Search Results (177)

In this article, the mechanism of relaxation polarization currents occurring at a constant temperature (isothermal process) in crystals with ionic-molecular chemical bonds (CIMBs) in an alternating electric field was investigated. Methods of the quasi-classical kinetic theory of dielectric relaxation, based on solutions of the nonlinear system of Fokker–Planck and Poisson equations (for the blocking electrode model) and perturbation theory (by expanding into an infinite series in powers of a dimensionless small parameter) were used. Generalized nonlinear mathematical expressions for calculating the complex amplitudes of relaxation modes of the volume-charge distribution of the main charge carriers (ions, protons, water molecules, etc.) were obtained. On this basis, formulas for the current density of relaxation polarization (for transient processes in a dielectric) in the k-th approximation of perturbation theory were constructed. The isothermal polarization currents are investigated in detail in the first four approximations (k = 1, 2, 3, 4) of perturbation theory. These expressions will be applied in the future to compare the results of theory and experiment, in analytical studies of the kinetics of isothermal ion-relaxation (in crystals with hydrogen bonds (HBC), proton-relaxation) polarization and in calculating the parameters of relaxers (molecular characteristics of charge carriers and crystal lattice parameters) in a wide range of field parameters (0.1–1000 MV/m) and temperatures (1–1550 K). Asymptotic (far from transient processes) recurrent formulas are constructed for complex amplitudes of relaxation modes and for the polarization current density in an arbitrary approximation k of perturbation theory with a multiplicity r by the polarizing field (a multiple of the fundamental frequency of the field). The high degree of reliability of the theoretical results obtained is justified by the complete agreement of the equations of the mathematical model for transient and stationary processes in the system with a harmonic external disturbance. This work is of a theoretical nature and is focused on the construction and analysis of nonlinear properties of a physical and mathematical model of isothermal ion-relaxation polarization in CIMB crystals under various parameters of electrical and temperature effects. The theoretical foundations for research (construction of equations and working formulas, algorithms, and computer programs for numerical calculations) of nonlinear kinetic phenomena during thermally stimulated relaxation polarization have been laid. This allows, with a higher degree of resolution of measuring instruments, to reveal the physical mechanisms of dielectric relaxation and conductivity and to calculate the parameters of a wide class of relaxators in dielectrics in a wide experimental temperature range (25–550 K). Full article

Vacuum Membrane Distillation (VMD) is a separation process applied to liquid solutions; however, there are phenomenological and operational differences depending on whether the component to be separated is the solute or the solvent. The objective of this article is to develop a mathematical and phenomenological model of the VMD process applied to the separation of volatile organic compound (VOCs) from aqueous solutions and the desalination of saline aqueous solutions. This approach enabled the evaluation of the influence of variables and operating conditions on both separation efficiency and system productivity. Under the analyzed conditions, increasing the temperature, flow rate, and vacuum pressure led to approximate increases in permeate flux of 400%, 10%, and 50%, respectively. In the case of concentration increase, the permeate flux increases linearly for VOC separation and decreases asymptotically for saline solution desalination. Therefore, adjusting the feed temperature is recommended to achieve significant changes in permeate flux. Full article

Thermo-mechanical fatigue remains one of the more difficult phenomena to analyze due to the interplay between temperature, mechanical properties, and microstructural features of the material. For austenitic stainless steel, thermo-mechanical fatigue plays a particularly critical role—temperature changes the affinity of $\gamma$ austenite to transform into ${\alpha }^{\prime }$ martensite under overcritical deformation. This paper presents the results of an in situ study of $\gamma \to {\alpha }^{\prime }$ deformation-induced transformation kinetics at elevated temperatures in AISI 347. Fatigue tests were conducted in the temperature range of 20 to 320 °C. A uniaxial magnetic balance was used to directly measure the change in ferromagnetic volume fraction of the fatigue specimens as the fatigue load was applied. From this data, an empirical mathematical model was found. This model describes the kinetics of $\gamma \to {\alpha }^{\prime }$ transformation as an exponential function of temperature, where the rate of phase transformation decreases with temperature, asymptotically approaching zero but never actually reaching it. Full article

