Forced Convective Cooling via Acoustic Streaming in a Narrow Channel Established by a Vibrating Piezoelectric Bimorph

Forced convection in a narrow channel is investigated both numerically and experimentally. The flow field is established through the mechanism of acoustic streaming. This is accomplished by high frequency vibration of one of the channel walls, which is composed of a piezoelectric bimorph. In the numerical computations, the Navier-Stokes equations are decomposed into the acoustic equations and the streaming equations by the perturbation method. The acoustic field is first numerically obtained, which provides the driving force for the streaming field. The streaming field and the associated temperature field are then obtained numerically. Heat losses from a heat source are measured to determine the efficiency of this as a cooling method. The air-flow patterns in the channel between the heat source and the bimorph actuator are visualized using the particle tracking velocimetry. The visualization clearly shows that vortical streaming (acoustic streaming) can be induced by bimorph vibration, which enhances heat transfer between the heat source and the surrounding air. The temperature decreases obtained computationally and experimentally are in good agreement.     

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper,we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field.The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account.The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity,induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli.The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables.It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder,while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder.These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases.It is also found that as the Hartmann number increases,there is a flattening tendency for both the velocity and the induced magnetic field.The influence of the induced magnetic field is to increase the velocity profiles.     

Variety of acoustic streaming in 2D resonant channels

Acoustic streaming in 2D resonant channels with uniform or non-uniform cross-sections is studied within this work. An inertial force as well as a vibrating boundary are assumed for driving the acoustic field. The method of successive approximations is employed to derive linear equations for calculation of primary acoustic and time-averaged secondary fields including the radiation pressure and the mass transport velocity. The model equations have a standard form which allows their numerical integration using a universal solver; in this case, COMSOL Multiphysics was employed. As this software is based on the finite element method, it is simple and straightforward to perform the calculations with moderate computational costs even for complex geometries, which makes the proposed approach an operative tool for study of acoustic streaming. The numerical results are validated for the case of a rectangular channel by comparison with previously published analytical results; an excellent agreement is found. The numerical results show that the acoustic streaming can be quite complex even in rectangular channels and its structure depends on the manner of driving. Examples of acoustic streaming in wedged and elliptical channels are given to demonstrate a strong dependence of the acoustic streaming structure on the resonator shape.     

Investigation on the influence of nonuniform initial temperature on the transient heat transfer measurement of film cooling

Numerical and experimental investigations on the influence of nonuniform initial temperature on the transient heat transfer measurements are presented in this paper. The case of film cooling is investigated. When the initial wall temperature is nonuniform, the results of heat transfer coefficient and film cooling effectiveness, which are calculated by the equations derived with constant initial temperature, could deviate from the true values badly, especially in the condition of short test duration. Using initial wall temperature which is higher than the real values causes the results of heat transfer coefficient and film cooling effectiveness lower than the true values. And lower initial wall temperature produces higher results of heat transfer coefficient and film cooling effectiveness. However, when the initial temperature distribution in the region where conduction plays more influence on the wall surface temperature than the convection is well fitted by the cubic polynomial, accurate results can be obtained by the new equation which is derived from 1-D unsteady conduction model with nonuniform initial wall temperature. Some suggestions are also introduced to reduce the influence of nonuniform initial temperature when the initial temperature distribution is difficult to obtain and the equation derived from constant initial temperature has to be employed.     

Acoustic streaming on spheres

The phenomenon of secondary motion (acoustic streaming) created by the oscillation of a fluid past a sphere is investigated through numerically solving the full Navier-Stokes equations. The main parameters that affect the structure of acoustic streaming are Reynolds number and Strouhal number. The results are presented in the form of steady streaming patterns as well as the relation between Reynolds and Strouhal numbers and the dimensions of the streaming region.     

