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.

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.

Improving Heat Transfer in Parabolic Trough Solar Collectors by Magnetic Nanofluids

A parabolic trough solar collector(PTSC)converts solar radiation into thermal energy.However,low thermal efficiency of PTSC poses a hindrance to the deployment of solar thermal power plants.Thermal performance of PTSC is enhanced in this study by incorporating magnetic nanoparticles into the working fluid.The circular receiver pipe,with dimensions of 66 mm diameter,2 mm thickness,and 24 m length,is exposed to uniform temperature and velocity conditions.The working fluid,Therminol-66,is supplemented with Fe3O4 magnetic nanoparticles at concentrations ranging from 1%to 4%.The findings demonstrate that the inclusion of nanoparticles increases the convective heat transfer coefficient(HTC)of the PTSC,with higher nanoparticle volume fractions leading to greater heat transfer but increased pressure drop.The thermal enhancement factor(TEF)of the PTSC is positively affected by the volume fraction of nanoparticles,both with and without a magnetic field.Notably,the scenario with a 4%nanoparticle volume fraction and a magnetic field strength of 250 G exhibits the highest TEF,indicating superior thermal performance.These findings offer potential avenues for improving the efficiency of PTSCs in solar thermal plants by introducing magnetic nanoparticles into the working fluid.

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.

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.

Fluctuation pressure on a bio-membrane confined within a parabolic potential well

A compliant bio-membrane with a nominally fiat reference configuration is prone to random transverse deflections when placed in water, due primarily to the Brownian motion of the water molecules. On the average, these fluctuations result in a state of thermodynamic equilibrium between the entropic energy of the water and the total free en- ergy of the membrane. When the membrane is in close proximity to a parallel surface, that surface restricts the fluctuations of the membrane which, in turn, results in an increase in its free energy. The amount of that increase depends on the degree of confinement, and the resulting gradient in free energy with degree of confinement implies the existence of a confining pressure. In the present study, we assume that the confinement is in the form of a continuous parabolic po- tential well resisting fluctuation. Analysis leads to a closed form expression for the mean pressure resulting from this confinement, and the results are discussed within the broader context of results in this area. In particular, the results provide insights into the roles of membrane stiffness, number of degrees of freedom in the model of the membrane and other system parameters.

Studies on the Second-Order Nonlinear Optical Properties of Parabolic andSemi-parabolic Quantum Wells with Applied Electric Fields

Within the framework of compact density matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG)susceptibility tensor is given in the electric-field-biased parabolic and semi-parabolic quantum wells (QWs). The simple analytical formula for the SHG susceptibility in the systems is also deduced. Numerical results on typical AlGaAs/GaAs materials show that, for the same effective width,the SHG susceptibility in semi-parabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semiparabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably.Moreover, the SHG susceptibility is also related to the parabolic confinement frequency and the relaxation rate of the systems.

Plasmons in a free-standing nanorod with a two-dimensional parabolic quantum well caused by surface states

The collective charge density excitations in a free-standing nanorod with a two-dimensional parabolic quantum well are investigated within the framework of Bohm-Pine＇s random-phase approximation in the two-subband model.The new simplified analytical expressions of the Coulomb interaction matrix elements and dielectric functions are derived and numerically discussed.In addition,the electron density and temperature dependences of dispersion features are also investigated.We find that in the two-dimensional parabolic quantum well,the intrasubband upper branch is coupled with the intersubband mode,which is quite different from other quasi-one-dimensional systems like a cylindrical quantum wire with an infinite rectangular potential.In addition,we also find that higher temperature results in the intersubband mode（with an energy of 12 meV（～ 3 THz）） becoming totally damped,which agrees well with the experimental results of Raman scattering in the literature.These interesting properties may provide useful references to the design of free-standing nanorod based devices.

Optical Conductivity of Impurity-Doped Parabolic Quantum Wells in an Applied Electric Field

The optical conductivity of impurity-doped parabolic quantum wells in anapplied electric field is investigated with the memory-function approach, and the analyticexpression for the optical conductivity is derived. With characteristic parameters pertaining toGaAs/Ga_(1-x)Al_xAs parabolic quantum wells, the numerical results are presented. It is shown that,the smaller the well width, the larger the peak intensity of the optical conductivity, and the moreasymmetric the shape of the optical conductivity; the optical conductivity is more sensitive to theelectric field, the electric Geld enhances the optical conductivity; when the dimension of thequantum well increases, the optical conductivity increases until it reaches a maximum value, andthen decreases.

Intersubband optical absorption of electrons in double parabolic quantum wells of Al_xGa_(1-x)As/Al_yGa_(1-y)As

Some realizable structures of double parabolic quantum wells（DPQWs） consisting of Al_xGa_（1-x）As/Al_yGa_（1-y）As are constructed to discuss theoretically the optical absorption due to the intersubband transition of electrons for both symmetric and asymmetric cases with three energy levels of conduction bands. The electronic states in these structures are obtained using a finite element difference method. Based on a compact density matrix approach, the optical absorption induced by intersubband transition of electrons at room temperature is discussed. The results reveal that the peak positions and heights of intersubband optical absorption coefficients（IOACs） of DPQWs are sensitive to the barrier thickness, depending on Al component. Furthermore, external electric fields result in the decrease of peak, and play an important role in the blue shifts of absorption spectra due to electrons excited from ground state to the first and second excited states. It is found that the peaks of IOACs are smaller in asymmetric DPQWs than in symmetric ones. The results also indicate that the adjustable extent of incident photon energy for DPQW is larger than for a square one of a similar size. Our results are helpful in experiments and device fabrication.

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-high-order Accuraqcy Implicit Difference Scheme for Solving the Equation of Parabolic Type

In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.

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.