Search Results (266)

It is revealed that the material derivative of a variable in gravity field is its directional derivative, from which and energy/complementary-energy conservations with exterior derivatives, two sets of gauge equations of Newton’s dynamic gravity field are derived, which has same mathematical structure with the gauge ones for the Maxwell equations in electromagnetic fields, revealing that gravity force and curl momentum in Newton’s gravity field, respectively, play the roles like the electric $\mathit{E}$ and the magnetic $\mathit{B}$ of the Maxwell equations in the electromagnetic field. The gravity tensor of Newton’s gravitational field is constructed, and an example is given to validate it. This finding allows Newton’s gravity to be governed by a gauge theory, addressing the historic issue that “Newton’s gravitation is an exception to the Yang–Mills gauge theory”. Full article

Urban rivers are essential resources for human societies; however, their degradation poses serious public health, economic, and environmental risks. Conventional physical remediation methods can partially mitigate pollution by targeting specific contaminants, but they are often limited in scope, lack long-term sustainability, and fail to restore ecological functions. In contrast, biotechnological approaches integrated with ecological engineering offer sustainable and nature-based solutions for river depollution, conservation, and revitalization. Although these strategies are supported by a solid theoretical framework and successful applications in other aquatic systems, their large-scale implementation in urban rivers has only recently begun to gain momentum. This review critically examines strategies for the revitalization of polluted urban rivers, progressing from conventional remediation techniques to advanced biotechnological interventions. It highlights real-world applications, evaluates their advantages and limitations, and discusses policy frameworks and management strategies required to promote the broader adoption of biotechnological solutions for sustainable urban river restoration. The goal is to demonstrate the transformative potential of integrated biotechnological, eco-engineering, and data-driven approaches—particularly microbial, phytoplankton-based, and biofilm systems—to reduce energy demand and carbon emissions in urban river restoration while highlighting the need for scalable designs, adaptive management, and supportive regulatory frameworks to enable their large-scale implementation. Full article

A small amount of mass is generally ejected with high exhaust velocities from the surface of materials irradiated by intense laser pulses, so that a net impulse is generated on the target because of momentum conservation. This phenomenon proved to be a potential solution to generate thrust on far objects, with promising application in space debris removal and control of nanosatellites. Among the different tested strategies, the deposition on the surface of the target of a layer transparent to laser radiation results in a considerable increase in the generated impulse, due to the confinement of the expansion of the ablation plume. In this work impulse generation was measured, using aluminum as target, and PVC, SiO₂, TiO₂ and CNCs (cellulose nanocrystals) as confinement layers with thickness $0.3\sim 5 \mathsf{\mu }\mathrm{m}$. The results show that the generated impulses increase with the thickness of the ejected confinement layer. Additionally, the kinetic energy of the confinement layer, for a given material, does not depend on its thickness, but it is affected by the energy dissipation paths during the interaction with the laser pulse, where the strength of substrate–film adhesion and the Young’s modulus of the latter are shown to play an important role. Full article

The traditional way to model the statistics of turbulent flow and dispersion is through averaged conservation equations, in which the turbulent transport terms are described by semi-empirical expressions. A new development has been reported by Brouwers in a number of consecutive papers published over the last 15 years. The new development is that presented descriptions can be obtained through the application of fundamental principles of statistical physics and making use of the asymptotic structure of turbulence at a high Reynolds number. They no longer rely on empirical constructions, minimise calibration factors, and are not limited to specific flow situations. This article updates the contents of these works and presents them in coherent manner. The first derivations are presented as expressions for turbulent diffusion. These are subsequently implemented in a closed set of equations expressing the conservation of mean momentum, mean fluctuating energy, and energy dissipation rate. Predictions from these equations are shown to compare favourably with the results of direct numerical simulations (DNS) of the Navier–Stokes equations of highly anisotropic and inhomogeneous channel flow. The presented model equations provide a solid basis to calculate the main statistical parameters of turbulent flow and dispersion in engineering praxis and environmental analysis. Full article

