Oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluid with free surface heat gain

Oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluid is studied. The effect of free surface heat transfer, especially heat gain, on the oscillation phenomenon is investigated experimentally and numerically. It is shown that the critical temperature difference (ΔT_cr) changes substantially when the free surface heat transfer changes from loss to gain in the case of nearly straight liquid bridges. In contrast, ΔT_cr is not affected by the free surface heat transfer with concave liquid bridges. The free surface heat transfer rate is computed numerically by simulating the interaction of the liquid and the surrounding air. The oscillatory flow is also investigated numerically by analyzing the liquid flow in three-dimensions for straight bridges. The computed results agree well with the experimental data. The simulation shows that the free surface heat gain enhances the surface flow and that the oscillatory flow is a result of interactions between the convection effect and buoyancy. The flow does not become oscillatory if there is no net heat gain at the free surface in the range of Marangoni number of the present work (⩽1.8 × 10⁴), so the present cause of oscillations is different from that in the free surface heat loss case we investigated in the past.     

Coupled thermocapillary convection on Marangoni convection in liquid layers with curved free surface

This paper numerically studied the coupled Marangoni convection and thermocapillary convection in a finite liquid layer (Pr = 11.6) in the microgravity conditions. The multi-cellular flow structure and the marginal instability boundary of the coupled convection are predicted. Oscillatory coupled convection is also reported in concave liquid layers of volume ratio between 0.80 and 0.85.     

Effect of copper surface wettability on the evaporation performance: Tests in a flat-plate heat pipe with visualization

The effects of copper surface wettability on the evaporation performance of a copper mesh wick were experimentally studied in an operating flat-plate heat pipe. Different degrees of wettability were obtained by varying the exposure times in air after the wicked plates were taken out of the sintering furnace. Three different working fluids: water, methanol and acetone, which possess different figures of merit, were investigated at the same volumetric liquid charge. The surface wettability was quantified by the static contact angle of sessile water drops on a flat copper surface. While the static contact angles of water drops varied from 10° to 40° for different degrees of wettability, the methanol and acetone drops still fully wetted the copper surface. A two-layer 100 + 200 mesh copper wick, 0.26 mm in thickness, was sintered on a 3 mm-thick copper base plate. A glass plate was adopted as the top wall of the heat pipe for visualization. Uniform heating was applied to the base plate near one end, and a cooling water jacket was connected at the other end. With increasing heat load, the evaporative resistance decreased with liquid film recession until a critical heat load showing the minimum evaporative resistance. Afterwards, partial dryout began from the front end of the evaporator. With decreasing wettability, the evaporating water film receded faster with increasing heat load and the critical heat loads were significantly reduced. In contrast, the critical heat loads for methanol and acetone seemed hardly affected by different wettability conditions. The minimum evaporative resistances, however, remained unaffected by surface wettability for all the three working fluids.     

Visualization and analysis of surface tension and cooling effects on differentially heated cavity using heatline concept

Convection in a square cavity with a free surface and heated from the side is visualized and analyzed by the heatline concept. The temperature gradient is applied along the top free surface and the heat balance at the surface is assumed to obey Newton’s law of cooling. The finite difference method has been used to solve the dimensionless governing equations. The governing parameters considered are the Marangoni number (0 ? Ma ? 1000), the Biot number (0 ? Bi ? 6) and the Prandtl number (0.054 ? Pr ? 6.2). The flows of heat and fluid are of a similar type except at a strong cooling condition. The heat transfer performance presents a minimum at Marangoni number of roughly 100, 200 and 600 for the cavity filled with liquid metal, mixture of noble gases and air, respectively.     

