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This paper is devoted to study the three-dimensional globally modified Navier–Stokes equations driven by additive white noise on some unbounded domains 풪. By using the Ornstein–Uhlenbeck process, we transfer the original equation to a random dynamical system, and then we prove the existence of pullback attractors for the random dynamical system equations under suitable conditions. Due to the unboundedness of the domains, we get the asymptotic compactness of the solutions by Ball's idea of energy equations. The periodicity of the attractors is also proved when the deterministic non-autonomous external terms are periodic in time. [ABSTRACT FROM AUTHOR]

To solve the problem, a numerical method and an effective algorithm were proposed, which made it possible to study heat and mass transfer processes in a confined plane-parallel and axisymmetric space of a complex configuration in a wide range of initial parameters both in a frozen flow regime and for chemical equilibrium between components. To describe the flow under consideration, a system of equations was used, derived from the Navier–Stokes equations for compressible gas. The original system of equations was written relative to the stream function of vorticity in dimensionless form in a Cartesian coordinate frame under the condition of axial symmetry. The processes of mixing and transfer of gases in a closed region of complex geometry, characteristic of the structures of gas-phase reactors, were studied under conditions of interaction of free and forced convection, considering conjugate heat transfer. It was revealed that at certain values of the flow rate of the injected gas and the geometric dimensions of the calculation domain, the formation of the main one-vortex and twin-vortex flow patterns is possible. [ABSTRACT FROM AUTHOR]

In winter, rivers in cold regions often experience flood disasters resulted from ice jams or ice dams. Investigations of the variation of ice jam thickness and water level during an ice jammed period are not only a practical need for ice prevention to avoid disaster and plan water resource, but also essential for the development of any mathematical model for predicting the evolution of ice jam. So far, some equations based on the energy equation have been proposed to describe the relationship between ice jam thickness and water level. However, in the derivation of these equations, the local head loss coefficient at the ice jam head and the riverbed slope factor were neglected. Obviously, those reported equations cannot be used to preciously describe the flow energy equation with ice jams and accurately calculate the ice jam thickness and water level. In the present study, a more comprehensive theoretical model for hydraulic calculation of ice jam thickness has been derived by considering important and essential factors including riverbed slope and local head loss coefficient at the ice jam head. Furthermore, based on the data collected from laboratory experiments of ice jam accumulation, the local head loss coefficient at the ice jam head has been calculated, and the empirical equation for calculating the local head loss coefficient has been established by considering flow Froude number and the ratio of ice discharge to flow discharge. The results of this study not only provide a new reference for calculating ice jam thickness and water level, but also present a theoretical basis for accurate CFD simulation of ice jams. [ABSTRACT FROM AUTHOR]

In the course of work on the energy perfection of thermal control systems for spacecraft with a twophase circuit, the issue of partial regeneration of thermal energy into electrical energy in a low-speed turbogenerator is considered, part of the design work requires computational modeling during the transport of swirling flows in the axial direction from the external input to the input plane into the impeller, which determines the need for theoretical and experimental elaboration of the problem. The paper considers transformations of equations for changing the amount of fluid motion in boundary conditions of an axial annular channel with fixed cylindrical surfaces. Assuming the symmetry axis of the flows using the integral form of writing the continuity equation, the relations are obtained in the form of two differential equations with expressed derivatives along the channel axis for the total pressure p* and the circumferential velocity constant Cu = UR (const — at the integration step). The equation forms the basis of the algorithm of integration in finite differences supplemented by a system of service equations describing the friction stress, thermodynamic parameters, etc. Test calculations are carried out using real parameters, the results are analyzed.

During the early post-Cold War period, the global order witnessed a significant shift, with Western liberal democracy emerging as the predominant force. However, this ascent of the United States in pursuit of global dominance gave rise to a Security Dilemma, fostering the emergence of alternative powers in various regions worldwide. Among these, Russia has played a prominent role, notably in the Middle East. This study seeks to examine Russia's historical and contemporary objectives in the Middle East, analyzing its political, economic, and security pursuits. Through the lens of the "Security Dilemma," the article underscores Russia's transformation into a potent regional counterbalance to Western influence in various respects. The article concludes that the sustainability of Russia's gains depends on the fluid Middle East landscape, the continuation of Putin's leadership, and the influence of potential Western sanctions. [ABSTRACT FROM AUTHOR]