Heat exchangers–adsorbers (HEX-As) are emerging as innovative technologies in many applications (CO₂ capture, gas purification and separation, thermal energy storage, etc). This review addresses the theoretical challenges within computational fluid dynamics (CFD) in modeling and simulating coupled heat and mass transfer within gas separation by using adsorbing porous media in fixed beds. Conservation equations of mass, momentum, and energy from different studies (1D, 2D-CFD, and 3D-CFD models) are presented and discussed with an emphasis on their ability to predict the complex multi-physics multi-scale heat and mass transfer phenomena involved, such as the adsorption kinematics, the thermal front propagation, and the multi-component fluid flow dynamics inside the beds. For the fist time, we show that mathematical theoretical modeling in CFD has been differently developed and applied by many authors in the literature in order to model the same physical phenomena. This sheds light on the present challenges and bottlenecks in theoretical and computational fluid dynamics when it comes to complex coupled heat and mass transfer in multi-component gas dynamics in porous media. This review make it easier for readers to understand the different models that exist in the literature for modeling and simulating HEX-As. It also opens questions on how accurately one can model multi-functional heat exchangers–adsorbers using CFD, e.g., physics multi-scale extrapolation from nano- to meso- and then to macro-scale behavior. Full article

In this work, we discuss the conditions that allow the establishment of an equivalence between $f(R,T)=R+\lambda h\left(T\right)$ gravity models and General Relativity (GR) coupled to a modified matter sector. We do so by considering a D-dimensional spacetime and the matter sector described by nonlinear electrodynamics and/or a scalar field. We find that, for this particular family of models, the action and field equations can indeed be written in terms of a modified matter source within GR. However, when several matter sources are combined, this interpretation is no longer possible if $h\left(T\right)$ is a nonlinear function, due to the emergence of crossed terms that mix together the scalar and vector sectors. Full article

This study investigates the thermal characteristics of two hybrid nanofluids, single-walled carbon nanotubes with titanium dioxide ($SWCNT-Ti{O}_2$) and multi-walled carbon nanotubes with copper ($MWCNT-Cu$), as they flow over an inclined, porous, and longitudinally stretched cylindrical surface with kerosene as the base fluid. The model takes into consideration all of the consequences of magnetohydrodynamic (MHD) effects, thermal radiation, and Arrhenius-like energy of activation. The outcomes of this investigation hold practical significance for energy storage systems, nuclear reactor heat exchangers, electronic cooling devices, biomedical hyperthermia treatments, oil and gas transport processes, and aerospace thermal protection technologies. The proposed hybrid ANN–numerical framework provides an effective strategy for optimizing the thermal performance of hybrid nanofluids in advanced thermal management and energy systems. A set of coupled ordinary differential equations is created by applying similarity transformations to the governing nonlinear partial differential equations that reflect conservation of mass, momentum, energy, and species concentration. The boundary value problem solver bvp4c, which is based in MATLAB (R2020b), is used to solve these equations numerically. The findings demonstrate that, in comparison to the $MWCNT-Cu/kerosene$ nanofluid, the $SWCNT-Ti{O}_2$/kerosene hybrid nanofluid improves the heat transfer rate (Nusselt number) by up to $23.6\%$. When a magnetic field is applied, velocity magnitudes are reduced by almost $15\%$, and the temperature field is enhanced by around $12\%$ when thermal radiation is applied. The impact of important dimensionless variables, such as the cylindrical surface’s inclination angle, the medium’s porosity, the magnetic field’s strength, the thermal radiation parameter, the curvature ratio, the activation energy, and the volume fraction of nanoparticles, is investigated in detail using a parametric study. According to the comparison findings, at the same flow and thermal boundary conditions, the $SWCNT-Ti{O}_2$/kerosene hybrid nanofluid performs better thermally than its $MWCNT-Cu$/kerosene counterpart. These results offer important new information for maximizing heat transfer in engineering systems with hybrid nanofluids and inclined porous geometries under intricate physical conditions. With its high degree of agreement with numerical results, the ANN model provides a computationally effective stand-in for real-time thermal system optimization. Full article

The spontaneous combustion of coal represents a common and serious safety challenge in underground mining. A frequent cause of mine fires is the ignition of residual coal accumulated in goafs. Based on the governing equations of continuity, momentum, and energy conservation, combined with the theory of flow through porous media, a three-dimensional numerical model was developed to simulate CO₂ injection for fire prevention in coal goafs. Using COMSOL Multiphysics software, the effects of different CO₂ injection parameters (location and flow rate) on oxygen distribution and the range of the oxidation zone within the goaf were investigated. The results indicate that with an injection point 15 m from the working face and a flow rate of 4.41 m³/min, the width of the oxidation zone was most significantly reduced, effectively suppressing the occurrence of coal spontaneous combustion. The location of the injection point was found to have a greater impact on the inerting effect than the injection flow rate. This study provides a theoretical basis and parameter optimization guidelines for CO₂ injection in goaf areas for fire prevention and control. Full article