Convection and instability of thermocapillary flow in a liquid bridge subject to a non-uniform rotating magnetic field

A three-dimensional liquid bridge is considered in this study to numerically investigate the effects of an external non-uniform rotating magnetic field (RMF) on the thermocapillary flow in semiconductor melt under microgravity. Simulations are carried out to examine the convection and instability features of the thermocapillary flow over a range of Marangoni numbers (Ma = 15–50) under a non-uniform RMF. The present results show that applying an external non-uniform RMF enhances the maximum tangential velocity and depresses the maximum axial velocity. As a consequence, an approximately axisymmetric flow is maintained in the melt under the effect of the non-uniform RMF, which is beneficial for growing high quality crystal. Further investigation of the thermocapillary flow subject to different non-uniform RMFs (corresponding to Taylor numbers Ta = 3.8 × 10²–1.86 × 10⁴ and Rotating Reynolds number Re_ω = 2.2 × 10⁴) reveals that the thermocapillary convection may undergo a transition from the approximately axisymmetric steady flow to a periodically oscillatory flow for Ma above a critical value. The critical Ma generally increases with the intensity of the non-uniform RMF.     

Linear stability analysis of Poiseuille–Bénard–Marangoni flow in a horizontal infinite liquid film

We present the first linear stability analysis of a Poiseuille–Bénard–Marangoni flow, which refers to a horizontal infinite liquid film flowing in one direction with uniform heating from below. This study concerns the two limiting cases of pure buoyancy effect (Ma = 0) and pure thermocapillary effect (Ra = 0). The stability thresholds of the flow and their variation with the control parameters (Biot, Reynolds and Prandtl numbers) are given and compared with those for a Poiseuille–Rayleigh–Bénard flow. The spatial structures of the flow are presented, and it is shown that the centers of the rolls are shifted upwards compared to the PRB case and that there is a loss of symmetry with respect to the vertical axis for the transverse rolls. These effects are directly linked to thermocapillary convection.     

Mixed convection from an open cavity in a horizontal channel

Heat transfer results for mixed convection from a bottom heated open cavity subjected to an external flow are reported in this study for a wide range of the governing parameters (i.e., 1 ≤ Re ≤ 2000, 0 ≤ Gr ≤ 10⁶) over cavities with various aspect ratios (A = 0.5, 1, 2 and 4). It has been found that the Reynolds number and Garshof number control the flow pattern and the occurrence of recirculating cells while the aspect ratio has a significant influence on the orientation of these cells. Heat transfer from the cavity base approaches that of natural convection at a low Reynolds number (i.e., the asymptotic natural convection regime) and approaches that of forced convection at a high Reynolds number (i.e., the asymptotic forced convection regime). In the mixed convection regime, the heat transfer rate is reduced and the flow may become unstable. A unique heat transfer correlation which covers all three convection regimes is also presented.     

Jet impingement cooling of a horizontal surface in an unconfined porous medium: Mixed convection regime

Two-dimensional slot jet impingement cooling of an isothermal horizontal surface immersed in an unconfined porous medium is simulated numerically to gain insight into thermal characteristics under mixed convection conditions with the limitation of the Darcy model. The jet direction is considered to be perpendicular from the top to the horizontal heated element; therefore, the jet flow and the buoyancy driven flow are in opposite directions. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Péclet number (1 ? Pe ? 1000), Rayleigh number (10 ? Ra ? 100), half jet width (0.1 ? D ? 0.5), and the distance between the jet and the heated portion (0.1 ? H ? 1.0). It is found that the average Nusselt number increases with increase in either Rayleigh number or jet width for high values of Péclet number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. It is shown that mixed convection mode can cause minimum average Nusselt number at two values of Péclet number and a maximum average Nusselt number occurs in between theses two Péclet numbers at higher Rayleigh number due to counteraction of jet flow against buoyancy driven flow. Hence careful consideration must be given while designing a system of jet impingement cooling through porous medium.     

Oscillatory double-diffusive mixed convection in a two-dimensional ventilated enclosure

By starting from a steady flow configuration based on the work of Deng et al. [Qi-Hong Deng, Jiemin Zhou, Chi Mei, Yong-Ming Shen, Fluid, heat and contaminant transport structures of laminar double-diffusive mixed convection in a two-dimensional ventilated enclosure, Int. J. Heat Mass Transfer 47 (2004) 5257–5269], a numerical investigation was conducted to analyse the unsteady double-diffusive mixed convection in two-dimensional ventilated room due to heat and contaminant sources. Owing to the large number of parameters, the results are reported only for a constant buoyancy ratio N equal to 1. The flow is found to be oscillatory for a fixed Reynolds number (700 ⩽ Re ⩽ 1000) when the Grashof number is varied in a wide range (10³ ⩽ Gr ⩽ 10⁶). Results of the simulations show that the onset of the oscillatory indoor airflow occurs for couples (Re, Gr) values that can be correlated as Re = aGr^b.     