带冷却气流的亥姆霍兹共振器的声类比模型

亥姆霍兹共振器(HR)作为典型的被动消声装置,常被安装于航空发动机和燃气轮机的燃烧室上用以吸收噪声进而抑制燃烧热声振荡.在实际应用中,为防止燃烧室内高温气体损坏HR,常引入冷却气流从HR的背部空腔通过其颈部流入燃烧室,以保护HR.该冷却气流的温度一般显著低于燃烧室内的燃气温度.将这样的HR安装到燃烧室上时,该温差可能影...     

Generalised Couette flow of two immiscible viscous fluids with heat transfer using Brinkman model

The present study deals with generalised Couette flow of two viscous, incompressible, immiscible fluids with heat transfer in presence of heat source through two straight parallel horizontal walls. The lower wall is bounded below, by a naturally permeable material of high porosity and the flow inside the porous medium is assumed to be of moderate permeability, modelled by Brinkman equation. The flow domain is divided into three zones to obtain analytical solutions of the momentum and energy equations. To link various flow regions, appropriate matching conditions have been used. The effects of permeability parameter, Reynolds number and viscous parameter on velocity field and the effects of Reynolds number, viscous parameter, permeability parameter, constant heat source and Brinkman number on temperature distribution in different zones are discussed graphically. The mass flow rate, skin-friction factor and rates of heat transfer at the upper boundary and porous interface are discussed with the help of tables.     

A numerical study of natural convection from a localized heat source in the lower plenum of a fast breeder reactor under failed conditions

A comprehensive numerical study has been done to investigate two-dimensional, steady state, conjugate natural heat convection in the hemi spherical lower plenum of a fast breeder reactor under failed conditions. The continuity, momentum and energy equations are solved over the entire domain, using the corresponding properties for the solid and fluid regions. The control volume approach is employed in order to discretize the governing equations for their numerical solution. A parametric study has been done to study the variation of the velocity vectors and isotherms for different constant temperature of the heat source, simulating different heat generation rates. The actual problem in a nuclear reactor involves a volumetric heat generation in the debris falling over the heat shield plate under failed conditions of the reactor and heat is removed by a decay heat exchanger serving as a sink. In this study we have reduced this transient problem to a quasi-steady problem with a prescribed temperature on the heat shield plate. This makes the problem more tractable. The fluid flow pattern, variation of the temperature along the axis in and around the heat source are presented to show the overall heat transfer characteristics inside the plenum.     

Inertial effects on acoustic Rayleigh streaming flow: Transient and established regimes

The effect of inertia on Rayleigh streaming generated inside a cylindrical resonator where a mono-frequency standing wave is imposed, is investigated numerically and experimentally. To this effect, time evolutions of streaming cells in the near wall region and in the resonator core are analyzed. An analogy with the lid-driven cavity in a cylindrical geometry is presented in order to analyze the physical meanings of the characteristic times.Inertial effects on the established streaming flow pattern are then investigated numerically using a code solving the time averaged Navier–Stokes compressible equations, where a mono-frequency acoustic flow field is used to compute the source terms.It is shown that inertia of streaming cannot be considered as the leading phenomenon to explain the mutation of streaming at high acoustic levels.     

Acoustic streaming measurements in standing wave resonator using Particle Image Velocimetry

This paper experimentally investigates the measurement of acoustic streaming in a 7 m long-standing wave air-filled acoustic resonator. One can describe the acoustic streaming as a second-order steady flow, which is superimposed on the dominant acoustic velocity. It is induced by the nonlinearities of the acoustic propagation inside the resonator. The exploration of the acoustic velocity field by the synchronized PIV (stands for Particle Image Velocimetry) technique enabled to highlight and quantify these secondary flows. The PIV measurements of the acoustic velocity fields at different phases over the excitation signal period gave information on streaming profiles and the post processing applied allowed plotting the acoustic velocity over time. These results were compared to the outcome of a 2D numerical study performed with the commercial software Fluent, where good agreements were found. It indicates the ability of this method to accurately measure second order steady flow variations of the acoustic velocity field.     

