A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6]

A Domain Decomposition method based on iterative Operator Splitting method.

In this article a new approach is proposed for constructing domain decomposition methods based on iterative operator splitting methods. We study the convergence properties of such a method. The main feature of the method is the decoupling the space and time dimension. We confirm with two numerical applications the effectiveness of the proposed iterative operator splitting method in comparison with classical Schwarz waveform relaxation method as a standard method for domain decomposition. We provide improved results and convergence rates. The efficiency of considering the whole domain in the case of the iterative operator splitting method allows more accurate results

Improved measurement technique for the characterization of organic and inorganic phase change materials using the T-history method

In the past decade, the interest in phase change materials (PCMs) has grown significantly due to their ability to store large amounts of thermal energy in relatively small temperature intervals. Accurate knowledge of thermo-physical properties is a prerequisite for any reliable utilization of these materials. The T-history method is widely used for the investigation of PCM. This paper presents an improved measurement technique for the characterization of PCM using the T-history method. The suggested improvements include the arrangements made in three different prospects: the experimental setup, data processing and data representation. T-history measurements of organic RT21 and inorganic SP22 A17 (RUBITHERM® GmbH) PCM were performed. The applied arrangements resulted in the temperature accuracy of ±0.3 °C and the reduction of uncertainty associated with heat stored/released between the cooling and heating measurements. The obtained results showed some important aspects of the T-history PCM investigation and could provide more effective design and development process of the thermal energy storage systems based on the investigated materials

Estimation of the thermal properties of PCMs through inverse modelling

The application of Phase Change Materials (PCMs) is promising to improve the energy efficiency of buildings. However, although the great interest that PCMs have gained, their practical application in the building sector is still very limited. One of the obstacles to the diffusion of PCMs is the lack of information regarding their thermo-physical properties. In the present work, a method for estimating the specific heat-temperature curve of a PCM through inverse modelling was presented. This method combined experimental data with a numerical tool that was capable of simulating multilayer walls with the inclusion of PCM materials. The experimental setup consisted in a sample of PCM which was subjected to controlled temperature variations on its surfaces. Given the measured surface temperatures of the sample as boundary conditions and the known thermo-physical properties of the material to the model, the specific heat-temperature curve which minimised the difference between measured and simulated heat fluxes was found through an optimisation algorithm. Results were validated against tests on different samples and discussed in comparison with a low-speed DSC measurement

A bifurcation-type theorem for the positive solutions of a nonlinear Neumann problem with concave and convex terms

We consider a nonlinear elliptic Neumann problem driven by the p-Laplacian with a reaction that involves the combined effects of a “concave” and of a “convex” terms. The convex term (p-superlinear term) need not satisfy the Ambrosetti-Rabinowitz condition. Employing variational methods based on the critical point theory together with truncation techniques, we prove a bifurcation type theorem for the equation

Experimental and numerical investigations of the optical and thermal aspects of a PCM-glazed unit

This paper reports on the thermal and optical characterisation of PCM (phase change material) RT27 using the T-history method and spectrophotometry principles, respectively, and the experimental and numerical performance evaluation of a PCM-glazed unit. Various relationships describing the variations in the extinction, scattering and absorption coefficients within the phase change region were developed, and were validated in a numerical CFD model. The results show that: (i) during rapid phase changes, the transmittance spectra from the PCM are unstable, while under stable conditions visible transmittance values of 90% and 40% are obtained for the liquid and phases, respectively; (ii) the radiation scattering effects are dominant in the solid phase of the PCM, while radiation absorption dominates in the liquid phase; (iii) the optical/radiation performance of PCM can be successfully modelled using the liquid fraction term as the main variable; (iv) the addition of PCM improves the thermal mass of the unit during phase change, but risks of overheating may be a significant factor after the PCM has melted; (v) although the day-lighting aspects of PCM-glazed units are favourable, the change in appearance as the PCM changes phase may be a limiting factor in PCM-glazed units

Comparison of thermistor linearization techniques for accurate temperature measurement in phase change materials

Alternate energy technologies are developing rapidly in the recent years. A significant part of this trend is the development of different phase change materials (PCMs). Proper utilization of PCMs requires accurate thermal characterization. There are several methodologies used in this field. This paper stresses the importance of accurate temperature measurements during the implementation of T-history method. Since the temperature sensor size is also important thermistors have been selected as the sensing modality. Two thermistor linearization techniques, one based on Wheatstone bridge and the other based on simple serial-parallel resistor connection, are compared in terms of achievable temperature accuracy through consideration of both, nonlinearity and self-heating errors. Proper calibration was performed before T-history measurement of RT21 (RUBITHERM® GmbH) PCM. Measurement results suggest that the utilization of serial-parallel resistor connection gives better accuracy (less than ±0.1°C) in comparison with the Wheatstone bridge based configuration (up to ±1.5°C)

On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics

We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for $$u_t = u \Delta u + u \int_\Omega |\nabla u|^2$$ in bounded domains \Om\sub\R^n which arises in game theory. We prove that solutions converge to $0$ if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with $\overline{\Omega}$, i.e. the finite-time blow-up is global