An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.     

Local Heating Effect of Flow Past a Circular Cylinder

Heating effects of air flows past a two-dimensional circular cylinder at low Reynolds numbers and low Mach numbers are investigated by numerical simulation. The cylinder wall is heated partially rather than heated on the whole surface as with previous researches. The heating effects are completely different for various heating locations on the cylinder surface. Heating either windward or leeward side stabilizes the flow and reduces or completely suppresses vortex shedding from the cylinder at supercritical Reynolds numbers, which is consistent with previous results of heating on the whole surface of the cylinder. However, as the lateral sides of the cylinder （perpendicular to the stream-wise direction） are heated, an adverse effect is found for the first time in that the flow is destabilized and vortex shedding can be excited at subcritical Reynolds numbers. As the lateral sides of the cylinder are cooled, the flow is stabilized.     

Entransy analyses of heat–work conversion systems with inner irreversible thermodynamic cycles

In this paper, we try to use the entransy theory to analyze the heat–work conversion systems with inner irreversible thermodynamic cycles. First, the inner irreversible thermodynamic cycles are analyzed. The influences of different inner irreversible factors on entransy loss are discussed. We find that the concept of entransy loss can be used to analyze the inner irreversible thermodynamic cycles. Then, we analyze the common heat–work conversion systems with inner irreversible thermodynamic cycles. As an example, the heat–work conversion system in which the working fluid of the thermodynamic cycles is heated and cooled by streams is analyzed. Our analyses show that larger entransy loss leads to larger output work when the total heat flow from the high temperature heat source and the corresponding equivalent temperature are fixed.Some numerical cases are presented, and the results verify the theoretical analyses. On the other hand, it is also found that larger entransy loss does not always lead to larger output work when the preconditions are not satisfied.     

Small signal gain and loss measurement of a CW Nd:YAG laser using an antiresonant ring interferometer

An antiresonant ring (ARR) interferometer configuration is introduced for the characterization of a continuous wave (CW) Nd:YAG laser output. The output of the ARR device is precisely characterized todetermine the gain and loss of a laboratory CW Nd:YAG laser by using the Findlay-Clay approach. TheARR arm is then experimentally arranged inside the cavity of an arranged high power side-pumped CWNd:YAG laser. A coated beam splitter with 50–50% reflectivity at normal incidence is placed inside thecavity to provide a wide range of reflectivity from 0 to 100%. This is performed by a rotatable stage and tilting the beam splitter by 10°with the steps of 0.05. By changing the input electrical power of the laser pump the variation of the output laser power is monitored for 20 individual reflectivity of ARR arm.Average pump threshold power of about 180 W is obtained. With the help of the derived equations and obtained threshold power, small signal gain and loss associated with the emerging beam is estimated. It is verified that the former is very dependent to the input parameters. Laser efficiency is also measures 5.6% which is quite comparable with the reported values.     

Sound scattering from partially water-filled elastic spherical shell with an internal elastic plate

According to the equation of motion in the elastic medium and integral equation of target scattering, the sound scattering from the partially water-filled elastic spherical shells with and without an inner plate is studied using the finite element and boundary element method, and the scattering normalized form functions of the shell filled with different volume of water are computed and the mechanism of resonance scattering is analyzed. The results show that the resonance of the shell with partially water-filled and without the plate is mainly related to the volume of water, and the resonance is produced by inner water and the spherical shell. The resonance characteristics of partially water-filled elastic shell with the plate are similar to that of empty structured elastic spherical shell, and the sound field in inner water is weaker which indicates the main resonance characteristics are decided by spherical shell and the plate. In addition, the scattering characteristics of spherical shell with plate and one side full water-filled are greatly different from the partially water-filled ones.     

Hydromagnetic flow of a Cu water nanofluid past a moving wedge with viscous dissipation

A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper （Cu）-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das （Tiwari I K and Das M K 2007 Int. J. HeatMass Transfer 50 2002）. A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter ~, solid volume fraction tp, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.     

Lattice Bhatnagar—Gross—Krook Simulations of Turbulent Natural Convection in a Cavity

A thermal lattice Bhatnagar-Gross-Krook (LBGK) model with a robust boundary scheme is developed for Boussinesq incompressible fluids.In the model the velocity and temperature fields are solved by two independent LBGK equations which are combined into a coupled equation for the whole system.The two-dimensional natural convection flow of air in a differentially heated cavity of an aspect ratio of four is simulated for the Rayleigh number up to 10^10.The numerical results are found to be in good agreement with those of previous studies.     

Wavelength division demultiplexing by photonic crystal waveguides with asymmetric corrugated surfaces

<正>We propose a new type of wavelength division demultiplexer composed of a photonic crystal waveguide with asymmetric corrugated exit surface.The focus displacement for different symmetric corrugated surfaces is relative to the intensity of the excited surface mode.By systematically investigating the effects of the parameters of the corrugated surface on the focus shift,we demonstrate an on-axis focus by a photonic crystal waveguide with an asymmetric corrugated exit surface at a specific wavelength.The precise equivalences of surface modes at each side of the exit surface are broken.Thus,for the light source with other wavelengths,the emerging beams are off-axis focused at different directions,similar to the function of a wavelength division demultiplexer.     