Low pressure evaporative cooling of micron-sized droplets of solutions and its novel applications

For free molecular regime the mathematical model of low pressure evaporative cooling of binary droplets in gas flow is developed. The model includes five ordinary differential equations and takes into account effects such as the release of the latent heat of condensation of both components and the release of the latent heat of dissolution. Simulations were made for weak aqueous solutions of ammonia. It was discovered that compositions of gas flow and the aqueous solution affect the rate of evaporative cooling of droplets. The ratio of mass flow of solution and gas flow is also an important parameter. The cooling rate of such binary droplets can reach the value of about 2 × 10⁵ K/s.As first applications we consider the air cooler based on evaporative cooling of droplets. For pressure of 20–80 Torr in aerosol reactor, it is shown that in the cooler with length of about 1 m temperature of air flow may drop to about 10–15 °C.The second application is the formation of nanoparticle in evaporating multicomponent droplet with two volatile components. Simulation was made for aqueous solution of ammonia which is widely used by experimentalists and engineers now. Effects of the number of precursors in droplet and supersaturation in droplet on the final size of nanoparticles were investigated.     

Convection heat and mass transfer along a vertical heated plate with film evaporation in a non-Darcian porous medium

A numerical analysis has been carried about to study the heat and mass transfer of forced convection flow with liquid film evaporation in a saturated non-Darcian porous medium. Parametric analyses were conducted concerning the effects of the porosity ε, inlet liquid Reynolds number Re_l, inlet air Reynolds number Re_a on the heat and mass transfer performance. The results conclude that better heat and mass transfer performances are noticed for the system having a higher Re_a, a lower Re_l, and a higher ε. Re_l plays a more important role on the heat and mass transfer performance than Re_a and ε. For the case of ε = 0.4 and Re_a = 10,000, the increases of Nu and Sh for Re_l = 50 are about by 33.9% and 35.3% relative to the values for Re_l = 250.     

Jet impingement cooling of a constant heat flux horizontal surface in a confined porous medium: Mixed convection regime

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions with the limitation of the Darcy model. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Péclet number (1 ? Pe ? 1000), Rayleigh number (10 ? Ra ? 100), half jet width (0.1 ? D ? 1.0), and the distance between the jet and the heated portion (0.1 ? H ? 1.0). It is found that the average Nusselt number increases with increase in either Rayleigh number or jet width for high values of Péclet number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The correlation for Nu_avg in the forced convection regime is suggested. It is shown that mixed convection mode can cause minimum average Nusselt number unfavorably due to counteraction of jet flow against buoyancy driven flow. Hence, careful consideration must be given while designing a system of jet impingement cooling through porous medium.     

Interfacial heat transfer during microdroplet evaporation on a laser heated surface

A comprehensive experimental and numerical investigation on water microdroplet impingement and evaporation is presented from the standpoint of phase-change cooling technologies. The study investigates microdroplet impact and evaporation on a laser heated surface, outlining the experimental and numerical conditions necessary to quantify the interfacial thermal conductance (G) of liquid-metal interfaces during two-phase flow. To do this, continuum-level numerical simulations are conducted in parallel with experimental measurements facilitating high-speed photography and in-situ time-domain thermoreflectance (TDTR). During microdroplet evaporation on laser heated Al thin-films at room temperature, an effective interfacial thermal conductance of G_eff = 6.4 ± 0.4 MW/m² is measured with TDTR. This effective interfacial thermal conductance (G_eff) is interpreted as the high-frequency (ac) interfacial heat transfer coefficient measured at the microdroplet/Al interface. Also on a laser heated surface, fractal-like condensation patterns form on the Al surface surrounding the evaporating microdroplet. This is due to the temperature gradient in the Al surface layer and cyclic vapor/air convection patterns outside the contact line. Laser heating, however, does not significantly increase the evaporation rate beyond that expected for microdroplet evaporation on isothermal Al thin-film surfaces.     

