Abstract.We study the well-posechiess of a class of models describing heat transfer by conduction and radiation.For that purpose we propose an abstract mathematical framework that allows us to prove existence, uniqueness and the comparison principle for the weak solution with minimal or almost minimal a priori assumptions for the data. The theory covers different types of grey materials, that is, both semitransparent and opaque bodies as well as isotropic or nonisotropic scattering/reflection provided that the material properties do not depend on the wavelength of the radiation. To demonstrate the use of the abstract theory we consider in detail two examples, heat transfer between opaque bodies with diffuse-grey surfaces and a model with semitransparent material and specularly reflecting surfaces.

Monitoring of harmful substances in an aquatic environment is based on spot sampling which is the only sampling technique accepted by environmental authorities in the European Union. Still the implementation of the European Union Water Framework Directive (WFD) requires novel sampling tools for monitoring priority pollutants since their concentrations in natural waters can often remain below the limit of detection when using the conventional spot sampling method. However, this does not necessarily mean that the pollutant is not present in the aquatic environment. Many chemicals that are considered to be harmful are bioaccumulative and can affect, e.g., reproduction of aquatic organisms even at very low concentration levels. Also the timing is crucial since with spot sampling the pulse of harmful substances can easily be missed. Passive samplers collect the compounds for a certain amount of time which allows the concentrations in the sampler to rise to the measurable level where they are easy to detect. Organotin compounds (OTCs) have been widely used as plastic stabilizers and antifouling agents in ship paints and in many industrial processes. Among the OTCs, tributyltin is listed as a WFD priority substance. In this study a small-scale flow simulation around the Chemcatcher passive sampler was performed to visualize the flow streamlines in the vicinity of the sampler and to study the pressure experienced by the receiving phase in different sampler positions. With laboratory experiments the sampling rates for each OTC were determined and the effect of the flow velocity and sampler orientation on the accumulation of OTCs is discussed. The pressure changes were observed on the surface of the receiving phase in simulations with varying sampler orientations. Despite that, the laboratory experiments discovered no difference in the accumulation of compounds when varying the sampler orientation. The concentrations of OTCs in the surrounding water calculated from the passive sampling results were equivalent to the spot sampling ones. Hence, the Chemcatcher passive sampler provides a practical tool for the implementation of WFD.

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Numerical simulation and automated optimization of Langevin-type ultrasonic transducers are investigated. These kind of transducers are standard components in various applications of high-power ultrasonics such as ultrasonic cleaning and chemical processing. Vibration of the transducer is simulated numerically by standard finite element method and the dimensions and shape parameters of a transducer are optimized with respect to different criteria. The novelty value of this work is the combination of the simulation model and the optimization problem by efficient automatic differentiation techniques. The capabilities of this approach are demonstrated with practical test cases in which various aspects of the operation of a transducer are improved.

Abstract.As a first step towards modelling the coupled Thermo-Hydro-Mechanical-Chemical (THMC) behaviour of bentonite, the Barcelona Basic Model (BBM) has been implemented into Numerrinfinite element code. This model has beenfully coupled with the single phase flow equation for unsaturated soils which models liquid water transport. Suction obtained from solving the flow equation is used as an input for the BBM model and the volumetric deformations from the mechanical analysis are used to update the pore water pressure field. As an alternative, BBM is used alongside the Kröhn's model which assumes that bentonite re-saturation is mainly driven by water vapour diffusion. The paper simulates one dimensional infiltration test on MX-80bentonite with both implemented modelsfor water transport and compares the results withthose from a laboratory experiments based on X-ray tomography.The numerical results of the simulations are similar despite taking into account different physical phenomena.