Unequal Temperatures Research Articles

Generalized hydrodynamics and approach to generalized Gibbs equilibrium for a classical harmonic chain

Abstract We study the evolution of a classical harmonic chain with nearest-neighbor interactions starting from domain wall initial conditions. The initial state is taken to be either a product of two Gibbs ensembles (GEs) with unequal temperatures on the two halves of the chain or a product of two generalized Gibbs ensembles (GGEs) with different parameters in the two halves. For this system, we construct the Wigner function and demonstrate that its evolution defines the generalized hydrodynamics (GHD) describing the evolution of the conserved quantities. We solve the GHD for both finite and infinite chains and compute the evolution of conserved densities and currents. For a finite chain with fixed boundaries, we show that these quantities relax as ∼ 1 / t to their respective steady-state values given by the final expected GE or GGE state, depending on the initial conditions. Exact expressions for the Lagrange multipliers of the final expected GGE state are obtained in terms of the steady-state densities. In the case of an infinite chain, we find that the conserved densities and currents at any finite time exhibit ballistic scaling while, at infinite time, any finite segment of the system can be described by a current-carrying non-equilibrium steady state (NESS). We compute the scaling functions analytically and show that the relaxation to the NESS occurs as ∼ 1 / t for the densities and as ∼ 1 / t 2 for the currents. We compare the analytical results from hydrodynamics with those from exact microscopic numerics and find excellent agreement.

Magnetized oscillatory Jeffrey fluid flow in a porous channel with unequal wall temperature

Magnetized oscillatory Jeffrey fluid flow in a porous channel with unequal wall temperature

Calculating a conductor’s temperature-related sag as the limiting value for a Dynamic Line Rating

The ampacity — a term that refers to the maximum current in amperes — of existing overhead lines can be increased using Dynamic Line Rating (DLR) systems. Based on ambient online conditions and electrical power flow measurements, together with a forecast of future ambient conditions, the ampacity of overhead lines can be dynamically adjusted. In essence, the ampacity of an overhead line is determined by the operating temperature of the conductor that still guarantees the required safe distances to the objects under the overhead line. This paper presents a calculation algorithm for the sag of a conductor that addresses an unequal temperature of the conductor along the line as a response to an expected problem in the future, when increasing numbers of DLR sensors will be installed on or even near overhead lines. A novel approach to the sag-temperature calculation useful for a DLR is developed based on the linearization of cable equations. As a result, the computational costs are greatly reduced, which is an important factor when the DLR system includes a large number of overhead lines and processes them simultaneously. The presented methods are open and can be adapted for an arbitrary DLR system.

Driving range evaluation of electric vehicle with transcritical CO2 thermal management system under different battery temperature controls

Improper battery temperature will lead to reduced battery discharge efficiency and electric vehicle driving range. Endeavors to find an efficient and precise battery temperature control method for the transcritical CO2 thermal management system of electric vehicles, two evaporation temperature control methods for battery cooling were proposed. First, the effects of the control methods on battery temperature, optimal discharge pressure and coefficient of performance (COP) were simulated under typical operating conditions. Subsequently, a comparative simulation was conducted on the battery temperatures and COP of the two control methods under full cooling conditions. The results revealed that equal evaporation temperature control induced a reduction in battery temperature to 11 °C (suboptimal levels) under conditions of low ambient temperature and vehicle speed. Conversely, while unequal evaporation temperature control could maintain the battery temperature within the optimal range of 20–45 °C, it would result in a maximum COP drop of more than 20% under certain conditions. Furthermore, the effects of the two control methods on driving range under different ambient temperatures and vehicle speeds were studied. The reasults indicated that the ultimate influence of uneuqal evaporation temperature control on the quarterly average driving range was virtually negligible, peaking at 1.35%. Given the dual-objective constraints pertaining to the driving range and the battery cooling performance, it was concluded that uneuqal evaporation temperature control was the optimal choice for direct battery cooling.