Acoustic streaming model for an intense sound beam in free space

Steady acoustic streaming in a barotropic liquid medium (water), excited by a plane circular emitter at frequencies in the mega-hertz range, is examined for large hydrodynamic Reynolds numbers. A region of the flow smaller than the diffraction length but including the zone of jump formation and nonlinear damping of the sawtooth finite-amplitude wave is investigated. Experiments show that under these conditions the direct flow hardly goes beyond the limits of the beam. Inflow into the main stream takes place at every point on the lateral surface of the beam [7], with the possible exception of the region near the emitter where the acoustic field is substantially nonuniform [8]. This region is not considered. It is also assumed that the acoustic streaming does not affect the parameters of the sound wave within the beam. The main effect of the constant flow on the acoustic field is the increase in the speed of sound in the moving medium [9]. For water it is less than 0.1%, i.e., negligibly small.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–7, November–December, 1989.     

Effect of working fluid on the performance of a miniature heat pipe system for cooling desktop processor

The heat transfer performance of a miniature heat pipe system (MHPS) used for cooling a desktop computer processor is presented in this paper. The MHPS consists of 6 parallel cylindrical miniature heat pipes (MHPs) which are connected to a copper block at the evaporator section and which are provided with 15 parallel perpendicular copper sheets at the condenser section, used as external cooling fins. Acetone and ethanol are used as working fluids. As heat source a processor is employed which is attached to the copper block. Heat transfer characteristics of the individual MHPs and the complete MHPS using the two working fluids are experimentally determined. The results show that the maximum and steady state temperature of the processor has been significantly reduced by using MHPs with acetone, more than with ethanol, instead of a conventional finned aluminum heat sink with cooling fan. Additional use of a fan results in a much lower processor temperature for both working fluids.     

Exact solutions for the incompressible viscous fluid of a porous rotating disk flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions with suction and injection through the surface included. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the exact velocity equations obtained. Making use of this solution, analytical formulas corresponding to the permeable wall shear stresses are extracted.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. As a result, exact formulas are obtained for the temperature field which take different forms depending on whether suction or injection is imposed on the wall. The impacts of several quantities are investigated on the resulting temperature field. In accordance with the Fourier‘s heat law, a constant heat transfer from the porous disk to the fluid takes place. Although the influence of dissipation varies, suction enhances the heat transfer rate as opposed to the injection.     

Influence of inhomogeneity on the nonlinear stabilization of acoustic vibrations of a heat releasing medium in a confined space

The problem of determining the amplitudes of unstable acoustic vibrations when they are stabilized in a confined heat releasing medium by transfer of energy from the unstable mode to the damped mode as a result of their nonlinear interaction has been considered by Artamonov and Vorob'ev [1]. Their treatment applied to a gas with volume heat release filling a channel of finite length under the assumption that the parameters of the gas in the steady state are constant over the volume. In the present paper an investigation is made in the nonlinear approximation of the stability of a weakly inhomogeneous heat releasing gas that fills a channel of finite length with respect to acoustic vibrations propagating along its axis in the direction of the gradients of the steady parameters. It is shown that the spatial inhomogeneity of the gas leads to breakdown of the resonance of the excited acoustic vibrations, which in turn leads to a higher level of the steady vibrations compared with the case of a spatially homogeneous medium.     

Natural convection in vertical concentric annuli under a radial magnetic field

Exact solutions for fully developed natural convection in open-ended vertical concentric annuli under a radial magnetic field are presented. Expressions for velocity field, temperature field, mass flow rate and skin-friction are given, under more general thermal boundary conditions. It is observed that both velocity as well as temperature of the fluid is more in case of isothermal condition compared with constant heat flux case when gap between cylinders is less or equal to radius of inner cylinder while reverse phenomena occur when the gap between cylinders is greater than radius of inner cylinder.     

