We continue our exploration of thermodynamics at long observational timescales, “slow time,” by including turbulent dynamics leading to a condition of fluctuating local equilibrium. Averaging these fluctuations in wind speed and temperature results in a velocity distribution with heavy tails which, however, are necessarily truncated at some large molecular speed preserving all moments of the velocity distribution including the energy. This leads to an expression for the ideal gas law in slow time which as its core has the superficially familiar term in addition to a term accounting for the large-scale fluctuations, which is also proportional to the particle number N; θ is a new temperature including thermalization of wind. The traditional temperature T no longer exists. Likewise, the additional energy term necessitates a new quantity that parallels entropy in the sense that it captures hidden degrees of freedom. Like entropy, it captures physical properties manifesting indirectly, but on scales larger than the familiar laboratory scales. We call this quantity epitropy.
Traditional equilibrium thermodynamics can only solve a few equilibrium processes composed of continuous stable equilibrium states. However, the vacuum flash evaporation process is a typical unsteady process. The study of non-equilibrium thermodynamics of the two-phase flow model is helpful to improve our understanding of the basic law of the flash evaporation process. Based on the theory of non-equilibrium thermodynamics, the flash chamber in the vacuum flash ice making system was studied in this paper, and the possibility of non-equilibrium steady state evaporation with superheat was obtained. The chemical potential difference between liquid water and water vapor under non-equilibrium steady state conditions was determined, and the corresponding evaporation entropy was calculated. It is shown that the results obtained by equilibrium thermodynamics are only related to the temperature difference, while the results obtained by non-equilibrium thermodynamics are not only related to the temperature difference, but also the state of the evaporation process. This is because non-equilibrium thermodynamics considers the cooling of liquid water and the evaporation of water vapor as a whole, taking into account the interaction between the two processes. However, the traditional equilibrium thermodynamics theory divides the steady state evaporation process into two independent processes and ignores the influence of each other.
Two types of additional variables were included in the set of state variables and were used for a thermodynamic description of diffusion in an ordinary thermodynamic system. Vacancies are included in the mass balance. Internal surfaces are massless but are characterized by some energy, which is included in the energy balance of the thermodynamic system. Fluxes of components, vacancies, and surfaces were expressed via two groups of thermodynamic constitutive equations of with cross effects. The first group follows from the Gibbs equation. These are state equations in a differential form. The second group relates generalized thermodynamic fluxes to generalized thermodynamic forces. It was shown for a binary system that only three of six transfer coefficients are independent even if the mass transfer mechanism caused by the stress gradient is taken into account.
The performance of the microchannel heat sink (MCHS) in electronic applications needs to be optimized corresponding to the number of channels (N). In this study optimization of the number of channels corresponding to the diameter of the microchannel () using an entropy generation minimization approach is achieved for the MCHS used in electronic applications. The numerical study is performed for constant total heat flow rate and total mass flow rate . The results indicate that the dominance of frictional entropy generation () increases with the reduction in diameter. However, the entropy generation due to heat transfer () decreases with the reduction in diameter. Therefore, the optimum diameter () is calculated corresponding to the minimum total entropy generation () for the optimum number of channels (). Furthermore, the entropy generation number () and Bejan number () are also calculated.
A mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of , the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.
This study deals with the entropy generation in magnetized blood flow through a channel. The blood is modeled as a non-Newtonian fluid that circulates by a uniform peristaltic wave with slip at the boundaries. An inertia free flow is considered using an approximation of the long-wavelength peristaltic wave. The governing equations of the flow are formulated and numerically solved using computational software to identify the characteristics of this non-uniform and time-dependent flow system. In addition, several closed-form solutions of the problem are explicitly presented.
A model of the S-entropy production in a system with a membrane which separates non-electrolyte aqueous solutions was presented. The differences between fluxes in non-homogeneous and homogeneous conditions for volume and solute fluxes, respectively, are non-linear functions of the glucose osmotic pressure difference (OPD) in ranges dependent on the initial ethanol OPD. A decrease of ethanol OPD causes a shift of this range into the lower values of glucose OPD; this shift is also observed for negative values of glucose and ethanol OPDs. The coefficient of concentration polarization of the membrane as a function of glucose OPD has a sigmoidal shape. For suitably great negative values of glucose OPD this coefficient is very small, while for suitably high positive glucose OPD this coefficient is equal to 0.5. An increase of ethanol OPD at the initial moment causes a shift of this curve towards the direction of positive values of glucose OPD. In turn the S-entropy production in non-homogeneous conditions has low values for negative values of glucose OPD (convective range) while for suitably high positive glucose OPD it has greater values (diffusive and convective range). A change of ethanol OPD at the initial moment causes a shift of this curve along the horizontal axis.