ignition cable by means of a long line gives positive results that can be used for the design of a spark plug with impedance equal to wave impedance of the ignition cable.