Pipe exits into cryogenic systems, such as an exit of a venting or sensor tube inside a cryogenic storage tank, can affect spontaneously occurring acoustic oscillations, known as Taconis oscillations. The amplitude which such oscillations will reach is dependent on losses at the pipe exit that prevent resonant oscillations from growing without bound. Consequently, being able to accurately determine minor losses at a pipe exit is important in predicting the behavior of these oscillations. Current thermoacoustic modeling of such transitions typically relies on steady-flow minor loss coefficients, which are usually assumed to be constant for a pipe entrance or exit. In this study, numerical simulations are performed for acoustic flow at a pipe exit, with and without a wall adjacent to the exit. The operating fluid is cryogenic hydrogen gas, while the pipe radius (2 and 4 mm), temperature (40 and 80 K), and acoustic velocity amplitudes (varying in the range of 10 m/s to 70 m/s) are variable parameters. The simulation results are compared with one-dimensional acoustic models to determine the behavior of minor losses. Results are also analyzed to find harmonics behavior and a build-up of mean pressure differences. Minor losses decrease to an asymptotic value with increasing Reynolds number, while higher temperatures also reduce minor losses (10% reduction at 80 K versus 40 K). A baffle sharply increases minor losses as the distance to pipe exit decreases. These findings can be used to improve the accuracy of oscillation predictions by reduced-order thermoacoustic models. Full article

The control of many industrial processes, such as superheated steam temperature control, exhibits poor robustness and degraded accuracy in the presence of model parameter uncertainties. This paper addresses this issue by developing a novel interval power integration-based nonlinear suppression scheme for a class of uncertain nonlinear systems with unknown but bounded parameters. The efficacy of this approach is specifically demonstrated for the superheated steam temperature control in thermal power plants. By integrating Lyapunov stability theory and homogeneous system theory, this method extends the traditional homogeneous degree theory to the interval domain, establishes interval boundary conditions for time-varying parameters, and constructs a Lyapunov function with interval numbers to recursively design the controller. Furthermore, the interval monotonic homogeneous degree and an admissibility index are introduced to ensure system stability under parameter uncertainties. The effectiveness of the proposed method is verified through numerical simulations of superheated steam temperature control. Simulation results demonstrate that the method effectively suppresses nonlinearities and achieves robust asymptotic stability, even when model parameters vary within bounded intervals. In the varying-exponent scenario, the proposed controller achieved an Integral of Absolute Error (IAE) of 70.78 and a convergence time of 37s for the superheated steam temperature control. This represents a performance improvement of 42.79% in IAE and 53.16% in convergence time compared to a conventional PID controller, offering a promising solution for complex thermal processes with inherent uncertainties. Full article

We investigate the temperature evolution in the three-dimensional skin tissue exposed to a millimeter-wave electromagnetic beam that is not necessarily perpendicular to the skin surface. This study examines the effect of the beam’s incident angle. The incident angle influences the thermal heating in two aspects: (i) the beam spot projected onto the skin is elongated compared to the intrinsic beam spot in a perpendicular cross-section, resulting in a lower power per skin area; and (ii) inside the tissue, the beam propagates at the refracted angle relative to the depth direction. At millimeter-wavelength frequencies, the characteristic penetration depth is sub-millimeter, whereas the lateral extent of the beam spans at least several centimeters in applications. We explore the small ratio of the penetration depth to the lateral length scale in a nondimensional formulation and derive a leading-term asymptotic solution for the temperature distribution. This analysis does not rely on a small incident angle and is therefore applicable to arbitrary angles of incidence. Based on the asymptotic solution, we establish scaling laws for the three-dimensional skin temperature, the skin surface temperature, and the skin volume in which thermal nociceptors are activated. Full article