ObjectivesThis paper aims to research the effects of the temperature and compressibility of liquid water on the super-cavitation phenomenon of an ultra-high-speed underwater vehicle and its motion characteristics. Methods First, based on CFD general software Fluent 19.2, the free motion of transonic and supersonic vehicles is computed using a numerical model that considers both the compressibility and temperature of the water. Qualitative and quantitative comparisons with the experimental results of reference [1] are made, and the effectiveness of the numerical method is verified. The motion characteristics at different initial speeds are then analyzed using the range at the sailing time of 0.008 s as the comparison base. Finally, the influence of the launch depth and environment temperature on the motion characteristics is discussed. Results It is found that when the speed is greater than 2 000 m/s, increasing the initial speed does not significantly increase the effective range; the critical speed is found between 1 450 m/s and 1 475 m/s, where the range variation is less than 3% with or without the influence of the temperature; as the launch depth increases, the resistance of the vehicle becomes greater and the sailing range gradually decreases; and the higher the environment temperature, the shorter the effective range. Conclusions It is shown that the numerical model proposed herein, which considers both the temperature and compressibility of liquid water, can provide valuable references for the motion analysis of ultra high-speed underwater vehicles and corresponding practical applications.

In this paper, the analytical solution to the problem of heat transfer and fluid flow was obtained by using the quadruple Laplace transform method. Temperature distribution and fluid flow distribution were shown, temperature and fluid flow increase when the value of z increases, as well as the effect of the radiation parameter shown, it was concluded that the temperature increase with the increase in the value of the radiation coefficient . Matlab was used to plot the results.

Traveling atmospheric disturbance (TAD) plays an important role in the energy and momentum transfer from the lower atmosphere to the upper atmosphere, and from high‐ to low‐latitudes. It is common to observe TADs propagating toward low latitudes because of enhanced Joule heating and/or the Lorentz force at the high‐latitude ionosphere during storm time. However, energy or momentum variation associated with their equatorward propagation remains unclear. Two geomagnetic storms occurred on 7–8 September 2017 and upper atmospheric disturbances are observed by the Swarm satellites and the Global Navigation Satellite System Total Electron Content network. We conduct a model simulation and term analysis of the energy equation to investigate the dominant terms of TAD. Adiabatic heating, conduction heating, and advection heating dominate the energy budget of TAD. Adiabatic heating plays an important role in the energy budget by transferring the most energy of TAD. An anti‐phase relationship between adiabatic and conduction heating is found in the propagation of these TADs. An in‐phase relationship between adiabatic and advection heating is also found. Physical processes behind these anti‐phase and in‐phase relationships are illustrated with a schematic. Finally, based on the dominant terms and the relationships between them, the whole process of generation, propagation, and dissipation of TAD is given. Plain Language Summary: Wave is a prevalent phenomenon in the atmosphere. They can transfer the energy and momentum from where they are generated to where they arrived. Traveling atmospheric disturbance (TAD) accompanied by gas expansion and compression is a specific wave type in the atmosphere. TAD often has a huge spatial scale of hundreds or even thousands of km, and it can propagate from one hemisphere to another hemisphere or even travel an entire circle around the earth. Many observations about TAD rise a challenge in explaining the mechanism of TAD's generation, propagation, and dissipation. This paper uses a physically based model to study TADs. We use the parameters calculated by the energy equation of the model to study the relatively effective heating processes in the energy budget of TAD. The relatively effective processes are found and relationships between them are shown. Further analysis and explanations are given to understand the relationships between these physical processes. Finally, the whole process from the generation of TAD to the dissipation of TAD is given. Key Points: Model‐data comparisons are used to understand the behavior of traveling atmospheric disturbance (TAD) during a geomagnetic storm on 7–8 September 2017A continental‐scale TAD/traveling ionospheric disturbance pair is observed simultaneouslyThe roles the dominant terms played during the propagation of TAD are given [ABSTRACT FROM AUTHOR]