Phase distribution in nanochannels of supercritical fluid with different fluid–wall interactions

Supercritical fluids (SFs) are classically regarded as single-phase fluids without bubbles or interfaces, but a recent study shows nanobubbles in SFs under unconfined conditions. The objective of this paper is to explore the phase distribution under confined conditions. Molecular dynamics simulations are performed for supercritical argon. Two walls containing the SF have equal fluid–wall interactions with equal and unequal wall temperatures. An external force is applied on the top wall to control the pressure at 1.5Pc, in which Pc is the critical pressure. Periodic boundary conditions are applied on the four side surfaces of the simulation box. The study indicates that the bulk fluid density is not only dependent on pressure and temperature, but also on fluid–wall interactions, this result deviates from the classical theory, where density depends on only pressure and temperature. For strong fluid–wall interactions, three- or five-layer structures are found, including liquid-like (LL) layers on the walls and two-phase-like (TPL) and gas-like (GL) layers (depending on bulk density) in the channel core. For weak fluid–wall interactions, the phase distribution becomes GL on the wall, and TPL and LL (depending on bulk density) in the channel core, which is inverse to those of strong fluid–wall interactions. Correspondingly, the phase distributions for strong and weak fluid–wall interactions can be analogous to annular or Leidenfrost patterns at subcritical pressures, respectively. The density profile is symmetric against the channel centerline at equal wall temperatures, but symmetry-breaking may exist when applying different wall temperatures. This work provides a phase-distribution link between subcritical and supercritical pressures, which is useful for the design and analysis of SF systems.

Lumbar Sympathetic Trunk Injury: An Underestimated Complication of Oblique Lateral Interbody Fusion.

Lumbar sympathetic trunk (LST) injury is one of the major complications after oblique lumbar interbody fusion (OLIF). LST injury often manifests as unequal skin temperature in lower limbs after operation, and there may be a large number of missed diagnoses due to the lack of attention and different diagnostic methods. The study aimed to investigate the incidence and clinical characteristics of LST injury after OLIF. The data of patients with lumbar degenerative diseases who underwent OLIF in our hospital from April 2016 to October 2017 were retrospectively analyzed. Finally, a total of 54 patients were included. There were 10 males and 44 females, aged 58.4 ± 10.9 years. The skin temperature of lower limbs was measured before and a day after surgery. The patients were followed up at 1 week, 6 weeks, 6 months, and 2 years after the surgery. Likert five-point scale was used to evaluate the discomfort caused by LST injury. Injury severity score was introduced to grade injury degree according to the recovery time of postoperative symptoms. The chi-square test was used to analyze the association of incidence of lumbar sympathetic trunk (LST) injury with contributing factors, such as gender and number of surgical segments. The unequal temperature was not found before surgery in all the patients. Postoperatively, 16 cases (29.6%) had difference of skin temperature more than 0.5°C and were diagnosed with LST injury. Eight patients (14.8%) had self-perception of skin temperature differences, and 12 patients (22.2%) had other symptoms, such as muscle pain, numbness, and weakness, which were not statistically different between patients with and without lumbar sympathetic trunk injury (p > 0.05). In the 16 patients with LST injury, the difference of skin temperature between the two legs was 0.6 ± 0.1 °C on the first day, and the temperature difference lasted for 1.5-~12months. According to Likert five-point scale, two cases (12.5%) were poor, and 14 cases (87.5%) were moderate immediately after surgery. Fifteen cases improved to some extent 6 weeks to 12months after surgery. Postoperative LST injury is mainly manifested by different temperature of lower limbs. The incidence was higher in patients with multi-segment OLIF than in those with single-segment OLIF, and the subjective experience of most patients with LST injury was moderate discomfort.

Thermal Performance Assessment for an Active Latent Heat Storage Tank by Using Various Finned-Coil Heat Exchangers

Paraffin-based latent heat storage has a higher thermal capacity than sensible heat storage. Despite that, the actual implementation of paraffin as an active latent heat storage (ALHS) system is limited due to low charging and discharging rate with unequal temperature distribution as the impact of mushy region formation. The present study evaluates the finned-coil heat exchanger for the ALHS tank to overcome the related problems. Three finned-coil configurations are tested experimentally: straight-fin, branched-fin and height-fin. The evaluation uses the ALHS arrangement to assess each configuration's charging/discharging rate. The branched fin provides an equal thermal distribution, promoting a higher final temperature of 112.3°C. It also achieves the highest power rate of 250.5 Watts. The height-fin minimizes the effect of void formation, which maintains a sufficient heat transfer rate during the discharging. However, the average power rate for each model is relatively low. The finding indicates that it is essential to provide adequate heat transfer for the center part of the tank, including adding a branched fin along with coil turn to provide a better heat transfer rate. It boosts the charging/discharging rate, making the system's response time desirable to achieve effective power during the operation.