Recently, Aydiner considered dark matter (DM) and dark energy (DE) as two open, non-equilibrium thermodynamic systems, which have heat changes and particle number changes but have no volume changes. These systems are described by nonlinear coupled equations for the description of mutual and self-interactions and satisfy the energy conservation of thermodynamics. Based on this idea, two three-dimensional (3D) models and a four-dimensional (4D) model are produced. Due to the conservation of the energy–momentum tensor of the sum of the DM and DE energy densities, the continuity equations of both energy densities are also included together in these 3D and 4D thermodynamic models. For the parameters satisfying some conditions, one of the 3D models has two marginal stable non-hyperbolic equilibrium points with a negative real root and a pair of conjugate purely imaginary roots. The marginal stability is highly sensitive to nonlinear terms and parameter noise. Another of the 3D models has unstable saddle-focus equilibrium points, which have a negative real root corresponding to a 1D stable manifold and two conjugate complex roots with positive real parts corresponding to a 2D manifold of unstable spiral. At these equilibria, no energy exchange occurs between the two energy densities, and both energy components reach equilibrium. When some perturbations from the nonlinear terms or parameter noise are given, the DM and DE energy densities are far from equilibrium and continue to exchange each other until they reach equilibrium. The energy exchanges between them may exhibit chaotic behavior like chaotic attractors. However, hyperchaos is not easily found. The 4D model also has unstable saddle-focus equilibrium points and can allow for the onset of chaotic attractors and hyperchaos. In fact, the chaotic dynamics of the 3D and 4D models are caused because of the coupled interactions of particle and thermodynamic systems between DM and DE. Under both the self-interactions and the mutual interactions, the energy exchanges are far from and close to the equilibrium. These interactions cause the energy exchanges to become random, irregular and unpredictable. Full article

The separable heat pipe, with its highly efficient heat transfer and flexible layout features, has become an innovative solution to the heat dissipation problem of batteries, especially suitable for the directional heat dissipation requirements of high-energy-density battery packs. However, most of the number–value models currently studied examine the flow of refrigerant working medium within the pump as an isentropic or isothermal process and are unable to effectively analyze the heat transfer characteristics of different internal regions. Based on the laws of energy conservation, momentum conservation, and mass conservation, this study establishes a steady-state mathematical model of the pump-driven microchannel-separated heat pipe. The influence of factors—such as the phase state change in the working medium inside the heat exchanger, the heat transfer flow mechanism, the liquid filling rate, the temperature difference, as well as the structural parameters of the microchannel heat exchanger on the steady-state heat transfer and flow performance of the pump-driven microchannel-separated heat pipe—were analyzed. It was found that the influence of liquid filling ratio on heat transfer quantity is reflected in the ratio of change in the sensible heat transfer and latent heat transfer. The sensible heat transfer ratio is higher when the liquid filling is too low or too high, and the two-phase heat transfer is higher when the liquid filling ratio is in the optimal range; the maximum heat transfer quantity can reach 3.79 KW. The decrease in heat transfer coefficient with tube length in the single-phase region is due to temperature and inlet effect, and the decrease in heat transfer coefficient in the two-phase region is due to the change in flow pattern and heat transfer mechanism. This technology has the advantages of long-distance heat transfer, which can adapt to the distributed heat dissipation needs of large-energy-storage power plants and help reduce the overall lifecycle cost. Full article

We consider the fourth-order PDE $u_{xxxx}+2u_{xxyy}+u_{yyyy}-u_{tt}=h\left(u\right)$. The Lie and Noether symmetry generators are constructed, and we reduce the PDE to simpler ODEs. Furthermore, we use some well-known methods to compute the conserved vectors associated with the PDE. An analysis of reduced ordinary differential equations (ODEs), invariant solutions, and their physical interpretations is presented. Full article

This study investigates hydrogen storage enhancement through adsorption in porous materials by coupling the Dubinin–Astakhov (D-A) adsorption model with H₂ conservation equations (mass, momentum, and energy). The resulting system of partial differential equations (PDEs) was solved numerically using the finite element method (FEM). Experimental work using activated carbon as an adsorbent was carried out to validate the model. The comparison showed good agreement in terms of temperature distribution, average pressure of the system, and the amount of adsorbed hydrogen (H₂). Further simulations with different adsorbents indicated that compact metal–organic framework 5 (MOF-5) is the most effective material in terms of H₂ adsorption. Additionally, the pair (273 K, 800 s) remains the optimal combination of injection temperature and time. The findings underscore the prospective advantages of optimized MOF-5-based systems for enhanced hydrogen storage. These systems offer increased capacity and safety compared to traditional adsorbents. Subsequent research should investigate multi-objective optimization of material properties and system geometry, along with evaluating dynamic cycling performance in practical operating conditions. Additionally, experimental validation on MOF-5-based storage prototypes would further reinforce the model’s predictive capabilities for industrial applications. Full article