The basic concepts of the breakage mechanics of rocks and soils are briefly introduced in this article. The underlying mechanism for the breakage evolution of loess in a natural acidic environment is detailed, and a method is presented for calculating the rate of reaction between the calcium carbonate (CaCO3, an insoluble salt) in loess and acid. A breakage variable that accounts for the effects of chemical factors is derived from energy equations and macroscopic and microscopic energy balance principles. The existing binary-medium model for loess is improved, considering the breakage mechanism for loess in an acidic environment and the rate at which calcareous bonds react with acid. In the improved model, loess is treated as a combination of structural bodies and weak zones that withstand changes in external stresses (hydrological, mechanical, and acidic). Simple mathematical expressions are used to represent the breakage patterns and characteristics of the structural bodies and weak zones in loess in an acidic environment. Each parameter in the model has a clear physical meaning and can be determined through laboratory testing. The model was validated by comparing the calculated results against the results of collapsibility and consolidated-drained triaxial tests on a loess sample in an acidic environment. The results show that the model can accurately simulate the deformation characteristics of loess in an acidic environment and serve as a reference for engineering construction on loess foundations under the influence of acidic wastewater and acid rain. [ABSTRACT FROM AUTHOR]

Overshot gates are used as a flow measuring device to fix the upstream water level. Flow through the overshot gates under submerged conditions often has many problems, mainly due to the need to measure the tail-water depth. In this research, the application of the brink depth, instead of tail-water depth, has been selected to overcome this problem. Many experiments were conducted with nine different angles of the overshot lip under free and submerged conditions. The discharge coefficient of the gate was estimated based on the brink depth. Besides, the flow discharge through the gate was evaluated through an equation based on the energy equation and the stage-discharge relation. The results showed good consistency and high accuracy under free and submerged conditions which refers to the suitability of the proposed equations for flow discharge and water depth because of their theoretical basis. [ABSTRACT FROM AUTHOR]

It is a well‐known fact, that hydrodynamically supported systems are prone to nonlinear vibrations. Their exact simulative prediction with respect to frequency and amplitude is complicated by the fact that different system properties interact. The paper at hand outlines an approach that takes all relevant influences like rigid body motions, elastic deformations, nonlinear relation between fluid film pressure and bearing kinematics as well as temperature increase due to power loss or adjacent heat sources into account as detailed as necessary. Both journal and thrust bearings are considered as they contribute to the system's stiffness and damping capabilities. The approach is applied to self‐excited pad vibrations of tilting pad thrust bearings as well as the run‐up simulation of a turbocharger rotor under different axial loads. Both models are validated against measurements. [ABSTRACT FROM AUTHOR]

Applications: The fins performance under natural convection is essential to make it more functional for large scale applications more specifically in thermal engineering. For this, it is important to introduce new techniques to enhance the fins performance instead of traditional way. Thus, this study introduces a new way to make the fin more efficient using ternary nanomaterial under nanoparticles shape factor. The annular fin significantly contributes in electronics to exhaust the hot air, injector pumps and applied thermal engineering. Purpose: and Methodology: This work focuses on the fin energy model using shape factors. Therefore, the ternary nanofluid, natural convection, thermal radiation and magnetic field used to develop the model. Then, the RKF-45 implemented to investigate physical results. Core findings: Keen analysis of the physical results reveal that the coefficient of thermal conductivity ranging from 0.0% < α1 < 3.0% and natural convection have major role in the fins energy performance. Induction of magnetic field and thermal radiation Rd are reliable for the fin cooling and, heating source Q1 = 0.2,0.4,0.6,0.8 promote the fin energy capability in the existence of (Al2O3–CuO–Cu) ternary nanomaterial with concentration factor up to 2%. On the comparative basis, ternary nanomaterial makes the fin more efficient than hybrid nanomaterial.

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Microstructured optical fibres (MOFs) are fibres that contain an array of air holes that runs through the whole fibre length. The hole pattern of these fibres can be customized to manufacture optical devices for different applications ranging from high-power energy transmission equipment to telecommunications and optical sensors. During the drawing process, the size of the preform is greatly scaled down and the original hole pattern result might be modified, potentially leading to unwanted optical effects. Because only a few parameters can be controlled during the fabrication process, mathematical models that can accurately describe the fibre drawing process are highly desirable, being powerful predictive tools that are significantly cheaper than costly experiments. In this manuscript, we derive a new asymptotic energy equation for the drawing process of a single annular capillary and couple it with existing asymptotic mass, momentum, and evolution equations. The whole asymptotic model only exploits the small aspect ratio of a capillary and relies on neither a fitting procedure nor on any empirical adjustable parameters. The numerical results of the simplified model are in good accordance with experimental data available in the literature both without inner pressurization and when internal pressure is applied. Although valid only for annular capillaries, the present model can provide important insights towards understanding the MOF manufacturing process and improving less detailed approaches for more complicated geometries. [ABSTRACT FROM AUTHOR]

