Nonlinear convection with variable coefficient of thermal expansion

Summary The problem of nonlinear convection in a horizontal layer of fluid with variable coefficient of thermal expansion is considered. It is found that square cells transport always more heat than two-dimensional rolls and that rolls are always unstable. Variable coefficient of thermal expansion can strongly affect the critical Rayleigh number and the horizontal scale of the motion. Subcritical instabilities can exist which are associated with either hexagon pattern convection or square pattern convection. Particular forms of the coefficient thermal expansion are essential to determine the preferred flow patterns which could be of the forms of squares or hexagons with either upward of downward motion at the cells' centers.     

Thermocapillary instability of a low Prandtl number fluid with negligible gravitational effects

Summary Finite amplitude fluid motion is investigated in a horizontal layer of a low Prandtl number fluid for the case where thermocapillary effects are significant and gravitational effects are negligible. The main result is that down-hexagons (where motion is downward at the cells' centers) are preferred for sufficiently small amplitude in contrast to uphexagons (where motion is upward at the cells' centers) that represent the preferred pattern for large Prandtl number.     

Effect of motion of a local heat source on thermocapillary deformation of a thin liquid film flowing down under the action of gravity

The influence of a moving local heat source on the structure of flow in a thin liquid film flowing down on an inclined substrate under the action of gravity has been theoretically studied. Two-dimensional steady-state and conjugated hydrodynamic heat transfer problem has been solved in a long-wave approximation. The characteristics of flow are compared for various regimes: from the liquid film flowing down on a vertical surface with an immobile heat source to the behavior of a horizontal liquid layer under the action of a moving heat source. It is shown that changes in the flow velocity profile related to an increase in the velocity of the heat source motion and a decrease in the substrate slope under other equal conditions (constant flow rate, film thickness, and heat release) lead to a sharply increased thermocapillary deformation of the liquid film.     

Thermal-wave-induced vorticity in a liquid film

We have theoretically studied the influence of a moving local heat source on the structure of flow in a thin liquid layer on a horizontal substrate. A two-dimensional problem is considered in the boundary layer approximation and a stationary equation that describes deformation of the liquid layer is obtained. Results of numerical calculations for a preset temperature distribution on the free surface are presented that demonstrate the formation of a vortex structure. It is established that, even in the absence of a gravity-driven flow, the motion of a local heat source ensures a stationary flow regime without film breakage and the formation of dry spots. The results justify a new scheme of experiments for the investigation of phenomena in nonisothermal liquid films.     

Buoyant plane plumes from heated horizontal confined wires and cylinders

Two-dimensional computations are reported for time-dependent laminar buoyancy-induced flows above a horizontal heated source immersed in an air-filled vessel. Two kinds of heated source were considered: a line heat source, modelled as a heat source term in the energy equation, and a heat-flux cylinder of small diameter. First, comparisons are presented for the results obtained for these two heated sources. Rather large discrepencies between the velocity fields appeared in the conduction regime due to the weak plume motion, while close agreements were found in the boundary layer regime. Nevertheless, same types of bifurcations occur with almost identical frequencies, whatever the Rayleigh number. It is concluded that for dimensions of the enclosures, which largely compared with the cylinder radius, the heat source term model is a promising way to study the behaviour of unsteady plumes owing to its simplicity, flexibility, and low computational costs. Second, transitions to unsteady flows were studied through direct flow simulations for various depths of immersion of a line heat source in the central vertical plane of a vessel. Different routes to chaos were shown to occur according to the aspect ratio of the vessel and the depth of immersion of the line source. Three distinct regimes were detected with different underlying physical mechanisms called natural swaying motion, penetrative convection and Rayleigh-Benard-like convection. The first bifurcations associated with these regimes are supercritical Hopf bifurcation, pitchfork bifurcation and subcritical Hopf bifurcation. Comparisons with experimental results of confined buoyant plumes above heated wires show very good agreement with laminar frequency correlations.     