Appropriate number of stages of an ORC driven by LNG cold energy to produce acceptable power with reasonable surface area of heat exchangers

Cold energy of LNG can generate power through Organic Rankine cycle (ORC). Although power output increases with number of stages, they become complex, expensive, maintenance-intensive and prone to failure due to the presence of increased number of components. In this paper, a cascaded three-stage ORC system has been progressively truncated finally to a single-stage system to arrive at the appropriate trade-off between the plant complexity and generation of power. Sea-water is used as the heat source and with ethene, ethane and propane as the working fluids, the generation of power is maximised for a given total surface area of heat exchangers. Calculation has been done initially with 5 K temperature approach in all the heat exchangers. However, an appropriate distribution of total surface area times overall heat transfer (UA) resulting in an unequal temperature approaches in the heat exchangers generated much higher output of power. The simulation shows that though cascaded three-stages delivers the highest power. A two-stage system with only the first stage cascaded reduces power generation by 8.6% compared to that in a three-stage system. However, the former gains enormously in simplicity of configuration and operation. The corresponding reduction in surface area of the heat exchanger is 20%.

Erratum: “Comment on ‘Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity’” [Phys. Fluids 33, 043321 (2021)

First Page

Higher order heat fluxes in a rarefied granular gas

Despite its general application, the Fourier's law of heat conduction is not always valid in dilute gases. One of the physical shortcomings of Fourier's law is the mismatch at the boundary; the temperature gradient in the Knudsen layer diverges in the boundary, but the heat flux does not. In this paper, we propose a more generalized constitutive relation for the heat flux to match the heat flux with the hydrodynamics in a rarefied granular gas. The proposed modified heat flux relation is then used to derive analytical solutions for the hydrodynamics of a granular gas bounded by equal and unequal temperature walls. The analytical solutions are then compared to direct simulation Monte Carlo simulations.

Performance of ceiling jet induced by dual unequal strong plumes in a naturally ventilated tunnel

• Thermal property of two unequal flames in a naturally ventilated tunnel is studied. • Temperatures induced by the small plume decay faster than that of the large plume. • A new model for maximum ceiling temperature of two unequal plumes is proposed. • Correlations for ceiling temperature decay profiles of dual plumes are developed. The catastrophic tunnel fire accidents are usually accompanied with multi-source burning. Ceiling gas temperature in tunnel is an important parameter in monitoring the daily operation process and unexpected combustion process. Previous studies are mainly focused on single fire or multiple equal fires in tunnel, while multiple unequal fires burning is common in real tunnel fires. Till now, the law of asymmetrical temperature distribution of multi-source below a ceiling is unknown. This paper aims to experimentally study the thermal performance of two unequal fire sources of propane in a naturally ventilated tunnel. A total of 90 experimental tests were conducted. The side lengths of two burners are fixed at 10 cm and 15 cm. The heat release rate (HRR) of each burner are changed with the HRRs ratio of 1–6. And the spacing between two sources along the longitudinal centerline of tunnel varied from 0–45 cm. Analysis shows that there is only one peak temperature with small spacings, while two peak temperatures appear with large spacings. Then the impingement point position and the maximum ceiling gas temperature of each burner are illustrated. The force analysis is adopted to explain the variation of impingement point position. A parameter α is innovatively introduced to characterize the promoting effect of spacing on maximum temperature at small spacings. Then a new normalized HRR is proposed to establish a unified model for the unequal maximum temperature rises below the ceiling of both sources, which indicates that the maximum temperature rise increases with the normalized HRR and then it maintains at 754 K. By introducing the plume radius, models for asymmetrical temperature decay profiles on both sides of two plumes below the ceiling are proposed, which shows that the temperature in the upstream of the small burner decays faster than that in the downstream of the large burner. The proposed models for maximum temperature and temperature decay profiles can be used to predict the ceiling gas temperatures of two unequal fires in tunnel.

Weakly Nonlinear Stability of Thermosolutal Convection in an Oldroyd-B Fluid-Saturated Anisotropic Porous Layer Using a Local Thermal Nonequilibrium Model

Abstract The two-temperature model of local thermal nonequilibrium (LTNE) is utilized to investigate a weakly nonlinear stability of thermosolutal convection in an Oldroyd-B fluid-saturated anisotropic porous layer. The anisotropies in permeability, thermal conductivities of the porous medium, and solutal diffusivity are accounted for by second-order tensors with their principal directions coinciding with the horizontal and vertical coordinate axes. A modified Darcy–Oldroyd model is employed to describe the flow in a porous medium bounded by impermeable plane walls with uniform and unequal temperatures as well as solute concentrations. The cubic-Landau equations are derived in the neighborhood of stationary and oscillatory onset using a modified perturbation approach and the stability of bifurcating equilibrium solutions is discussed. The advantage is taken to present some additional results on the linear instability aspects as well. It is manifested that the solutal anisotropy parameter also plays a decisive role on the instability characteristics of the system. It is found that the stationary bifurcating solution transforms from supercritical to subcritical while the oscillatory bifurcating solution transforms from supercritical to subcritical and revert to supercritical. The Nusselt and Sherwood numbers are used to examine the influence of LTNE and viscoelastic parameters on heat and mass transfer, respectively. The results of Maxwell fluid are outlined as a particular case from this study.