The well-posedness and global attraction are proved for nonautonomous 2D nonlinear damped Schrödinger equations with almost periodic external source in a bounded region. The proofs rely on a development of the method of energy equation. The research is inspired by the problems of laser and maser coherent radiation. [ABSTRACT FROM AUTHOR]

An event of mesoscale vortex with MCS occurred in Shandong region on 3 August 2015 was investigated and analyzed using the WRF mesoscale numerical model based on NCEP/NCAR analysis data and Doppler radar observation data. The study revealed the reason for the occurrence and development of the mesoscale vortex and its effect on the mesoscale convection system under the environment of the northeast cold vortex. The results are as follows. (1) The upper-level jet stream' s strong divergence in front of the trough of the synoptic-scale northeast cold vortex and the low-level instability energy release provided favorable condition for the lower mesoscale vortex and convection occurrence. The generation of the low-level mesoscale vortex promoted the occurrence of the MCS. (2) When the mesoscale vortex forms and develops, the positive vorticity of the lower layer is mainly affected by the horizontal divergence term and the vertical transport term, with the former having a greater effect. The positive vorticity of the middle layer is mainly affected by the vertical transport term. Due to positive contributions of the two terms, the positive vorticity increases, and the vortex develops.When the mesoscale vortex weakens, the horizontal divergence term in the middle and lower layers weakens and the vertical transport term becomes negative, leading to the decrease of positive vorticity generation and the increase of negative vorticity generation, and therefore the vortex decreases. (3) When the MCS develops, the increase of perturbation effective potential energy mainly comes from the latent heat release and the conversion from zonal mean effective potential energy to disturbance effective potential energy, and then the perturbation effective potential energy is transformed into the perturbation kinetic energy through the vertical motion. The increase of the perturbation kinetic energy promotes the development of convections. The mesoscale vortex not only provides energy for the severe convection, but also influences the evolution of the strong convection.

Flow problems are solved using so-called fundamental equations and the corresponding initial and boundary conditions. The fundamental equations are the motion equation, the continuity equation, the energy conservation equation, and the state equations. In our paper, we extend the validity of the equation of motion used to describe one-dimensional, steady-state tubular flow to a case in which the mass flow of the medium changes along the tubular axis during the flow. Such flows occur in perforated and/or porous pipes and air ducts. The research in this direction was motivated by the fact that the extension and formulation of the equation of motion in this direction has not been carried out with completely general validity. In the equation of motion used to solve the problems, the isochoric and isotherm nature were assumed. In our paper, we present fundamental equations that formulate differential equations to describe polytrophic and expanding flows. [ABSTRACT FROM AUTHOR]

This paper presents a finite-element-based computational model to evaluate the thermal behaviour of composite slabs with a steel deck submitted to standard fire exposure. This computational model is used to estimate the temperatures in the slab components that contribute to the fire resistance according to the load-bearing criterion defined in the standards. The numerical results are validated with experimental results, and a parametric study of the effect of the thickness of the concrete on the temperatures of the slab components is presented. Composite slabs with normal or lightweight concrete and different steel deck geometries (trapezoidal and re-entrant) were considered in the simulations. In addition, the numerical temperatures are compared with those obtained using the simplified method provided by the standards. The results of the simulations show that the temperatures predicted by the simplified method led, in most cases, to an unsafe design of the composite slab. Based on the numerical results, a new analytical method, alternative to the simplified method, is defined in order to accurately determine the temperatures at the slab components and, thus, the bending resistance of the composite slabs under fire conditions. [ABSTRACT FROM AUTHOR]

This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers. [ABSTRACT FROM AUTHOR]