Nonlinear thermal instability in a horizontal porous layer with an internal heat source and mass flow

Linear and nonlinear stability analyses of Hadley–Prats flow in a horizontal fluid-saturated porous medium with a heat source are performed. The results indicate that, in the linear case, an increase in the horizontal thermal Rayleigh number is stabilizing for both positive and negative values of mass flow. In the nonlinear case, a destabilizing effect is identified at higher mass flow rates. An increase in the heat source has a destabilizing effect. Qualitative changes appear in R_z as the mass flow moves from negative to positive for different internal heat sources.     

Effect of stretching on interfacial stability

Summary. The effect of stretching on the stability of a horizontal interface between two fluids with different viscosities and densities is discussed. A local elongational flow acts to reduce the amplitude of perturbations and increase the wavelength of periodic waves, and thereby alter the instantaneous growth rate of disturbances. Linear stability analysis for Stokes flow reveals that, in the case of a horizontal interface between two semi-infinite fluids subjected to orthogonal stagnation-point flow, interfacial stretching is not able to suppress the Rayleigh-Taylor instability of unstably stratified fluids. In contrast, stretching is able to suppress the growth of periodic waves on the surface of a flat film resting on a horizontal surface. Numerical simulations based on the boundary-integral method for Stokes flow confirm that localized perturbations on the film surface are suppressed when the elongational flow is sufficiently strong.     

地源热泵能效比试验与研究

采用对比试验,对不同型号井埋管的散热能力、传热能力进行研究,从而得出不同井埋管对地源热泵的不同影响。对地源热泵能效比研究前景作简单介绍,在试验部分,通过对传感器进行校正与误差分析,保证试验中数据的精确性,使散热试验和取热试验一样。应用传热模型,根据散热和取热中管内水流的流量和温度,就可以计算出水平管在各种工况下的平均散热和取热能力,鉴于在地源热泵系统应用中,地埋管换热器的设计是最关键的部分,而地源热泵的能效比又与其有密切联系,可以由此知道不同型号井埋管对地源热泵能效比的影响。     

Evidence for the hydrodynamic origin of critical heat currents in helium II

It is found that the critical heat current measured in a modulated heat flow in superfluid He II is substantially larger than in a steady flow. The variation of critical heat current with the modulation frequency and amplitude is shown to be analogous to the enhancement of stability observed in the flow of conventional fluids.Work supported by a grant from the National Foundation, GP13381.     

Transport phenomena in a sidewall-moving bottom-heated cavity using heatlines

The understanding of basic feature of energy transport from a heat source is important from the fundamental point of view as well as from various engineering and technological applications. To enrich the knowledge in this area, this paper presents energy transport phenomena from the heated bottom of an air-filled enclosure using heatfunction and heatlines. Both upward motion and downward motion of sidewalls and the alteration of cooling between sidewalls and top wall are considered, which yields four different cases. All the cases are investigated to identify the proper combination of wall motion and thermal condition for better thermal performance, considering different convection regimes. The highly nonlinear nature of flow is solved numerically using an in-house code, taking into account different speeds of wall motion and relative strength of buoyant flow and shear flow. The results reveal that the case with side cooling and downward translation of sidewalls performs maximum heat transfer compared with other cases. Higher speed of wall translation also causes higher heat transfer. Under natural convection regime, heat transfer is significantly high. Furthermore, the order of thermal mixing in a cavity is analysed and it is found that top cooling causes higher thermal mixing. To demonstrate the vortical flow structure in the cavity, streamfunction and streamlines are used. Evolutions of symmetric and asymmetric flow vortices with centre and saddle points and energy recirculation cells are found in the cavity.     