Numerical study on mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows

Fluid flow and heat transfer of mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows have been simulated based on the projection method with two dimensional exponential stretched staggered cylindrical meshes. Cycle mean temperature and secondary streaming are obtained by the method of partial sums of the Fourier series. Present numerical results are validated by comparing the heat transfer results of free convection and the secondary streaming of pure oscillating flow over a circular cylinder to published experimental and numerical results. The complete structures of the cycle mean temperature and secondary streaming patterns are provided by numerical simulations over wide ranges of the Reynolds number, the Keulegan–Carpenter number and the Richardson number. Based on turning points of the curves of the overall Nusselt numbers versus Reynolds numbers and the characteristics of the cycle averaged temperature and flow patterns, the heat transfer can be divided into three linear regimes (conduction, laminar convection, and turbulent convection dominated regimes) and two non-linear transition regimes. The effects of wave directions, amplitudes, frequencies, and buoyancy forces on the enhancement of heat transfer are also investigated. The effective ranges of the governing parameters for heat transfer enhancement are identified.     

3-dimensional laser heating model including a moving heat source consideration and phase change process

The use of a Fourier heating model in high intensity laser material processing is limited due to the assumptions made in the model. An electron-kinetic theory may offer an alternative solution to the problem. Consequently, in the present study an electron-kinetic theory approach is introduced to model the 3-dimensional laser heating process. The phase change and conduction effects are encountered when driving the governing equations. To simulate the moving heat source, a scanning velocity of the laser beam is considered, in this case, the laser beam scans the workpiece surface with a constant velocity. The governing heat transfer equation is in the form of integro-differential equation, which does not yield the analytical solution. Therefore, a numerical method employing an explicit scheme is introduced to discretize the governing equations. To validate the theoretical predictions, an experiment is conducted to measure the surface temperatures of the workpiece substrate during Nd YAG laser heating process. It is found that the rapid increase in temperature occurs in surface vicinity due to the successive electron-lattice site atom collisions. The depth of melting zone increases as the heating progresses and the temperature remains almost constant at the melting temperature of the substrate in the surface vicinity. In addition, the theoretical predictions agree well with the experimental findings. Received on 4 August 1997     

Natural convection heat transfer from a thin rectangular fin with a line source at the base — a finite difference solution

This paper presents an analysis of the problem of a thin fin of finite thermal conductivity, with an isothermal line source at the base, dissipating heat to the surrounding air by natural convection. The horizontal surface to which the fin is attached is adiabatic so that heat is dissipated only through the fin. The temperature and velocity distributions in the field, the temperature profile in the fin, local Nusselt numbers along the fin and the average heat transfer coefficient of the fin are obtained by solving the governing equations in the field and the heat transfer equation in the fin simultaneously, using an explicit unsteady Finite Difference formulation leading to the steady state result. Numerical experiments are performed to study the influence of parameters namely the fin height, temperature of the heating source and the fin material on the average heat transfer coefficient. Comparison is made with fins of infinite thermal conductivity and the vertical isothermal flat plate.     

Influence of a magnetic field on the thermoacoustic stability of a high-temperature heat releasing gas

The conditions of thermoacoustic stability are found for a high-temperature electrically conducting gas with internal heat release in a constant magnetic field which transforms acoustic waves into fast and slow magnetoacoustic oscillations, and also introduces Joule dissipation. The investigation is by means of the energy balance method, and also by direct solution of the equations for small perturbations in the special case of wavelengths of the acoustic oscillations that are short compared with the inhomogeneity scales in the region of heat release. The limits of stability with respect to fast and slow magnetoacoustic oscillations are found.Translated from Izvestiya Akademii Nauk SSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 102–107, July–August, 1979.     

Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure

This article presents a numerical study of natural convection cooling of a heat source embedded on the bottom wall of an enclosure filled with nanofluids. The top and vertical walls of the enclosure are maintained at a relatively low temperature. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The results indicate that adding nanoparticles into pure water improves its cooling performance especially at low Rayleigh numbers. The type of nanoparticles and the length and location of the heat source proved to significantly affect the heat source maximum temperature.