Bump foil journal bearings (BFJBs) are widely used in the superchargers of aviation piston engines (APEs). This paper proposes a method to evaluate the operating state of superchargers by monitoring the bearing temperature. A numerical model with a repeating symmetrical structure in the axial direction is established based on a certain type of supercharger, which solves the temperature field of BFJBs with the non-isothermal Reynolds equation and energy equation. It can be used to analyze the effect of thermal expansion on lift-off speed and stop-contact speed. A new test rig and six various BFJBs were designed to check the temperature characteristics of the BFJBs with variable load and speed. By comparing the numerical results with the experimental results, it was shown that the air film temperature increased almost linearly with the increase in bearing load and speed. However, the temperature increase caused by the rotation speed was significantly greater than the load. The structural parameters of the BFJB affected the bearing support stiffness, which had a nonlinear effect on the lift-off speed and air film temperature. Therefore, the proposed method to evaluate the state of superchargers with BFJBs was effective. These thermal characteristics can be used to guide BFJB design and predict the life cycle of BFJBs. [ABSTRACT FROM AUTHOR]

FAME (biodiesel) is an alternative fuel that can be produced from vegetable oils. There is growing interest in the research and development of renewable energy sources. A possible solution is a biofuel usable in compression-ignition engines (diesel engines) produced from biomass rich in fats and oils. This paper contains a new and safer design of an esterification reactor for producing FAME (biodiesel) by utilizing high boiling point fluid (called phenyl-naphthalene). CFD simulation of biodiesel production by using methyl imidazolium hydrogen sulfate ionic liquid has been carried out. Ionic liquids (ILs) are composed of anions and cations that exist as liquids at relatively low temperatures. They have many advantages, such as chemical and thermal stability, low flammability, and low vapor pressures. In this work, the ionic liquids have been applied in organic reactions as solvents and catalysts of the esterification reaction. The great qualities of high boiling temperature fluids, along with advances in the oil and gas industries, make the organic concept more suitable and safer (water coming into contact with liquid metal may cause a steam explosion hazard) for heating the esterification reactor. The COMSOL Multiphysics code has been employed and simultaneously solves the continuity, fluid flow, heat transfer, and diffusion with chemical reaction kinetics equations. It was shown that the heat flux could provide the necessary heat flux required for maintaining the esterification process. It was found that the mass fractions of methanol and oleic acid decrease along the reactor axis. The FAME mass fraction increased along the reactor axis. The maximal biodiesel yield obtained in the esterification reactor was 86%. This value is very similar to the experimental results obtained by Elsheikh et al. [ABSTRACT FROM AUTHOR]

This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries. Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation. Because of little maintenance, the heat exchanger of such type is extensively used. Here, we generate simulation of flow and heat transfer using nonisothermal flow interface in the Comsol multiphysics 5.4 which executes the Reynolds averaged Navier stokes equation (RANS) model of the turbulent flow together with heat equation. Simulation is tested with Prandtl number (Pr = 0.7) with inlet velocity magnitude in the range from 1 to 2 m/sec which generates the Reynolds number in the range of 2.2 × 105 to 4.4 × 105 with turbulence kinetic energy and the dissipation rate in ranges (3.75 × 10−3 to 1.5 × 10−2) and (3.73 × 10−3−3 × 10−2) respectively. Two correlations available in the literature are used in order to check validity. The results are displayed through streamlines, surface plots, contour plots, isothermal lines, and graphs. It is concluded that by retaining such an arrangement a quick distribution of the temperature over the domain can be seen and also the velocity magnitude is increasing from 333.15% to a maximum of 514%. The temperature at the middle shows the consistency in value but declines immediately at the end. This process becomes faster with the decrease in inlet velocity magnitude. [ABSTRACT FROM AUTHOR]

[Display omitted] • Clarification of DPG performance during winter night by experiment and simulation. • Unsteady CFD modeling of microclimate in cropped greenhouse. • Applying a new sensible heat term to energy equation for cropped greenhouse. • Improvement of computational modeling of complex biological system. • Extension of ANSYS FLUENT's (or CFD) capability by UDF coding. Feasibility of winter-cultivation of fruit vegetables was studied in a solar double plastic covered greenhouse in a temperate zone. An experment for 24-hour-course including a cold night was performed and an unsteady numerical model was developed to predict microclimate in the greenhouse. Sensible heat term with separated air and leaf temperatures was applied to energy equation. Modeling of plant transpiration and outside boundary conditions were accomplished by applying a user defined function added to FLUENT. Comparisons between measured and simulated air/leaf temperatures showed a good agreement for the 24-hour-course. Simulations were performed to examine the feasibility of ensuring the inside air temperature higher than 12 ℃ (the lowest temperature limit for fruit vegetables) in inner greenhouse during the coldest winter night. When covering both the outer and inner films with quilts, it could overcome the night with the lowest outside air temperature of −18.6 ℃. A necessity of heat shield for north wall outside surface was confirmed. Results show that the double plastic covered greenhouse can be a good passive solar system for winter-cultivating the fruit vegetables in some temperate zones. [ABSTRACT FROM AUTHOR]