Investigation of electric fields inside and outside a magnetised cold plasma sphere

Based on the scales transformation of electromagnetic theory,the analytical expressions of electric fields inside and outside a magnetised cold plasma sphere are presented by reforming the spherical electromagnetic parameter.The obtained results are in good agreement with that in the literature.The angle between the direction of inside field and that of outside field is derived.In S wave band,calculations for the effects induced by parameters of the inner field are established.Simulations show that the angle between incident field and the outside magnetic field influences the inner field remarkably.The inner field will increase as the electron density increases.The inner field varies with frequency nonlinearly.There is an angle between the inner field and the incident field,it changes nonlinearly with the frequency.     

Design and test of the microwave cavity in an optically-pumped Rubidium beam frequency standard

We are developing a compact rubidium atomic beam frequency standard with optical pumping and detection.The cavity for microwave interrogation is an important part of the clock.The cavity in our design is a Ramsey-type,E-bend one,which is the same as the conventional method in most cesium beam clocks.Requirements for the design are proposed based on the frequency shift associated with the cavity.The basic structure of the cavity is given by theoretical analysis and detailed dimensions are determined by means of electromagnetic field simulation with the help of commercial software.The cavity is manufactured and fabricated successfully.The preliminary test result of the cavity is given,which is in good agreement with the simulation.The resonant frequency is 6.835 GHz,equal to the clock transition frequency of87Rb,and the loaded quality factor is 500.These values are adjustable with posts outside the cavity.Estimations on the Ramsey line width and several frequency shifts are made.     

Experimental Investigation of Opposing Mixed Convection in a Channel with an open Cavity Below

Abstract

In this article, mixed convection in an open cavity with a heated wall bounded by a horizontal unheated plate is investigated experimentally. The heated wall is on the opposite side of the forced inflow. The results are reported in terms of wall temperature profiles of the heated wall and flow visualization. The range of pertinent parameters used in this experiment are Reynolds numbers (Re) from 100 to 2,000 and Richardson numbers (Ri) from 4.3 to 6,400. Also, the ratio between the length and the height of cavity (L/D) ranges from 0.5–2.0, and the ratio between the channel and cavity height (H/D) is equal to 1.0. The lack of experimental results on mixed convection in a channel with an open cavity below was an impetus for investigating this configuration when one cavity vertical wall is heated at uniform heat flux. The present results show that at the lowest investigated Reynolds number, the surface temperatures are lower than the corresponding surface temperatures for Re = 2,000 at the same ohmic heat flux. The flow visualization shows that for Re = 1,000, there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100, the effect of a stronger buoyancy determines a penetration of thermal plumes from the heated plate wall into the upper channel. Moreover, the flow visualization shows that for lower Reynolds numbers, the forced motion penetrates inside the cavity, and a vortex structure is adjacent to the unheated vertical plate. At higher Reynolds numbers, the vortex structure has a larger extension while L/D is held constant.     

Experimental and numerical investigation of natural convection of magnetic fluids in a cubic cavity

In this article, natural convections of a magnetic fluid in a cubic cavity under a uniform magnetic field are investigated experimentally and numerically. Results obtained from experiments and numerical simulations reveal that the magnetic field and magnetization are influenced by temperature. There exist relative larger magnetization and magnetic forces in the regions near the upper wall and center inside the cavity than in the region near the bottom and side walls. A weak flow roll occurs inside cavity under the magnetic force, and it brings the low temperature fluid downward in the center region, and streams the high temperature fluid upward along the regions near the sidewalls. With the magnetic field imposed, the heat transfer inside the cavity is enhanced significantly compared to that without the magnetic field, and increasing the strength of the magnetic field the heat transfer is increased further.     

Experimental Investigation of Mixed Convection in a Channel With an Open Cavity

Mixed convection in an open cavity with a heated wall bounded by a horizontally unheated plate is investigated experimentally. The cavity has the heated wall on the inflow side. Mixed convection fluid flow and heat transfer within the cavity is governed by the buoyancy parameter, Richardson number (Ri), and Reynolds number (Re). The results are reported in terms of wall temperature profiles of the heated wall and flow visualization for Re = 100 and 1000, Ri in the range 30–110 (for Re = 1000) and 2800–8700 (for Re = 100), the ratio of the length to the height of cavity (L/D) is in the range 0.5–1.5, and the ratio of the channel height to cavity height (H/D) is in the range of 0.5 and 1.0. The present results show that the maximum dimensional temperature rise values decrease as the Reynolds and the Richardson numbers decrease. The flow visualization points out that for Re = 1000 there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100 the effect of a stronger buoyancy determines a penetration of thermal plume from the heated plate wall into the upper channel. Nusselt numbers increase when L/D increase in the considered range of Richardson numbers.     