Interaction of Marangoni convection with mass transfer effects at droplets

For the system water–acetone–toluene the mass transfer is measured up to a pressure of 200 bar at a constant temperature of 20 °C for two different concentrations at quiescent pendant droplets. The measurements are compared to empirical predictions. The influence of a surfactant is investigated.A three-mode magnetic suspension balance is used to measure the transfer. Additionally, a Schlieren optic is applied to visualise the convection.Only in case of the transfer direction from the droplet into the continuous phase Marangoni convection is detected. A good agreement of measurement and evaluation is achieved. The surfactant damps the interfacial convection.     

Effect of vent aspect ratio on unsteady laminar buoyant flow through rectangular vents in large enclosures

The effects of vent aspect ratio on oscillatory flow regime through a horizontal opening were studied numerically. The physical model consisted of a vertical rectangular enclosure divided into two chambers by a horizontal partition. The partitions contained a slot that connected the two chambers. The upper chamber contains cold air and the lower chamber contains hot air. A density differential due to the different temperatures drives the interaction between the two chambers. The opposing forces at the interface between the two chambers create a gravitationally unstable system, and an oscillating exchange of fluid develops. Results were obtained for cases with L/D = 1, 0.5, and 2.0, where L represents the thickness of the partition and D represents the slot width of the opening in the partition. Results indicate that the flow exchange increases with partition thickness L/D = 0.5 and decreases for L/D = 2. The frequency of the oscillatory flow pattern is also examined for the different cases. Sudden bursts of upflow with a corresponding downflow have been documented and compared with experimental observations in the literature. The time traces of velocity and temperature fields for this flow regime reveal interesting mechanisms, which have been explained.     

Investigation of natural circulation in cavities with uniform heat generation for different Prandtl number fluids

Natural convection in enclosures with uniform heat generation and isothermal side walls is studied here. For the rectangular enclosure, two-dimensional conservation equations are solved using SIMPLE algorithm. Parametric studies are conducted to examine the effects of orientation of the cavity, fluid properties (Pr number), and aspect ratio for Rayleigh numbers up to 10⁶. For a horizontal square cavity, the flow becomes periodically oscillating at Ra = 5 × 10⁴ and chaotic at Ra = 8 × 10⁵. With a slight increase in the inclination angle, the oscillations die and for inclination angles greater than 15⁰, the flow attain a steady state over a range of Ra. It is found that for tall cavities (aspect ratio > 1), the steady-state solution is obtained for all values of Ra considered here. However, for wide cavities (aspect ratio < 1), an oscillatory flow regime is observed. The maximum temperature within the cavity is calculated for the range of Ra, aspect ratio and Pr number. Correlations for the maximum cavity temperature is presented here. The values of critical Rayleigh number at which the convection sets in the rectangular cavity are also studied and two distinct criteria are determined to evaluate the critical Rayleigh number. Further, a three-dimensional simulation is performed for a cubic cavity. It is found that the steady state solutions are obtained for all Rayleigh number, except at Ra = 10⁶. This is in contrast to the predictions for a two-dimensional square cavity, which has an oscillatory zone from Ra = 5 × 10⁴ onwards.     