Gas foil bearings are often used in high-speed turbomachinery such as turboexpanders and turbochargers due to their merits over simple gas-lubricated bearings. The merits of gas foil bearings include their ability to tailor dynamic parameters such as stiffness and damping. Gas foil bearings usually have low clearance and operate at a high rotational speed, which eventually leads to velocity slip at the solid–fluid interface. This article investigates the effect of slip flow on various parameters of gas foil thrust bearings. A numerical model is formulated to predict pressure, film thickness and temperature distribution of helium lubricated gas foil thrust bearing at high rotating speed. The Reynolds equation is modified by assuming first-order slip coupled with the structural (compliant) and energy equation. The temperature-dependent viscosity and density of the fluid are also considered in the Reynolds equation to predict the thermohydrodynamic behaviour of gas foil thrust bearings. The numerical model thus developed uses a finite-difference method and the Newton–Raphson method to solve the Reynolds equation,whereas the successive over-relaxation method is used to solve the energy equation. Various performance parameters are compared for slip and no-slip conditions for gas foil thrust bearings. The results show a considerable difference between the two phenomena. Also, the conventional Reynolds equation tends to overestimate the load-carrying capacity. [ABSTRACT FROM AUTHOR]

The purpose of the article is to analytically solve the conjugate problem of heat transfer in a viscous shock layer on a blunt object and thermal conductivity in an anisotropic half-space. A feature of the flow around such bodies near the critical point is that in this case, the boundary layer equations are not satisfied and it is necessary to solve the Navier-Stokes equations together with the equations of continuity, state, and energy, however, in a stationary formulation of an incompressible flow. The problem of coupled heat transfer between a viscous shock gasdynamic layer and anisotropic half-space with the assumption of incompressibility of the gasdynamic flow behind the normal part of the shock wave is posed. An analytical solution to this problem is obtained with a boundary condition at the gas-solid object interface in the form of a parameter – temperature, as well as an analytical solution to the thermal conductivity problem in an anisotropic half-space with the same boundary condition.

The process of oil-water displacement is one of the key technologies in offshore underwater tank. When hot oil is contacting the normal-temperature water, the interfacial heat transfer should be investigated as the heat loss may result in wax precipitation and solidification which will reduce the flowing of oil and thus affect the process. As for the numerical simulation of heat transfer, the calculation is costly as the underwater tank is usually large and the displacement period is long. A high precision computing method would greatly reduce the mesh scale. Therefore, this research is performed to establish a high precision computing solver. Based on volume of fluid (VOF), a new form of energy equation is proposed. This equation is derived from temperature equation and the variable internal energy per volume is used. This variable is additive and has a close relationship with volume fraction. With algorithm implantation to OpenFOAM, two non-isothermal VOF solvers are established corresponding to temperature equation and the new equation respectively. After an analytical solution is built, the two solvers are compared. The solver based on the new equation presents far more accurate results than the solver based on temperature equation. An energy weighted scheme is more reasonable than a linear temperature distribution for the mixture phase. [ABSTRACT FROM AUTHOR]

Microstructured optical fibres (MOFs) are fibres that contain an array of air holes that runs through the whole fibre length. The hole pattern of these fibres can be customized to manufacture optical devices for different applications ranging from high-power energy transmission equipment to telecommunications and optical sensors. During the drawing process, the size of the preform is greatly scaled down and the original hole pattern result might be modified, potentially leading to unwanted optical effects. Because only a few parameters can be controlled during the fabrication process, mathematical models that can accurately describe the fibre drawing process are highly desirable, being powerful predictive tools that are significantly cheaper than costly experiments. In this manuscript, we derive a new asymptotic energy equation for the drawing process of a single annular capillary and couple it with existing asymptotic mass, momentum, and evolution equations. The whole asymptotic model only exploits the small aspect ratio of a capillary and relies on neither a fitting procedure nor on any empirical adjustable parameters. The numerical results of the simplified model are in good accordance with experimental data available in the literature both without inner pressurization and when internal pressure is applied. Although valid only for annular capillaries, the present model can provide important insights towards understanding the MOF manufacturing process and improving less detailed approaches for more complicated geometries.

