Heat Transfer Enhancement of the Absorber Tube in a Parabolic Trough Solar Collector through the Insertion of Novel Cylindrical Turbulators

This study includes an experimental and numerical analysis of the performances of a parabolic trough collector(PTC)with and without cylindrical turbulators.The PTC is designed with dimensions of 2.00 m in length and 1.00 m in width.The related reflector is made of lined sheets of aluminum,and the tubes are made of stainless steel used for the absorption of heat.They have an outer diameter of 0.051 m and a wall thickness of 0.002 m.Water,used as a heat transfer fluid(HTF),flows through the absorber tube at a mass flow rate of 0.7 kg/s.The dimensions of cylindrical turbulators are 0.04 m in length and 0.047 m in diameter.Simulations are performed using the ANSYS Fluent 2020 R2 software.The PTC performance is evaluated by comparing the experimental and numerical outcomes,namely,the outlet temperature,useful heat,and thermal efficiency for a modified tube(MT)(tube with novel cylindrical turbulators)and a plain tube(PT)(tube without novel cylindrical turbulators).According to the results,the experimental outlet temperatures recorded 63.2°C and 50.5°C for the MT and PT,respectively.The heat gain reaches 1137.5 Win the MT and 685.8 Win the PT.Compared to the PT collector,the PTC exhibited a(1.64 times)higher efficiency.

WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).

A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces

In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.

一类退化抛物方程高初始能量下解的有限时刻爆破及整体存在性

We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions.

Optimization of the Physical Aperture of the Parabolic Reflector Antenna

In fields like astronomy and radar technology, high-gain antennas are required for long-distance communication. Due to its relatively large gain, the use of parabolic antennas has become very popular over time, because they can easily achieve gains of above 30 dB at microwave and higher frequencies. Today, most systems’ success depends on how well the antennas perform. These antennas are available in different types and sizes. Each antenna’s effective area usually has less than the actual physical area of the antenna surface. This means that the unused area of the antenna is massive, and a waste. The aim of the research is to show that the actual physical aperture of a parabolic antenna can be reduced as much as possible to equal the effective area, as given by the antenna formula, thereby saving manufacturing costs, improve the aesthetics. In other words, the focus of this work is to experimentally show that reflector antenna can be made of smaller sizes but better performance. Measurements were taken from different positions from a parabolic antenna, the signal level measured and compared with signal levels for optimal performance.

Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.

Design and Development of a Parabolic Trough Solar Air Heater for a Greenhouse Dryer

Design and Development of a Parabolic Trough Solar Air Heater (PTSAH) for a Greenhouse Dryer (GD) was done to improve the dryer’s performance. The materials used for the fabrication of the PTSAH included galvanized sheets covered with aluminium foil, an absorber tube made of GI pipe painted matt black to increase heat absorbance at the focal line, mild steel square tubes, shutter plywood, and an axial fan to push air through the absorber tube. Key geometrical parameters used for the design of the PTSAH were a rim angle of 98 degrees, focal length of 0.2608 m, height of 0.3451 m, length of 2 m, and an aperture width of 1.2 m. The PTSAH’s total aperture surface area was 2.4 m2, while its absorber tube surface area was 0.1587 m2. The PTSAH was experimentally tested to establish its thermal performance. It was found that the ambient air recorded an average value of 31.1˚C and that the air heater could increase the air temperature by 45.6˚C above ambient with a thermal efficiency of 5.3%. It can, therefore, be concluded that the PTSAH can significantly improve the performance of a GD by supplying the GD with air at a higher temperature than ambient.

Nonautonomous Breather and Rogue Wave in Spinor Bose–Einstein Condensates with Space-Time Modulated Potentials

To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose–Einstein condensates with spatiotemporal modulation,we focus on a system of three coupled Gross–Pitaevskii equations with spacetime-dependent external potentials and temporally modulated gain-loss distributions.With different external potentials and gain-loss distributions,various solutions for controlled nonautonomous matterwave breathers and rogue waves are derived by the Darboux transformation method,such as breathers and rogue waves on arched and constant backgrounds which have the periodic and parabolic trajectories.Effects of the gain-loss distribution and linear potential on the breathers and rogue waves are studied.Nonautonomous two-breathers on the arched and constant backgrounds are also derived.

