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## Continuous mathematical models of airlift bioreactors: Families, affinity, diversity and modelling for single-substrate kinetics

### Abstract

This paper presents a method of describing an airlift bioreactor, in which biodegradation of a carbonaceous substrate described by single-substrate kinetics takes place. Eight mathematical models based on the assumption of liquid plug flow and axial dispersion flow through the riser and the downcomer in the reactor were proposed. Additionally, the impact of degassing zone with assumed complete mixing on the obtained results was analyzed. Calculations were performed for two representative hydrodynamic regimes of reactor operation, i.e. with the presence of gas bubbles only within the riser and for complete gas circulation. The conclusions related to the apparatus design and process performance under sufficient aeration of the reaction mixture were drawn on the basis of the obtained results.
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## Modeling the Performance of Water-Zeolite 13X Adsorption Heat Pump

### Abstract

The dynamic performance of cylindrical double-tube adsorption heat pump is numerically analysed using a non-equilibrium model, which takes into account both heat and mass transfer processes. The model includes conservation equations for: heat transfer in heating/cooling fluids, heat transfer in the metal tube, and heat and mass transfer in the adsorbent. The mathematical model is numerically solved using the method of lines. Numerical simulations are performed for the system water-zeolite 13X, chosen as the working pair. The effect of the evaporator and condenser temperatures on the adsorption and desorption kinetics is examined. The results of the numerical investigation show that both of these parameters have a significant effect on the adsorption heat pump performance. Based on computer simulation results, the values of the coefficients of performance for heating and cooling are calculated. The results show that adsorption heat pumps have relatively low efficiency compared to other heat pumps. The value of the coefficient of performance for heating is higher than for cooling
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## Mathematical Simulation of Reinforced Concrete Beams with the External Reinforcement in the Form of Steel Cut and Stretchy Sheet

### Abstract

The results of bearing capacity, deformability and fracture toughness of reinforced concrete beams with the external reinforcement in the form of steel cut and stretchy sheet, obtained due to the conducting of the experiment and mathematical simulation which were made of concrete of C40/50 class are given in the article. Mathematical simulation of beam structures is done on the basis of the deformation model which allows to conduct calculations of the unified methodological positions of different elements with diverse configuration of cross section and reinforcement as well as take into consideration elastic and plastic properties of concrete and reinforcement, assessing the actual stress-strain state of sections of reinforced concrete elements at different loading levels, including ultimate one. The deformation model is based on the actual diagrams use of concrete and reinforcement materials deformation and conditions of efforts balance in the normal section and hypothesis of flat sections. The theoretical value of bearing capacity and deformability, obtained as a result of the mathematical simulation was compared to the experimental data. The satisfactory coincidence of the mathematical calculation of bearing capacity, deformability, fracture toughness and experimental data gives an opportunity to use the algorithm not only for beam structures with bar reinforcement but also for beam structures with the external reinforcement in the form of steel cut and stretchy sheet.
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