Volume 47, Issue 2 - Special Issue: The 16th Joint European Thermodynamics Conference (JETC 2021)

We discuss spatio-temporal pattern formation in two separate thermal convective systems. In the first system, hydrothermal waves (HTW) are modeled numerically in an annular channel. A temperature difference is imposed across the channel, which induces a surface tension gradient on the free surface of the fluid, leading to a surface flow towards the cold side. The flow pattern is axially symmetric along the temperature gradient with an internal circulation for a small temperature difference. This axially symmetric flow (ASF) becomes unstable beyond a given temperature difference threshold, and subsequently, symmetry-breaking flow, i. e., rotational oscillating waves or HTW appear. For the second system, Rayleigh–Bénard convection (RBC) is experimentally studied in the non-turbulent regime. When a thin film of liquid is heated, the competing forces of viscosity and buoyancy give rise to convective instabilities. This convective instability creates a spatio-temporal non-uniform temperature distribution on the surface of the fluid film. The surface temperature statistics are studied in both these systems as “order” and “disorder” phase separates. Although the mechanisms that give rise to convective instabilities are different in both cases, we find an agreement on the macroscopic nature of the thermal distributions in these emergent structures.

A complete thermodynamical analysis for a non-reacting binary mixture exhibiting the features of a third grade fluid is analyzed. The constitutive functions are allowed to depend on the mass density of the mixture and the concentration of one of the constituents, together with their first and second order gradients, on the specific internal energy of the mixture with its first order gradient, and on the symmetric part of the gradient of barycentric velocity. Compatibility with the second law of thermodynamics is investigated by applying the extended Liu procedure. An explicit solution of the set of thermodynamic restrictions is obtained by postulating a suitable form of the constitutive relations for the diffusional mass flux, the heat flux, and the Cauchy stress tensor. Taking a first order expansion in the gradients of the specific entropy, the expression of the entropy flux is determined. It includes an additional contribution due to non-local effects.

Density gradient theory describes the evolution of diffuse interfaces in both mixtures and pure substances by minimization of the total free energy, which consists of a non-convex bulk part and an interfacial part. Minimization of the bulk free energy causes phase separation while building up the interfacial free energy (proportional to the square of gradients of the species’ densities) and it results in the equilibrium shape of the interface. However, direct minimization of the free energy is numerically unstable and the coefficients in the interfacial part of the free energy are often estimated from experimental data (not determined from the underlying physics). In this paper we develop a robust physics-based numerical approach that leads to the interface density profiles for both pure substances and mixtures. The model is free of fitting parameters and validated by available experimental data.

We show that a confined viscous liquid emits a dynamic thermal response upon applying a low frequency (∼1 Hz) shear excitation. Hot and cold thermal waves are observed in situ at atmospheric pressure and room temperature, in a viscous liquid (polypropylene glycol) at various thicknesses ranging from 100 µm up to 340 µm, upon applying a mechanical oscillatory shear strain. The observed thermal effects, synchronous with the mechanical excitation, are inconsistent with a viscous behaviour. It indicates that mesoscopic liquids are able to (partly) convert mechanical shear energy in non-equilibrium thermodynamic states. This effect called thermo-elasticity is well known in solid materials. The observation of a thermal coupling to the mechanical shear deformation reinforces the assumption of elastically correlated liquid molecules. The amplitude of the thermo-elastic waves increases linearly by increasing the shear strain amplitude up to a transition to a non-linear thermal behavior, similar to a transition from an elastic to plastic regime. The thermo-elastic effects do not give rise to any change in stress measurements and thus the dynamic thermal analysis provides unique information about dynamic liquid properties.

The relation between heat flux and temperature gradient has been considered as a constitutive structure or as a balance law in different approaches. Both views may allow a description of heat conduction characterized by finite speed propagation of temperature disturbances. Such a result, which overcomes Fourier’s drawback of infinite speed propagation, can be obtained also by considering insufficient the representation of a conductor, even when it is considered to be rigid, rather than the sole relation between heat flux and temperature gradient. We comment this last view and describe the intersection with previous proposals. Eventually, we show how under Fourier’s law we can have traveling-wave-type temperature propagation when thermal microstructures are accounted for.