The onset of double diffusive convection in a sparsely packed porous layer using a thermal non-equilibrium model

We examine the effect of local thermal non-equilibrium on double diffusive convection in a fluid-saturated sparsely packed porous layer heated from below and cooled from above, using both linear and nonlinear stability analyses. The Brinkman model is employed as the momentum equation. A two-field model that represents the fluid and solid phase temperature fields separately is used for the energy equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. It is found that a small inter-phase heat transfer coefficient has significant effect on the stability of the system. There is a competition between the processes of thermal and solute diffusion that causes the convection to set in through either oscillatory or finite amplitude mode rather than stationary. The effect of solute Rayleigh number, porosity modified conductivity ratio, Lewis number, ratio of diffusivities, Vadasz number and Darcy number on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method predicts the occurrence of subcritical instability in the form of finite amplitude motions. The effect of thermal non-equilibrium on heat and mass transfer is also brought out.     

Convective heat transfer enhancement produced by secondary heat sources in a liquid nitrogen pool

This paper studies the influence of secondary heat sources on the convective heat transfer from a vertical cylindrical heater immersed in a LIN pool. Two types of secondary heat source have been used. In the first case, the heat leak through the vessel walls into the pool was varied without causing nucleation, so as to retain convective heat transfer. It was found that the convective flow loops induced in the pool produced a small enhancement of the heat transfer from the cylindrical heater. In the second case, a small horizontal heater loop was introduced into the pool below the cylindrical heater. The secondary heat flux used was such that boiling occurred at the loop to give rising bubbles surrounding the cylindrical heater. This produced a large enhancement of the convective heat transfer from the cylindrical heater. The enhancement ratio is presented as a function of the power supplied to the loop heater.     

Heat transfer and pressure drop for boiling nitrogen flowing in a horizontal tube: 1. Saturated flow boiling

Forced convection boiling of liquid nitrogen in a smooth horizontal copper tube with 14 mm id has been studied experimentally. The measured local heat transfer coefficients in nucleate boiling depend on the heat flux as well as on the mass flow rate. Furthermore, the influence of the vapour quality cannot be neglected.Our own experimental heat transfer data were correlated by an empirical equation. Mass flow rate, pressure, and diameter dependence of para-hydrogen data of other authors can also be correlated with this equation. A relationship for the critical heat flux is also given.     

Effect of a non-constant magnetic field on natural convection in a horizontal porous layer heated from the bottom

An analytical and numerical investigation is conducted to study the effect of an electromagnetic field on natural convection in a horizontal shallow porous cavity filled with an electrically conducting fluid. The magnetic field is assumed to be induced by two long wires, carrying current, parallel to the horizontal boundaries of the system. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. The governing parameters of the problem under study are the thermal Rayleigh number, Ra, Hartmann number, Ha, position of the electrical wires, d, current intensity ratio, r, and aspect ratio of cavity, A. An analytical solution, valid for a shallow layer (A ? 1), is derived on the basis of the parallel flow approximation. The critical Rayleigh number, Ra _c , for the onset of motion is derived in closed form in terms of the parameters of the problem. For finite-amplitude convection the heat and flow characteristics predicted by the analytical model are found to agree well with a numerical study of the full governing equations.     

Characterisation of the hydraulic maldistribution in a heat exchanger by local measurement of convective heat transfer coefficients using infrared thermography

A methodology was developed to characterise the heat exchangers' performance decrease due to two-phase flow maldistribution. It consists in measuring the spatial distribution of the local heat transfer coefficients with a rapid, non-invasive and fluid independent method. The method is based on the infrared (IR) thermography measurement of the temperature response to an oscillating heat flux. The amplitude of the measured temperatures is compared to the solution of an analytical model. The problem is solved iteratively to obtain the heat transfer coefficients. This method has been applied to evaluate the uneven phase distribution of an air–water mixture in a compact heat exchanger. The exchanger is composed of seven multiport flat tubes, a vertical downward header and horizontal channels. Experiments were performed for mass flux from 29 kg m⁻² s⁻¹ to 116 kg m⁻² s⁻¹ and for quality from 0.10 to 0.70.     