Computation of thermo-solutal convection with soret-dufour cross diffusion in a vertical duct containing carbon/metallic nanofluids

Duct flows constitute an important category of modern thermal engineering. Optimizing efficiency has become a significant objective in the 21st century in, for example, heating ventilation and air-conditioning (HVAC), coolant or heat transfer fluid flows in a nuclear power reactor, heat exchanger design etc., and this has been achieved by either new materials (improved thermal insulation properties) constituting the duct walls, novel geometric designs, or improved working fluids. Nanotechnology has infiltrated into duct design in parallel with many other fields of mechanical, medical, and energy engineering. Motivated by the excellent potential of nanofluids, a subset of materials engineered at the nanoscale, in the present work, a new mathematical model is developed for natural convection in a rectangular vertical duct containing nanofluid. The left and right walls of the duct are maintained at constant and unequal temperatures, while the front and rear walls of the duct are insulated. Thermo-solutal (double-diffusive) natural convection of aqueous nanofluid containing various metallic nanoparticles (e. g., copper and titanium oxide) or carbon-based nanoparticles (e. g., diamond and silicon oxide) is simulated. The Tiwari–Das nanoscale volume fraction model is used in addition to the Brinkman and Maxwell models for defining the properties of the nanofluid. The partial differential conservation equations for mass, momentum and energy are non-dimensionalized via appropriate transformations and the resulting boundary value problem is solved with a second-order accurate implicit finite difference technique employing Southwell-Over-Relaxation (SOR). Mesh independence tests are conducted. Extensive visualization of the solutions for velocity, temperature, and nanoparticle concentration (volume fraction) are presented for five different nanoparticles (silicon oxide, diamond, copper, titanium oxide, and silver), thermal Grashof number, nanoparticle species (solutal) Grashof number, volume fraction of nanoparticles (i.e., percentage doping), Dufour number, Soret number, Prandtl number, Schmidt number, and duct aspect ratio. It is observed that the heat transfer rate (Nusselt number) at both the walls is maximized for diamond nanoparticles and minimized for silicon oxide nanoparticles. Further, the heat transfer rate for clear fluid is lower when compared with nanofluid, confirming that nanoparticles achieve the desired thermal enhancement at the boundaries also. The mass transfer at both walls (Sherwood number), however, is not significantly influenced by any particular type of nanoparticle, thermal and concentration Grashof number and is depleted with higher values of Dufour, Prandtl, Soret, and Schmidt numbers in addition to aspect ratio. However, Sherwood numbers at both the left and right duct walls are substantially boosted with greater solid volume fraction of nanoparticles.

Improving Power Density of a Three-Level ANPC Structure Using the Electro-Thermal Model of Inverter and a Modified SPWM Technique

Multilevel inverter structures have become an interesting substitute for the well-known two-level inverters in a variety of applications due to their exceptional characteristics when compared to conventional inverters. One major issue regarding multilevel structures is the unequal junction temperature of the switches which deteriorates the power density and increase the cost of the inverter by reducing the maximum achievable output power with a given thermal model and cooling system. Hence, on account of the aggressive goals of power density and cost in a majority of power electronic applications, this article proposes a new technique for reducing the maximum junction temperature of switches in a three-level active neutral-point clamped (ANPC) inverter based on a junction temperature estimation method and a modified SPWM control scheme. This technique can ensure up to a 12% rise in the power density value when compared to basic SPWM techniques with no loss distribution algorithm. Moreover, the suggested approach can be used as a protection stage in the inverter which protects the inverter in transient loads, while allowing for reaching the maximum power capability of the inverter. Finally, the simulations of the proposed technique are validated with experimental results of a 400 V, 20 kW three-level ANPC inverter, controlled by the conventional and proposed techniques.