In composites, fiber–matrix thermal mismatch induces stress heterogeneity that is beyond the resolution of macroscopic approaches. The asymptotic expansion homogenization method is used to create a multi-scale thermo-mechanical coupling model that predicts the elastic modulus, thermal expansion coefficients, and thermal conductivity of ceramic matrix composites at both the macro- and micro-scales. These predictions are verified to be accurate with a maximum relative error of 9.7% between the measured and predicted values. The multi-scale analysis method is then used to guide the vane’s thermal stress analysis, and a macro–meso–micro multi-scale model is created. The thermal stress distribution and stress magnitudes of the guide vane under a transient high-temperature load are investigated. The results indicate that the temperature and thermal stress distributions of the guide vane under the homogenization and lamination theory models are rather comparable, and the locations of the maximum thermal stress are predicted to be reasonably close to one another. The homogenization model allows for the rapid and accurate prediction of the guide vane’s thermal stress distribution. When compared to the macro-scale stress values, the meso-scale predicted stress levels exhibit excellent accuracy, with an inaccuracy of 11.7%. Micro-scale studies reveal significant stress concentrations at the fiber–matrix interface, which is essential for the macro-scale fatigue and fracture behavior of the guide vane. Full article

Prefabricated unidirectional carbon fiber reinforced polymer (CFRP) composite strips are extensively used as a means of infrastructure rehabilitation through adhesive bonding to the external surface of structural concrete elements. Most data to date are from laboratory tests ranging from a few months to 1–2 years providing an insufficient dataset for prediction of long-term durability. This investigation focuses on the assessment of the response of three different prefabricated CFRP systems exposed to water, seawater, and alkaline solutions for 5 years of immersion in deionized water conducted at three temperatures of 23, 37.8 and 60 °C, all well below the glass transition temperature levels. Overall response is characterized through tensile and short beam shear (SBS) testing at periodic intervals. It is noted that while the three systems are similar, with the dominant mechanisms of deterioration being related to matrix plasticization followed by fiber–matrix debonding with levels of matrix and interface deterioration being accelerated at elevated temperatures, their baseline characteristics and distributions are different emphasizing the need for greater standardization. While tensile modulus does not degrade appreciably over the 5-year period of exposure with final levels of deterioration being between 7.3 and 11.9%, both tensile strength and SBS strength degrade substantially with increasing levels based on temperature and time of immersion. Levels of tensile strength retention can be as low as 61.8–66.6% when immersed in deionized water at 60 °C, those for SBS strength can be 38.4–48.7% at the same immersion condition for the three FRP systems. Differences due to solution type are wider in the short-term and start approaching asymptotic levels within FRP systems at longer periods of exposure. The very high levels of deterioration in SBS strength indicate the breakdown of the materials at the fiber–matrix bond and interfacial levels. It is shown that the level of deterioration exceeds that presumed through design thresholds set by specific codes/standards and that new safety factors are warranted in addition to expanding the set of characteristics studied to include SBS or similar interface-level tests. Alkali solutions are also shown to have the highest deteriorative effects with deionized water having the least. Simple equations are developed to enable extrapolation of test data to predict long term durability and to develop design thresholds based on expectations of service life with an environmental factor of between 0.56 and 0.69 for a 50-year expected service life. Full article

A two-dimensional time-dependent model is presented for upward-propagating internal gravity waves generated by an imposed thermal forcing in a layer of fluid with uniform background velocity and stable stratification under the anelastic approximation. The configuration studied is representative of a situation with deep or shallow latent heating in the lower atmosphere where the amplitude of the waves is small enough to allow linearization of the model equations. Approximate asymptotic time-dependent solutions, valid for late time, are obtained for the linearized equations in the form of an infinite series of terms involving Bessel functions. The asymptotic solution approaches a steady-amplitude state in the limit of infinite time. A weakly nonlinear analysis gives a description of the temporal evolution of the zonal mean flow velocity and temperature resulting from nonlinear interaction with the waves. The linear solutions show that there is a vertical variation of the wave amplitude which depends on the relative depth of the heating to the scale height of the atmosphere. This means that, from a weakly nonlinear perspective, there is a non-zero divergence of vertical momentum flux, and hence, a non-zero drag force, even in the absence of vertical shear in the background flow. Full article