Modified gravity theories with a nonminimal coupling between curvature and matter offer a compelling alternative to dark energy and dark matter by introducing an explicit interaction between matter and curvature invariants. Two of the main consequences of such an interaction are the emergence of an additional force and the non-conservation of the energy–momentum tensor, which can be interpreted as an energy exchange between matter and geometry. By adopting this interpretation, one can then take advantage of many different approaches in order to investigate the phenomenon of gravitationally induced particle creation. One of these approaches relies on the so-called irreversible thermodynamics of open systems formalism. By considering the scalar–tensor formulation of one of these theories, we derive the corresponding particle creation rate, creation pressure, and entropy production, demonstrating that irreversible particle creation can drive a late-time de Sitter acceleration through a negative creation pressure, providing a natural alternative to the cosmological constant. Furthermore, we demonstrate that the generalized second law of thermodynamics holds: the total entropy, from both the apparent horizon and enclosed matter, increases monotonically and saturates in the de Sitter phase, imposing constraints on the allowed particle production dynamics. Furthermore, we present brief reviews of other theoretical descriptions of matter creation processes. Specifically, we consider approaches based on the Boltzmann equation and quantum-based aspects and discuss the generalization of the Klein–Gordon equation, as well as the problem of its quantization in time-varying gravitational fields. Hence, gravitational theories with nonminimal curvature–matter couplings present a unified and testable framework, connecting high-energy gravitational physics with cosmological evolution and, possibly, quantum gravity, while remaining consistent with local tests through suitable coupling functions and screening mechanisms. Full article

A continuum model for describing pseudo-turbulent flows of a dispersed phase is developed using a statistical approach based on the kinetic equation for the probability density of particle velocity and temperature. The introduction of the probability density function enables a statistical description of the particle ensemble through equations for the first and second moments, replacing the dynamic description of individual particles derived from Langevin-type equations of motion and heat transfer. The lack of detailed dynamic information on individual particle behavior is compensated by a richer statistical characterization of the motion and heat transfer within the particle continuum. A numerical simulation of the unsteady flow of a gas–particle suspension generated by the interaction of a shock wave with a particle cloud is performed using an interpenetrating continua model and equations for the first and second moments of both gas and particles. Numerical methods for solving the two-phase gas dynamics equations—formulated using a two-velocity and two-temperature model—are discussed. Each phase is governed by conservation equations for mass, momentum, and energy, written in a conservative hyperbolic form. These equations are solved using a high-order Godunov-type numerical method, with time discretization performed by a third-order Runge–Kutta scheme. The study analyzes the influence of two-dimensional effects on the formation of shock-wave flow structures and explores the spatial and temporal evolution of particle concentration and other flow parameters. The results enable an estimation of shock wave attenuation by a granular backfill. The extended pressure relaxation region is observed behind the cloud of particles. Full article

Reliable simulations of any flow require proper preservation of the fundamental principles governing the mechanics of its motion, whether in differential or integral form. When these principles are solved in differential form, discretization schemes introduce errors by transforming the continuous physical domain into a discrete representation that only approximates it. This paper analyzes the numerical performance of the solver for supersonic chemically active flows, rhoCentralRfFoam, using integral conservation principles of mass, momentum, energy, and chemical species as a validation tool in a classical test case with a highly refined mesh under nonlinear pre-established reference conditions. The analysis is conducted on this specific test case; however, the methodology presented here can be applied to any problem under study. It may serve as an a posteriori verification tool or be integrated into the solver’s workflow, enabling automatic verification of conservation at each time step. The resulting deviations are evaluated, and it is observed that the numerical errors remain below $0.25\%$, even in cases with a high degree of nonlinearity. These results provide preliminary validation of the solver’s accuracy, as well as its ability to capture physically consistent solutions using only information generated internally by the solver for validation. This represents a significant advantage over validation methods that require external comparison with reference solutions, numerical benchmarks, or exact solutions. Full article