Dynamically Characterizing the Structures of Dirac Points via Wave Packets

Topological non-trivial band structures are the core problem in the field of topological materials.We investigate the topological band structure in a system with controllable Dirac points from the perspective of wave packet dynamics.By adding a third-nearest-neighboring coupling to the graphene model,additional pairs of Dirac points emerge.The emergence and annihilation of Dirac points result in hybrid and parabolic points,and we show that these band structures can be revealed by the dynamical behaviors of wave packets.In particular,for the gapped hybrid point,the motion of the wave packet shows a one-dimensional Zitterbewegung motion.Furthermore,we also show that the winding number associated with the Dirac point and parabolic point can be determined via the center of mass and spin texture of wave packets,respectively.The results of this work could motivate new experimental methods to characterize a system’s topological signatures through wave packet dynamics,which may also find applications in systems of other exotic topological materials.

ALMOST SURELY TIME-SPACE INTERMITTENCY FOR THE PARABOLIC ANDERSON MODEL WITH A LOG-CORRELATED GAUSSIAN FIELD

In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.

Investigation and simulation of parabolic trough collector with the presence of hybrid nanofluid in the finned receiver tube

The present study discusses the thermal performance of the receiver tube,which contains a wall with various fin shapes in the parabolic trough collector.Inserted fins and bulge surfaces of the inner wall of the receiver tube increase the turbulent fluid flow.In pursuance of uniform distribution of heat transfer,various fin shapes such as square-shape,circle-shape,triangle-shape,and combined square-circle shapes were inserted,examined,and compared.A study of the temperature differences and fluid flow is meaningful for this project therefore finite volume method was used to investigate heat transfer.Also,hybrid Nano-Fluid AL_(2)O_(3-)CuO,TiO_(2-)Cu,and AgMgO were applied to increase thermal diffusivity.When the combined square-circle-shaped fin was inserted,the thermal peak of fluid flow in the receiver tube was lower than the other studied fin shapes by almost 1%.Besides,the hybrid nano-fluid Ag-MgO Syltherm-oil-800 has lower thermal waste in comparison to others by more than 3%.

Glancing incidence x-ray fluorescence spectrometry based on a single-bounce parabolic capillary

Glancing incidence x-ray fluorescence spectrometry using a single-bounce parabolic capillary is proposed for the analysis of layered samples.The divergence of the x-ray beam was 0.33 mrad.In this paper,we used this instrumental setup to analyze a Si single crystal and a 50 nm HfO_(2) single-layer film deposited on a Si substrate.

A general method to calculate passive earth pressure on rigid retaining wall for all displacement modes

A general analytical method to calculate the passive rigid retaining wall pressure was deduced considering all displacement modes. First, the general displacement mode function was setup, then the hypotheses were made that the lateral passive pressure is linear to the corresponding horizontal displacement and the soil behind retaining wall is composed of a set of springs and ideal rigid plasticity body, the general analytical method was proposed to calculate the passive rigid retaining wall pressure based on Coulomb theory. The analytical results show that the resultant forces of the passive earth pressure are equal to those of Coulomb＇s theory, but the distribution of the passive pressure and the position of the resultant force depend on the passive displacement mode parameter, and the former is a parabolic function of the soil depth. The analytical results are also in good agreement with the experimental ones.

An Explicit Difference Scheme with High Accuracy and Branching Stability for Solving Parabolic Partial Differential Equation

This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.

A Family of High_order Accuracy Explicit Difference Schemes for Solving 2-D Parabolic Partial Differential Equation

A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).

Oscillation of Systems of Parabolic Differential Equations with Deviating Arguments

To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.

Consistency of Water Production Function Models of Two Crops

On basis of test information, the research performed analysis on water production function models of two crops, which indicated that water model of crops in whole growth stage and water model of crops indifferent growth stages have consistency as well as differences, providing references for optimization of irrigation water. Meanwhile, the research analyzed the deficiency of optimization on irrigation water for crops just by Jensen model.

Influence of the Interaction Between Phonons and Coulomb Potential on the Properties of a Bound Polaron in a Quantum Dot

The properties of a bound polaron in a parabolic quantum dot with weak electron-LO-phonon coupling under a Coulomb field are studied. The ground state energy of the bound polaron is derived by using a linear combination operator and the perturbation method. The influence of the interaction between phonons with different wave vectors in the recoil process on the ground state energy of the bound polaron is discussed. Numerical calculations are performed,and the results show that the ground state energy increases significantly as the effective confinement length of the quantum dot decreases,considering of the interaction between phonons. When l0〉1.0, the influence of the interaction between phonons on the ground state energy cannot be ignored.

A Fractional-Dimension Variational Approach for the Bound Polaron in Parabolic Quantum Wells

The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional- dimensional variational method. The numerical results for the binding energies of the bound polaron and longitudinal-optical phonon contributions in GaAs/Al0.3 Ga0.7 AS parabolic quantum well structures are obtained as functions of the well width. It is shown that the binding energies of the bound polaron are obviously reduced by the electron-phonon interaction and the phonon contribution is observable and cannot be neglected.