This article is concerned with the existence as well as regularity of pullback attractors for a wide class of non-autonomous, fractional, nonclassical diffusion equations with (p, q)-growth nonlinearities defined on unbounded domains. We first establish the well-posedness of solutions as well as the existence of an energy equation, and then prove the existence of a unique pullback attractor in the fractional Sobolev space H s (R N) for all s ∈ (0 , 1 ] . Finally, we show that this attractor is a bi-spatial (H s (R N) , L r (R N)) -attractor in two cases: 2 ≤ r ≤ max (p , q) for s = 1 ; and 2 ≤ r < max (p , q) for s ∈ (0 , 1). The idea of energy equations and the method of asymptotic a priori estimates are employed to establish the pullback asymptotic compactness of the solutions in H s (R N) ∩ L r (R N) in order to overcome the non-compactness of the Sobolev embedding on the unbounded domain as well as the weak dissipation of the equations. This is the first time to study the bi-spatial attractor of the equation when the initial space is H s (R N) , and the result of this article is new even in H 1 (R N) ∩ L r (R N) when the fractional Laplace operator reduces to the standard Laplace operator. [ABSTRACT FROM AUTHOR]

Electrohydrodynamics (EHD) instability of a vertical cylindrical interface is tackled in the present study. The interface separates two viscous, homogeneous, porous, incompressible, and dielectric fluids which totate about the common cylindrical axis with different uniform angular velocities. A uniform axial electric field acts upon the considered system. Additionally, the influence of heat transfer is incorporated into the buoyancy term as well as the surface tension parameter, giving rise to the thermo-capillary effect. In this context, the viscous potential theory as well as the standard normal modes analysis are employed. The distributions of temperature, pressure, and velocity fields are evaluated. The linear stability approach resulted in an exceedingly complicated transcendental dispersion relation. The non-dimensional analysis revealed some physical Ohnesorge, Darcy, Rayleigh, Prandtle and Weber numbers. Actually, the dispersion relation has no closed form solution. Consequently, a numerical technique is utilized to display the stability profile. The relation between the growth rate and the wavenumber of the surface waves is constructed. The influences of various physical parameters on the stability profile are illustrated. It is found that the Ohnesorge number plays a dual role in the stability configuration. [ABSTRACT FROM AUTHOR]

This paper presents a finite-element-based computational model to evaluate the thermal behaviour of composite slabs with a steel deck submitted to standard fire exposure. This computational model is used to estimate the temperatures in the slab components that contribute to the fire resistance according to the load-bearing criterion defined in the standards. The numerical results are validated with experimental results, and a parametric study of the effect of the thickness of the concrete on the temperatures of the slab components is presented. Composite slabs with normal or lightweight concrete and different steel deck geometries (trapezoidal and re-entrant) were considered in the simulations. In addition, the numerical temperatures are compared with those obtained using the simplified method provided by the standards. The results of the simulations show that the temperatures predicted by the simplified method led, in most cases, to an unsafe design of the composite slab. Based on the numerical results, a new analytical method, alternative to the simplified method, is defined in order to accurately determine the temperatures at the slab components and, thus, the bending resistance of the composite slabs under fire conditions.

In this article, we have presented a parametric finite difference method, a numerical technique for the solution of two point boundary value problems in ordinary differential equations with mixed boundary conditions. We have tested proposed method for the numerical solution of a model problem. The numerical results obtained for the model problem with constructed exact solution depends on the choice of parameters. The computed result of a model problem suggests that proposed method is efficient.