In this paper we explore several aspects of the influence of fixed and of mobile defects on the thermal conductivity of materials. In particular, we investigate the effects of the temperature and defect concentration dependence of the conductivity on phononic diodes and transistors and on the non-linear thermal conductivity dependent on the heat flux in thermal superlattices.

In a series of papers we have obtained results for nonlinear heat transport when thin wires exchange heat non-linearly with the surroundings, with particular attention to propagating solitons. Here we obtain and discuss new results related to the propagation of nonlinear heat fronts and some conceptual aspects referring to the application of the second principle of thermodynamics to some nonlinear steady states related to non-propagating solitons.

The ideal Stirling cycle provides a clear control strategy for the piston paths of ideal representations of Stirling cycle machines. For non-equilibrium Stirling cycle machines however, piston paths aiming to emulate the ideal cycle’s four strokes will not necessarily yield best performance. In this contribution, we ask the question: What are the COP -optimal piston paths for specific non-equilibrium Stirling cryocoolers? To this end, we consider a low-effort Stirling cryocooler model that consists of a set of coupled ordinary differential equations and takes several loss phenomena into account. For this model and an exemplary parameter set, piston path optimizations are done with an indirect iterative gradient method based on optimal control theory. The optimizations are repeated for two different kinds of volume constraints for the working spaces: one representing an alpha-Stirling configuration, the other a beta-Stirling configuration. Compared to harmonic piston paths, the optimal piston paths lead to significant improvements in COP of ca. 88 % for the alpha-Stirling and ca. 117 % for the beta-Stirling at the maximum- COP operational frequency. Additionally—and even though the optimizations were performed for maximum COP —cooling power was increased with even lager ratios.

We discuss the role of thermodynamics in non-linear stability analysis of spatially distributed dissipative systems governed by non-linear partial differential equations. We document profound interplay between various concepts in thermodynamics on one side and non-linear stability analysis on the other side, and subsequently we summarize and comment on various results regarding the non-linear stability of thermodynamically isolated as well as thermodynamically open systems.

We present a framework to systematically derive variational formulations for fluid-structure interaction problems based on thermodynamical driving functionals and geometric structures in different coordinate systems by suitable transformations within this formulation. Our approach provides a promising basis to construct structure-preserving discretization strategies.

Some tools of Non-Equilibrium Thermodynamics of closed discrete systems are considered: the non-equilibrium state space, the non-equilibrium entropy as a state function and its connection with the entropy production, Clausius’ inequality, equilibrium and accompanying processes. Why can the thermostatic temperature be used successfully in thermal engineering even in cases of non-equilibrium?

The general concept of temperature is thermodynamically defined in equilibrium somehow predictable even for non-equilibrium; however, it presents some still controversial aspects, as has been shown in a number of studies and reviews that have been published so far. Equilibrium concepts are often extrapolated to apply in micro-localized equilibrium and then appended to non-equilibrium in its entirety, which helps to define out-of-equilibrium temperature on both the macroscopic and microscopic bases. Unfortunately, these theoretical analyses do not provide any guidance on how to assess and understand temperature in practical measurements, such as for conventional thermal analysis. Insufficient use of alternative thermodynamic attitudes is evident especially in the field of thermophysical studies, which do not use static measurements, because they usually involve heating from an external source, i. e., the effect of thermal dynamics on the laboratory sample. This paper presents the applied nonequilibrium thermodynamic concept, historically known as thermotics. This approach takes into account the existence of gradients and heat fluxes, which it assesses from the point of view of the average user, and considers additional influences, going beyond the description of thermodynamics in traditional textbooks. The goal is to extend their validity, even to the state of constant first-time derivatives. At the same time, it points to changes in the temperature due to thermal inertia, which has long been ignored, suggesting that the heat spreads immediately. Moreover, special techniques enabling measurements during its extreme changes probably then require an alternative concept for temperature (tempericity). This opinion paper may provide stimuli for further discussion with regard to the practice of measurements done in the customary nonisothermal mode.