On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium

The effect of elasticity of the flexible walls on the MHD peristaltic flow of a Newtonian fluid in a two-dimensional porous channel with heat transfer has been studied under the assumptions of long-wavelength and low-Reynolds number. The analytical solution has been obtained for the stream function, temperature and heat transfer coefficient. The effect of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The numerical results show that the trapped bolus increases in size and more trapped bolus appears with increasing permeability parameter, elastic tension and mass characterizing parameters but decreases for large values of Hartmann number.     

ADDENDUM

Abstract

Experiments have been performed to provide basic heat transfer data for thermal convection in a horizontal concentric annulus partially filled with water. A real-time holographic interferometry was employed to map the temperature distribution and a laser shadowgraph system was used to measure local heat transfer coefficients along the heated inner cylinder. Experimental results demonstrate that a minimum average Nusselt number for the water-wetted portion of the inner cylinder occurs at the air-water interface situated flush with the top of the inner cylinder. Corresponding numerical simulations were conducted for the cases of either fully or half-filled with water and the predictions agree well with the experimental results.     

Experimental studies of influence of the turbulent flow structure on temperature distribution in a compact heat exchanger

Results of experimental investigation of temperature distribution over the surface of a complex heat exchanger (the Frenkel packing type) are presented. Measurements were carried out in the air flow between two sheets with triangular corrugations directed at 90° to each other. Measurements were carried out by the microthermocouples glued on the heated outer surface. The effect of Reynolds numbers, a gap between corrugated sheets, and substitution of one corrugated sheet by the smooth one on temperature distribution over the heat exchanger surface in the turbulent air flow is analysed. According to the performed experiments, there is a significant effect of a gap and applied perturbations on the type of temperature distribution over the perimeter of a heated cell.     

Correlation for Nusselt number in pure magnetic convection ferrofluid flow in a square cavity by a numerical investigation

Magnetic convection heat transfer in a two-dimensional square cavity induced by magnetic field gradient is investigated numerically using a semi-implicit finite volume method. The side walls of the cavity are heated with different temperatures, the top and bottom walls are isolated, and a permanent magnet is located near the bottom wall. Thermal buoyancy-induced flow is neglected due to the nongravity condition on the plane of the cavity. Conditions for the different values of non-dimensional variables in a variety of ferrofluid properties and magnetic field parameters are studied. Based on this numerical analysis, a general correlation for the overall Nusselt number on the side walls is introduced for a wide range of effective parameters. Results showed that maximum error produced by use of this correlation is about 6 percent.     

EXPERIMENTAL STUDY OF HEAT TRANSFER FROM A DISCRETE SOURCE TO A CIRCULAR LIQUID JET WITH ANNULAR COLLECTION OF THE SPENT FLUID

This study reports an experimental investigation of evaporative heat transfer and pressure drop of R-134a flowing downward inside vertical corrugated tubes with different corrugation pitches. The double tube test section is 0.5 m long with refrigerant flowing in the inner tube and hot water flowing in the annulus. The inner tubes are comprised of one smooth tube and three corrugated tubes with different corrugation pitches of 6.35, 8.46, and 12.7 mm. The test runs are performed at evaporating temperatures of 10°C, 15°C, and 20°C; heat fluxes of 20, 25, and 30 kW/m²; and mass fluxes of 200, 300, and 400 kg/m²s. The experimental data obtained from the smooth tube are plotted with flow pattern map for vertical flow. Comparisons between smooth and corrugated tubes on the heat transfer and pressure drop are also discussed. It is observed that the heat transfer coefficient and frictional pressure drop obtained from the corrugated tubes are higher than those from the smooth tube. Furthermore, the heat transfer coefficient and frictional pressure drop increase as the corrugation pitch decreases. The maximum heat transfer enhancement factor and penalty factor are up to 1.22 and 4.0, respectively.     

Numerical investigation of the two-dimensional natural convection inside the system based on phase change material with a source of volumetric heat generation

The work is devoted to the numerical investigation of unsteady regimes of the paraffin convective melting inside a closed rectangular region heated from the energy source with a constant density of the volumetric heat generation. The problem has been formulated in dimensionless transformed variables “stream function?vorticity?temperature” and solved by using a finite difference method. The main characteristics of the melting process and heat transfer in a liquid medium have been obtained and analyzed at different powers of the energy source (from 5 to 100 Watt). The influence of heat transfer from the source on the temperature distributions inside the region containing paraffin has been analyzed.     

Temperature mapping in a two-phase water-steam horizontal flow

This experimental study focuses on the investigation of a flow boiling that occurs during the cooling process of a high temperature heated horizontal channel. Unpressurized water is used as working fluid. An intrusive thermally instrumented cell enables the phase change to be detected at different positions inside the channel. Alongside, welded thermocouples on the external wall of the channel give information about the influence of the phase change. Several cooling flowrates are tested in order to study their influence on the phase change duration. Finally, experimental results are compared to numerical simulations to determine some characteristic parameters as bulk temperature and heat transfer coefficient.