Modeling and Design of Cookware for Induction Heating Technology With Balanced Electromagnetic and Thermal Characteristics

Improving the cooking experience of induction-heating users involves, among other factors, an optimized power distribution at the bottom of the cooking vessel. Conventional ferromagnetic cookware presents high efficiency but unequal temperature distribution with flat inductors, which subsequently leads to uneven cooking results. In this work, we propose an alternative to the traditional cookware arrangement by inserting some aluminum pieces in the ferromagnetic bottom of cookware. This arrangement combines the optimal inductive performance of the ferromagnetic iron an the high thermal conductivity of aluminum. The performance of the proposed arrangement is analyzed by means of a multiphysics tool including electromagnetic and heat transfer sub-models which is applied to predict both the equivalent electrical circuit and the temperature distribution in cookware. As a result, a balanced trade-off between efficiency and temperature distribution is evidenced with the proposed solution. Experimental results also corroborates the predictions of the proposed solution.

Electron mirror and cyclotron instabilities for solar wind plasma

ABSTRACT The solar wind plasma is characterized by unequal effective kinetic temperatures defined in perpendicular and parallel directions with respect to the ambient magnetic field. For electrons, the excessive perpendicular temperature anisotropy leads to quasi-parallel electromagnetic electron cyclotron (or whistler) instability and aperiodic electron-mirror instability with oblique wave vectors. The present paper carries out a direct side-by-side comparison of quasi-linear (QL) theory and particle-in-cell (PIC) simulation of combined mirror and cyclotron instabilities acting upon the initially anisotropic electron temperatures, and find that the QL theory satisfactorily encapsulates the non-linear aspect of the combined instability effects. However, a discrepancy between the present study and a previous PIC simulation result is also found, which points to the need for further investigation to resolve such an issue.

Rayleigh-Benard Convection in Nanofluids Layer saturated in a Rotating Anisotropic Porous Medium with Feedback Control and Internal Heat Source

Control strategy on Rayleigh-Benard convection in rotating nanofluids saturated in anisotropic porous layer heated from below is studied in the presence of uniformly internal heat source for rigid-rigid, free-free, and lower-rigid and upper-free boundaries. Feedback control strategy with an array of sensors situated at the top plate and actuators located at the bottom plate of the nanofluids layer are considered in this study. Linear stability analysis based on normal mode technique has been performed, the eigenvalue problem is obtained numerically by implementing the Galerkin method and computed by using Maple software. Model employed for the nanofluids includes the mechanisms of Brownian motion and thermophoresis. The problem of the onset of convective rolls instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures known as Horton-Roger-Lapwood model based on the Darcy model for the fluids flow is used. The influences of internal heat source’s strength, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection, meanwhile the mechanical anisotropy parameter, thermal anisotropy parameter, porosity, rotation, and controller effects are to slow down the process of convective instability. No visible observation on the modified particle density increment and rigid-rigid boundaries are the most stable system compared to free-free and rigid-free boundaries.

Comment on “Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity” [Phys. Fluids 33, 043321 (2021)

Comment on the paper J. Solsvik and E. Manger, "Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity," Phys. Fluids \textbf{33}, 043321 (2021).

Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity

Kinetic theory for granular mixtures with a separate granular temperature for each solid phase is considered. The particle phases are assumed to follow a Maxwellian distribution with zero-order approximation of the Boltzmann equation. A solution strategy for solving the integrals of the collisional closure relations is presented. The present analysis enables the solution of these integrals without neglecting the solid particle hydrodynamic velocities in the distribution function. However, the solution strategy limits the validity of the closure relations to relatively small and moderate hydrodynamic velocity differences. Dependent on the magnitude of the hydrodynamic velocity difference, the present closure relations can differ significantly from the simplified models where such velocity difference is traditionally neglected.

Kinetic theory models for granular mixtures with unequal granular temperature. Derivation of analytical constitutive equations

We consider kinetic theory of granular mixtures in which each solid phase is described by its own granular temperature. The particle velocities are assumed to follow a Mawellian distribution with zero-order approximation of the Boltzmann equation. The literature proposes a number of approximate solutions to the constitutive equations resulting from particle collisions. Here, we derive and show that analytical solutions exist, and reveal that some of the proposed approximate solutions are inaccurate whereas others might give good approximations.We also review the balance laws and constitutive relations resulting from the mono- and poly-disperse kinetic granular flow model frameworks. Such a review has been done here because the model framework on kinetic theory of mono-disperse granular flow systems has sometimes been adopted in models for granular mixtures. The consequence of such a simplification is that the kinetic energy loss in a collision between two particles of different species is equally shared among them.