This study systematically investigates continuous and discrete spectra methodologies for determining time-domain viscoelastic response functions (creep compliance and relaxation modulus) in asphalt mixtures. Through complex modulus testing of three asphalt mixtures (base asphalt mixture, SBS-modified asphalt mixture, and crumb rubber-modified asphalt mixture), we established unified master curves using a Generalized Sigmoidal model with approximated Kramers–Kronig (K-K) relations. Discrete spectra can be obtained by Prony series of Maxwell/Kelvin modeling, while continuous spectra derived through integral transformation produced complementary response functions by numerical integration. Comparative analysis demonstrated that discrete and continuous spectra methods yield highly consistent predictions of the relaxation modulus and creep compliance within conventional time scales (10⁻⁷–10⁵ s), with significant deviations emerging only at extreme temporal extremities. Compared to discrete spectra results, material parameters (relaxation modulus and creep compliance) derived from continuous spectra methods invariably asymptotically approach upper and lower plateaus. Notably, the maximum equilibrium values derived from continuous spectra methods consistently surpassed those obtained through discrete approaches, whereas the corresponding minimum values were consistently lower. This comparative analysis highlights the inherent limitations in the extrapolation reliability of computational methodologies, particularly regarding spectra method implementation. Furthermore, within the linear viscoelastic range, the crumb rubber-modified asphalt mixtures exhibited superior low-temperature cracking resistance, whereas the SBS-modified asphalt mixtures demonstrated enhanced high-temperature deformation resistance. This systematic comparative study not only establishes a critical theoretical foundation for the precise characterization of asphalt mixture viscoelasticity across practical engineering time scales through optimal spectral method selection, but also provides actionable guidance for region-specific material selection strategies. Full article

Sadi Carnot’s seminal work laid the foundation for exploring the effects of thermodynamics across diverse domains of physics, stretching from quantum to cosmological scales. Here, we build on the principles of the original Carnot heat engine, and apply it in the context of a particular toy model black brane. This theoretical construct of an effectively two-dimensional, stable, and stationary gravitational object in four-dimensional spacetime derives from a hypothetical flat planet collapsed under the influence of gravity. By constructing a thermodynamic cycle involving three such black branes, we explore the possibility of energy extraction or mining, driven by the temperature gradients and gravitational potential differences characteristic of curved spacetime. Analytic solutions obtainable within this toy model illuminate key aspects of black hole thermodynamics in general, particularly for spacetimes that are not asymptotically flat. Central to these findings is the relation between gravitationally induced temperature ratios and entropy changes, which collectively offer a novel perspective on obtainable energy transfer processes around gravitational structures. This analysis highlights potential implications for understanding energy dynamics in gravitational systems in general, including for black hole evaporation and experimentally implemented black hole analogues. The presented findings not only emphasise the universality of the thermodynamic principles first uncovered by Carnot, but also suggest future research directions in gravitational thermodynamics. Full article

This study investigates the effects of warming water on growth in seven demersal fish species including Atlantic cod (Gadus morhua), American plaice (Hippoglossoides platessoides), Greenland halibut (Reinhardtius hippoglossoides), roughhead grenadier (Macrourus berglax) and three species of redfish (Sebastes spp.) in the Northwest Atlantic and compares the changes in growth across species. Length-at-age data were collected from EU bottom trawl surveys from 1993 to 2018, and bottom temperature data were obtained from the Copernicus Marine Service. Generalised additive mixed models (GAMMs) were used to describe the temperature effects on growth. The analysis was carried out separately for males and females. Both sexes of all species except American plaice showed significant temperature effects on growth. To obtain the growth parameters, von Bertalanffy growth functions (VBGFs) were fitted to the predictions from best-fit GAMMs for all species and both sexes under five different bottom temperature scenarios (3, 3.5, 4, 4.5 and 5 °C). The predictions from all best-fit GAMMs were broadly similar in form to the fitted von Bertalanffy growth functions (R² > 90%). Increased bottom temperature generally resulted in a decrease in the asymptotic length (L_∞) and an increase in the growth rate (k). The species with the most dramatic increase in k over the temperature range of 3 °C to 5 °C was Atlantic cod, for which k increased from 0.05 to 0.13 year⁻¹ in females and from 0.08 to 0.14 year⁻¹ in males. The maximum length (L_max), predicted by the VBGF at maximum age generally declined from 3 °C to 5 °C. The species with the most pronounced decline in L_max was beaked redfish (S. mentella). An increase in the proportion of smaller individuals could impact population productivity and result in lower biomass available to fisheries. Uneven changes in fish growth in the warming ocean could also have wider ecological implications and alter the trophic landscape. Full article