Experimental investigation of two-phase closed thermosyphon used in heavy duty extrusion pelleting line

Efficient cooling system is an essential part of heavy duty extrusion pelleting line which plays an important role in production engineering of megaton polyolefin. In this paper, a new cooling system based on two-phase closed thermosyphon (TPCT) used in heavy duty extrusion pelleting line was presented. Comparative experimental results show that thermal performance of TPCT is more efficient, and the temperature uniformity is much better than traditional extruder (similar to coiled heat exchanger) in preheating process and extrusion reaction process. The effects of different operation conditions: filling ratio (0.2, 0.35, 0.5, 0.65 and 0.8), flow rate of cooling water (120 L/h, 180 L/h, 240 L/h, 300 L/h and 360 L/h) and heating power (7 kW, 9 kW and 11 kW) on thermal characteristics were experimental investigated, respectively. The results show that temperature of barrel inner wall increased significantly as filling ratio increased and evaporator appeared dry out when filling ratio is 0.2. The flow rate of cooling water affected the condenser section obviously, but had little influence on evaporation section. With increase of heating power, the start-up time decreases and the heat transfer coefficient increased. An ideal cooling scheme was concluded: the liquid filling ratio was 0.35, the cooling water flow rate was 180 L/h and the heating power was 11 kW when working medium was water.     

Effect of optical properties on oscillatory hydromagnetic double-diffusive convection within semitransparent fluid

The effect of radiative heat transfer on the hydromagnetic double-diffusive convection in two-dimensional rectangular enclosure is studied numerically for fixed Prandtl, Rayleigh, and Lewis numbers, Pr = 13.6, Ra = 10⁵, Le = 2. Uniform temperatures and concentrations are imposed along the vertical walls while the horizontal walls are assumed to be adiabatic and impermeable to mass transfer. The influences of the optical thickness and scattering albedo of the semitransparent fluid on heat and mass transfer with and without magnetic damping are depicted. When progressively varying the optical thickness, multiple solutions are obtained which are steady or oscillatory accordingly to the initial conditions. the mechanisms of the transitions between steady compositionally dominated flow and unsteady thermally dominated flow are analyzed.     

Spray evaporative cooling to achieve ultra fast cooling in runout table

Spray evaporative cooling, in lieu of conventional laminar jet impingement cooling, has potential to achieve the anomalously high strip cooling rate of Ultra Fast Cooling – 300 °C/s for a 4 mm thick carbon steel strip – in Runout Table of Hot Strip Mill. In the present study, evaporation time of a single droplet impinging on a hot carbon steel strip surface has been analytically evaluated as a function of droplet diameter from fundamental heat transfer perspective based on the premise that a spray can be considered as a multi-droplet array of liquid at low spray flux density. Droplet evaporation time thus evaluated has been used to estimate strip cooling rate achievable in Runout Table of Hot Strip Mill by spray evaporative cooling. The proposed analytical model predicts that it is indeed possible to achieve the ultra-high cooling rate of Ultra Fast Cooling by spray evaporative cooling by suitable reduction of droplet size. A general analytical expression has also been developed to estimate critical droplet size to achieve Ultra Fast Cooling as a function of steel strip thickness. Predictions of the analytical model have been validated using CFD simulation with a modified Discrete Phase Model.     

Critical heat flux on flow boiling of methanol–water mixtures in a diverging microchannel with artificial cavities

This study constitutes an experimental investigation into the convective boiling heat transfer and critical heat flux (CHF) of methanol–water mixtures in a diverging microchannel with artificial cavities. Flow visualization shows that bubbles are generally nucleated at both the artificial cavities and side walls of the channel. This confirms the proper functioning of such artificial cavities. Consequently, the wall superheat of the onset nucleate boiling is significantly reduced. Experimental results show that the boiling heat transfer and CHF are significantly influenced by the molar fraction (x_m) as well as the mass flux. The CHF increases with an increase in mass flux at the same molar fraction. On the other hand, the CHF increases slightly from x_m = 0 to 0.3, and then decreases rapidly from x_m = 0.3 to 1 at the same mass flux. The maximum CHF is reached at x_m = 0.3, particularly for a mass flux of 175 kg/m² s, due to the Marangoni effect. Flow visualization confirms that the Marangoni effect helps a region with a liquid film breakup persist to a higher heat flux, and therefore a higher CHF. Moreover, a new empirical correlation involving the Marangoni effect for the CHF on the flow boiling of methanol–water mixtures is developed. The present correlation prediction shows excellent agreement with the experimental data, and further confirms that the present correlation may predict the Marangoni effect on the CHF for the convective boiling heat transfer of binary mixtures.