On the effect of tool offset in hybrid-FSW of copper-aluminium alloy

Tool offset is one the most significant parameters in joining of dissimilar materials by friction stir welding (FSW) process. An investigation is carried out on the effect of tool offset toward thermal history, material flow pattern, mechanical properties, welding force, and weld joint morphology. It was found that offsetting toward aluminum side along with a plasma-assisted heat source is an efficient approach to address one of the most important apprehensions in aluminum-copper solid-state welding process. The offset influences the amount of intermetallic at the joint interface and in-effect impacts on final strength and material flow behavior. The optimum and continuous layer of intermetallic produces the maximum weld joint strength. The specimen welded with optimum tool offset shows the highest strength using 55 A plasma current in hybrid friction stir welding process.     

磁场辅助电弧焊接旋转等离子体行为的数值模拟

目的 研究外加纵向磁场对倾斜电极TIG焊接的电弧温度分布、流动模式和工件所受热力作用的影响.方法 建立磁场-电弧复合焊接热、电、磁、流动的三维数学模型.通过数值模拟和高速摄像实验,揭示倾斜电极电弧在外加磁场作用下的流动、形貌及温度演化机制.结果 外加纵向磁场后,电弧流动速度明显增加,流动模式由沿电极方向喷射变为近似沿竖直方向旋转向下的流动模式;电弧对工件的热作用均匀性提高,热作用中心向电极正下方靠近,但在焊接横向方向上存在偏离;工件受到表面的电弧旋转拖拽力和内部的旋转洛伦兹力作用,最大洛伦兹力可达50000 N/m3.结论 基于所建立数学模型的模拟结果与实验电弧形貌吻合良好,结果表明,外加纵向磁场能够显著改变电弧的形态及流动模式,提高电弧热流密度的均匀性,并能够对熔池产生有效的搅拌作用.     

Thermocapillary instability of an infinite Prandtl number fluid with negligible gravitational effects

Summary Finite amplitude fluid motion is investigated in a horizontal layer of an infinite Prandtl number fluid with an upper free surface for the case where thermocapillary effects are significant and gravitational effects are negligible. It is found that subcritical instability exists and that two-dimensional rolls and down-hexagons (where motion is downward at the cells' centers) are always unstable. But up-hexagons (where motion is upward at the cells' centers) are stable for sufficiently small amplitude , while both uphexagons and squares are stable in a range of larger where hysteresis effects exist.With 1 Figure     

Numerical modeling of precessing vortex core in the presence of local heat sources

Based on the results of numerical simulation of a nonstationary, nonaxisymmetric turbulent swirling gas flow in a tube with local sources of heat release, it is shown that a precessing vortex core (PVC) appears at supercritical values of the swirl parameter as a result of the development of instability of a left-handed bending mode. The dependence of the PVC frequency on the mass flow rate of the gas and the heat-source power has been studied. As the heat-source power increases, the frequency of precession grows while the amplitude of vortex core oscillations drops.     

Forced convection of a temperature-sensitive ferrofluid in presence of magnetic field of electrical current-carrying wire: A two-phase approach

This research examines laminar forced convection of a temperature-sensitive magnetic nanofluid flowing within a horizontal tube through the two-phase mixture model. The ferrofluid flowing in the tube is exposed to the magnetic field generated by electrical current-carrying wire(s) along the tube, and the effect of such magnetic field is studied on heat and mass transfer phenomena. It is observed that due to the dependency of magnetization on temperature, the cold fluid flowing at the central regions of the tube is attracted more significantly towards the source of the magnetic field, which results in creation of secondary flow. Such mixing in the flow, subsequently, disturbs the thermal and hydrodynamic boundary layers, especially at the vicinity of the magnetic field source, leading to better heat transfer rate and also higher pressure drop. Furthermore, increasing the strength of the magnetic field leads to greater enhancement in heat transfer, while increasing the Reynolds number decreases the effectiveness of the magnetic field on the ferrofluid flow and heat transfer. Moreover, placing two wires above and under the tube can enhance the heat transfer even more significantly, such that the average convective heat transfer coefficient in this case is about 34.5% higher than that of the case without magnetic field.