Background/Motivation: Viscous dissipation enhances temperature. Determination of its impact is needed to avoid degradation of products in industrial processes. Methodology: The inlet-filled thermal entrance region model addresses the Graetz–Brinkman problem of viscous dissipation in developing heat transfer in a tube subject to a constant heat flux at the wall, considering Newtonian, pseudoplastic, and dilatant fluids. The inlet-filled region concept is used to solve for developing heat transfer, with the thermal entrance region divided into a thermal boundary layer zone, called the thermal inlet region, ending at the point where the thermal boundary layer fills the whole tube cross section, followed by a thermally filled region where fully developed conditions are asymptotically reached. Key Results: The model is essentially analytical. The results include profiles of the dimensionless thermal boundary layer thickness, Nusselt number, dimensionless bulk, wall and centerline temperatures, and entrance region length for different values of the Brinkman number and power-law index, with validation against the derived fully developed solution and published results. Implications: New results are obtained for the case of nonzero viscous dissipation. Results can be obtained with minor computational tasks needed. Full article

In fourth-generation district heating systems (DHSs), the supply temperature of modern heat sources such as heat pumps and waste heat can potentially be reduced by mixing in hot water from combustion-based producers, thereby increasing efficiency and facilitating integration into networks with unrenovated buildings. However, this approach introduces the risk of thermo-hydraulic oscillations driven by mixing dynamics, transport delays, and mass flow adjustments by consumers. These oscillations can increase wear and cost and may potentially lead to system failure. This study addresses the asymptotic stability of multi-supplier DHSs by combining theoretical analysis and practical validation. Through linearization and Laplace transformation, we derive the transfer function of a system with two suppliers. Using pole-zero analysis, we show that transport delay can cause instability. We identify a new control law, demonstrating that persisting oscillations depend on network temperatures and low thermal inertia and enabling stabilization through careful temperature selection, thorough choice of the slack supplier, or installation of buffer tanks. We validate our findings using dynamic simulations of a nonlinear delayed system in Modelica, highlighting the applicability of such systems to real-world DHSs. These results provide actionable insights for designing robust DHSs and mitigating challenges in multi-supplier configurations by relying on thoughtful system design rather than complex control strategies. Full article

The identification of the orders of time series models plays a crucial role in their accurate specification and forecasting. The Autocorrelation Function (ACF) is commonly used to identify the order q of Moving Average (MA(q)) models, as it theoretically vanishes for lags beyond q. This property is widely used in model selection, assuming the sample ACF follows an asymptotic normal distribution for robustness. However, our examination of the sum of the sample ACF reveals inconsistencies with these theoretical properties, highlighting a deviation from normality in the sample ACF for MA(q) processes. As a natural extension of the ACF, the Extended Autocorrelation Function (EACF) provides additional insights by facilitating the simultaneous identification of both autoregressive and moving average components. Using simulations, we evaluate the performance of q-order identification in MA(q) models, which is based on the properties of ACF. Similarly, for ARMA($p,q$) models, we assess the ($p,q$)-order identification relying on EACF. Our findings indicate that both methods are effective for sufficiently long time series but may incorrectly favor an ARMA($p,q-1$) model when the $a_q$ coefficient approaches zero. Additionally, if the cumulative sums of ACF (SACF) behave consistently and the Ljung–Box test validates the proposed model, it can serve as a strong candidate. The proposed models should then be compared based on their predictive performance. We illustrate our methodology with an application to wind speed data and sea surface temperature anomalies, providing practical insights into the relevance of our findings. Full article