Volume 29, Issue 2

An analytical formula for the macroscopic kinetic energy per unit mass of a small macroscopic fluid particle is derived. The macroscopic kinetic energy per unit mass is presented as a sum of the macroscopic translational kinetic energy per unit mass and three Galilean invariants: the classical macroscopic internal rotational kinetic energy per unit mass, a new macroscopic internal shear kinetic energy per unit mass and a new macroscopic internal kinetic energy of a shear-rotational coupling per unit mass with a small correction. The obtained formula generalizes the classical de Groot and Mazur expression by taking into account the shear component of the velocity field. The evolution equation for the average macroscopic internal kinetic energy per unit mass is derived within the frame of the model of an incompressible homogeneous viscous Newtonian fluid for the statistical ensemble of randomly and isotropically oriented and sheared small-scale turbulent eddies. The practical significance of the macroscopic internal shear kinetic energy is evaluated by the realistic prediction of the theoretical “shear-rotational” transition energy dissipation rate per unit mass for the transition of grid-generated stratified turbulence to internal gravity waves.

The consequences of the Causality Principle for the constitutive equations of non-equilibrium thermodynamics are investigated. It is proved that such a principle, once interpreted in the light of the experimental results, is compatible with both the hyperbolic and parabolic thermodynamic theories. As an example, a diffusive-hyperbolic model of heat conduction is presented.

The radial flow between two parallel circular disks is investigated with the aim to determine the optimum convective heat transfer conditions at the external disk surfaces in order to minimize the intrinsic irreversibilities. A general situation is considered where the fluid is electrically conducting and may be under the influence of a transversal magnetic field. The velocity and electric current density fields are obtained analytically and used to solve the heat transfer equation under boundary conditions of the third kind. The analysis is in the absence of fluid inertia, under creeping flow conditions (Reynolds number ≪ 1). A perturbation approach in order to include the convective heat transfer effects in the flow is used. The Péclet number is assumed to be small. The analytic expressions for the velocity, electric current density and temperature fields are used to calculate explicitly the global entropy generation rate. When the convective heat transfer coefficients for each wall are different, this function displays a minimum for specific heat exchange conditions. The results are shown for both the hydrodynamic and the magnetohydrodynamic cases. It is also found that the mean Nusselt number at the upper wall shows a maximum value for a given value of the Hartman number, when the dimensionless heat transfer coefficients for each disk and the Péclet number are fixed. This mean Nusselt number for maximum heat transfer is near its value for minimum entropy generation conditions.

The concept of thermodynamic efficiency (ratio of real cycle efficiency by Carnot efficiency) is well-known. The concept of numbers of entropy-production and of exergy-loss proposed by A. Bejan are also known, but rarely used. The present study firstly evidences that these two last numbers are actually identical, thus being a common number of irreversibility , independent of the method used for obtaining it. The study also evidences a non-dimensional irreversibility balance that applies to any energy conversion process. This balance correlates the thermodynamic efficiency of a whole process (which in most cases equals the exergetic efficiency) and the numbers of irreversibility of the different components or sub-processes involved in this process. Moreover, the basic additivity of entropy-productions and exergy-losses is maintained in this balance. This balance applies to the basic cycles (heat-engines, refrigerators, heat-pumps and heat-transformers), either work- or heat-powered. It also applies to more complex cycles (heat-powered cycles consuming electricity, four-temperature heat-powered cycles, cogeneration processes), thus giving a robust framework for analyzing these cycles.

Considerable work has already been undertaken to study the behaviour of an evaporating meniscus. Because of the complexity of the wetting process much work needs to be done to fully understand the phenomenon. Although it has been demonstrated that the shape of such an evaporating meniscus depends on the intermolecular stress field and forces intervening during the process, the exact determining factors, which dictate the wetting properties, remain not fully understood and quantified. The shape of an evaporating meniscus at the exit of a capillary tube filled with a pure liquid evaporating in dry air is studied by measuring the curvature and the macroscopic steady wetting angle. Evaporation leads to strong thermocapillary convection, which in turn is closely coupled to the wetting properties. The aim of this work is to show the effect of thermocapillary forces on the shape of an evaporating meniscus. The experimental procedure controls the air temperature around the capillary as well as the capillary wall and bulk liquid temperature; the shape of the meniscus is studied for varied temperature conditions. Results show a strong correlation between the steady wetting angle during evaporation at pinned meniscus and an ad hoc defined Marangoni number. It has been observed that increasing the wall temperature would ultimately lead to a slow down of the thermocapillary convection. At a given wall temperature the convection stops. A model has been developed to account for diffusion in the vapour phase. The relevant dimensionless number is found to be the ratio between the partition factor and the Marangoni number.