The paper presents analytical relationships based on the theory of Green’s functions. The relationships refer to instantaneous and continuous as well as point and ring heat sources which are discussed. The relationship relating to continuous ring source is the basis for modelling and designing of spiral ground heat exchangers. Heat transfer in the infinite and semi-infinite body was considered. In the latter case, the image method was discussed. Using the results of measurements regarding heat transfer in the ground with a heat exchanger in the form of a single coil installed, a comparison of calculated ground temperatures with measured values was presented.

Knowledge of the temperature distribution in subsurface layers of the ground is important in the design, modelling and exploitation of ground heat exchangers. In this work a mathematical model of heat transfer in the ground is presented. The model is based on the solution of the equation of transient heat transfer in a semi-infinite medium. In the boundary condition on the surface of the ground radiation fluxes (short- and long-wave), convective heat flux and evaporative heat flux are taken into account. Based on the developed model, calculations were carried out to determine the impact of climatic conditions and the physical properties of the ground on the parameters of the Carslaw-Jeager equation. Example results of calculated yearly courses of the daily average temperature of the surface of the ground and the amount of particular heat fluxes on the ground surface are presented. The compatibility of ground temperature measurements at different depths with the results obtained from the Carslaw–Jaeger equation is evaluated. It was found that the temperature distribution in the ground and its variability in time can be calculated with good accuracy.

Periodic adsorption in a perfect mixing tank of a limited volume was considered. It was assumed that the adsorption rate is limited by diffusion resistance in a pellet. The approximate model of diffusion kinetics based on a continued fraction approximation was compared with the exact analytical solution. For the approximate model an algorithm was developed to determine a temporal variation of the adsorbate concentration in the pellet. The comparison was made for different values of the adsorbent load factor. In the numerical tests different shapes of pellets were considered. Both the numerical tests as well as our own experimental results showed that the approximate model provides results that are in good agreement with the exact solution. In the experimental part of this work adsorption of p-nitrophenol and acetic acid from aqueous solutions on cylindrical pellets of activated carbon was conducted.