The Samani, Magallanez, Baiamonte, Ferro (SMBF) flume is a simple and inexpensive instrument for indirect discharge measurement that was originally proposed for use in a horizontal channel and then also applied in sloping channels. The contraction of the flow cross section, aimed at establishing a critical flow condition, is simply obtained by applying two half cylinders to the walls of a rectangular cross section. In this paper a theoretical approach previously proposed for a horizontal SMBF flume is first extended to a sloping SMBF flume and a new stage-discharge relationship is deduced. Then, this equation is experimentally tested using laboratory measurements from literature for different values of the contraction ratio and flume slope, and its reliability is compared to the reliability of the equation originally proposed in the literature. [ABSTRACT FROM AUTHOR]

Turbulent energy plays a vital role in science and industries. Fiber suspension in turbulent flows has received significant attention since the electrical, thermal, and mechanical characteristics of the relating fiber composites are tactful to the spatial configuration and orientation of fibers. Turbulent energy can be affected by the fibers passes through the turbulent flow. It is further influenced by the occurrence of dust or other particles. The impact of the fibers along with such particles needs to be studied. To analyze the impact, it is very important to model dusty fluid turbulent fiber motion which can be substantially utilized in science and industries. Therefore, this study aims to construct a model for dusty fluid turbulent energy of fiber suspensions. The energy equation for turbulent flow was taken into account to develop the model. The turbulent fiber motion for dusty fluid was derived in correlation tensors, where the tensors are the function of distance, time, and space coordinates.

Bump foil journal bearings (BFJBs) are widely used in the superchargers of aviation piston engines (APEs). This paper proposes a method to evaluate the operating state of superchargers by monitoring the bearing temperature. A numerical model with a repeating symmetrical structure in the axial direction is established based on a certain type of supercharger, which solves the temperature field of BFJBs with the non-isothermal Reynolds equation and energy equation. It can be used to analyze the effect of thermal expansion on lift-off speed and stop-contact speed. A new test rig and six various BFJBs were designed to check the temperature characteristics of the BFJBs with variable load and speed. By comparing the numerical results with the experimental results, it was shown that the air film temperature increased almost linearly with the increase in bearing load and speed. However, the temperature increase caused by the rotation speed was significantly greater than the load. The structural parameters of the BFJB affected the bearing support stiffness, which had a nonlinear effect on the lift-off speed and air film temperature. Therefore, the proposed method to evaluate the state of superchargers with BFJBs was effective. These thermal characteristics can be used to guide BFJB design and predict the life cycle of BFJBs.

Spar Drilling Production Storage and Offloading (SDPSO) is a new type of deep ocean platform developed in recent years. The process of oil-water displacement is used for oil storage and offloading and the research on the accompanying heat flow has been significant. The wax precipitation and solidification at low temperature will particularly affect the flowing of oil in the displacement process. When the heat flow is concerned, numerical simulation requires large computation. It is necessary to develop an efficient numerical method for this calculation. As a kind of interface tracking method, the volume of fluid (VOF) method needs less computing resources compared with other multiphase numerical methods. As for thermal expressions, there are mainly two kinds of governing equations, i.e. temperature equation and enthalpy equation, and two kinds of interpolation scheme of heat conductivity, i.e. algebraic interpolation scheme and harmonic interpolation scheme. There is a need to find out which combination of governing equation and interpolation scheme of heat conductivity would result in a better precision for the heat flow. Therefore, four non-isothermal solvers, corresponding to the four combinations, are established. After comparison with an analytical solution, it is found that the temperature equation together with the harmonic interpolation scheme of heat conductivity results in better precision. [ABSTRACT FROM AUTHOR]

The purpose of the article is to analytically solve the conjugate problem of heat transfer in a viscous shock layer on a blunt object and thermal conductivity in an anisotropic half-space. A feature of the flow around such bodies near the critical point is that in this case, the boundary layer equations are not satisfied and it is necessary to solve the Navier-Stokes equations together with the equations of continuity, state, and energy, however, in a stationary formulation of an incompressible flow. The problem of coupled heat transfer between a viscous shock gasdynamic layer and anisotropic half-space with the assumption of incompressibility of the gasdynamic flow behind the normal part of the shock wave is posed. An analytical solution to this problem is obtained with a boundary condition at the gas-solid object interface in the form of a parameter – temperature, as well as an analytical solution to the thermal conductivity problem in an anisotropic half-space with the same boundary condition. [ABSTRACT FROM AUTHOR]

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