David M. Christopher

Prandtl number effects for Marangoni convection over a flat surface

Abstract Marangoni convection, which is induced by the variation of the surface tension with temperature along a surface, influences crystal growth melts and other processes with liquid–vapor interfaces, such as boiling in both microgravity and in normal gravity in some cases. This paper presents a similarity solution for Marangoni flow over a flat surface for both the momentum equations and the energy equation assuming a developing boundary layer along a surface. Solutions are presented for the surface velocity, the total flow rate and the heat transfer for various temperature profiles and various Prandtl numbers. The analysis also shows how the heat transfer variation with Prandtl number changes for Prandtl numbers from much less than one to much greater than one. For large bubbles, the predicted boundary layer thickness would be less than the bubble diameter, so the curvature effects could be neglected and this analysis could be used as a first estimate of the effect of Marangoni flow around a vapor bubble.

Dynamics of Bubble Motion and Bubble Top Jet Flows From Moving Vapor Bubbles on Microwires

Rapid bubble sweeping along heated wires was observed during subcooled nucleate boiling experiments on very fine wires with jet flows emanating from the tops of the vapor bubbles for a variety of conditions. This paper presents experimental results with a numerical analysis of the physical mechanisms causing the experimentally observed bubble motion and jet flows. The results show that the moving bubble creates a nonuniform temperature distribution in the wire by cooling the wire as it moves along the wire with significant heat transfer in the wake behind the bubble. The results verify that the bubble motion is driven by the temperature difference from the front to the back of the bubble, which causes Marangoni flow. The Marangoni flow then thrusts the bubble forward along the wire with the calculated bubble velocities agreeing well with experimental measurements. In addition, the temperature difference from the bottom to the top of the bubble creates a vertical component to the Marangoni flow that results in the jet flows from the bubble tops

Similarity simulation for Marangoni convection around a vapor bubble during nucleation and growth

Abstract Marangoni convection occurs around vapor bubbles during nucleation and growth due to the temperature variation along the surface. The surface tension variation resulting from the temperature gradient along the surface causes Marangoni convection. Marangoni convection is of importance in crystal growth melts and may influence other processes with liquid–vapor interfaces, in addition to boiling. The influence of Marangoni induced convection is more obvious under microgravity but also occurs in earth gravity. This paper presents a similarity solution for Marangoni induced flow both for the velocity profile and the temperature profile, assuming developing boundary-layer flow along a surface with various imposed temperature profiles. The surface velocity, the total flow rate and the heat transfer characteristics are given for various temperature profiles and various Prandtl numbers. Since the predicted boundary layer thickness would be much less than the diameter of vapor bubbles during nucleate boiling, the bubble surface curvature effects can be neglected and this analysis can be used as a first estimate of the effect of Marangoni flow around a vapor bubble.

Jet Flows Around Microbubbles in Subcooled Boiling

Strong jet flows were observed emanating from micro bubbles on a 100 μm diameter wire during subcooled nucleate boiling. The flow velocities were visualized with high-speed photography and quantified with a PIV analysis. The bubble-top jet flows were characterized by a single jet at the bubble top. Both experiments and simulations indicated that the bubble-top jet flows are induced by Marangoni effects due to temperature gradients near the wire, rather than due to condensation at the bubble top. The evaporation and condensation does, however, control the jet flow intensity. Multiple jets from a single bubble were sometimes observed on bubbles that were generally larger than the heater wire. The jets were driven by the Marangoni flow at cool regions on the bubble sides resulting from upward flow of subcooled liquid. Bubble-top jet flow

Heat Transfer in the Microlayer Under a Bubble During Nucleate Boiling

Many studies have shown that a very thin liquid microlayer forms under vapor bubbles during nucleate boiling. The heat transfer from the surface to the bubble is then significantly affected by this microlayer and the curved region leading into the microlayer. Various models have been developed to predict the microlayer shape and the heat transfer along the curved interfacial region, but they tend to have inconsistent boundary conditions or unrealistic results. This paper presents a theoretical model to predict the microlayer thickness and the heat transfer rates for a variety of conditions. The results show how the wall superheat, the Hamaker constant, the bubble radius, and the accommodation coefficient at the interface affect the evaporation heat transfer rates and the microlayer shape for a large range of conditions for water and FC 72. The microlayer results are then shown to compare well with predictions made by solving the Navier-Stokes equations in the microlayer.

Non-Darcy natural convection around a horizontal cylinder buried near the surface of a fluid-saturated porous medium

Abstract Natural convection around a horizontal, isothermal cylinder buried in a fluid-saturated porous medium is modeled analytically using the Forchheimer-extended Darcy flow model. The governing equations are solved numerically to obtain the flow field, the temperature distribution, and the local and average Nusselt numbers around the cylinder as functions of the cylinder depth, H, the modified Rayleigh number, Ra∗, and the Darcy number, Da. The results show that the presence of an impermeable surface above the cylinder significantly alters the flow field and reduces the heat transfer from the cylinder. Recirculating zones may develop above the cylinder creating regions of low and high heat transfer rates. The Forchheimer term in the velocity equation reduces the flow velocity and, hence, the heat transfer for the case of large Darcy number and results in a significant decrease in the average Nusselt number around the cylinder when Red is greater than approximately five.

Near-Wall Liquid Layering, Velocity Slip, and Solid–Liquid Interfacial Thermal Resistance for Thin-Film Evaporation in Microchannels

Heat transfer and liquid flow near solid–liquid interfaces for evaporating thin films in microchannels were investigated based on the augmented Young-Laplace equation and kinetic theory. A wall-affected nanolayer was used to correlate the Kapitza resistance with the liquid layering and velocity slip for both hydrophilic and hydrophobic surfaces. This nanolayer physical model was developed to show the combined effects of the solid–liquid interfacial temperature slip and the velocity slip on the thin-film evaporation. The results show that the liquid velocity slip elongates the thin-film region and enhances the evaporation. A minimum slip length exists for the extremely wetting case. The Kapitza resistance and nanolayer disordering for hydrophobic surfaces tend to reduce the thin liquid film superheat and overall heat transfer, leading to a larger U-shaped temperature drop. The nanolayer ordering enhances the thin-film evaporation but cannot entirely counteract the Kapitza resistance.

Dynamic Bubble Behaviour during Microscale Subcooled Boiling

Bubble cycles, including initiation, growth and departure, are the physical basis of nucleate boiling. The present investigation, however, reveals unusual bubble motions during subcooled nucleate boiling on microwires 25 or 100 μm in diameter. Two types of bubble motions, bubble sweeping and bubble return, are observed in the experiments. Bubble sweeping describes a bubble moving back and forth along the wire, which is motion parallel to the wire. Bubble return is the bubble moving back to the wire after it has detached or leaping above the wire. Theoretical analyses and numerical simulations are conducted to investigate the driving mechanisms for both bubble sweeping and return. Marangoni flow from warm to cool regions along the bubble interface is found to produce the shear stresses needed to drive these unusual bubble movements.

Similarity Solution for Marangoni Convection Over a Flat Surface

A similarity solution is presented for Marangoni flow over a flat surface for both the velocity and temperature profiles assuming developing boundary layer flow along the surface with various imposed temperature profiles. Marangoni flow results from variations of the surface tension along a liquid-vapor interface and is especially noticeable in microgravity. Solutions are presented for the surface velocity, the total flow rate and the heat transfer for various temperature profiles and various Prandtl numbers

Experimental Investigation of Spray Cooling on Nano- and Hybrid-Structured Surfaces

The heat transfer during spray cooling was studied experimentally using deionized water to investigate the spray characteristics and the differences between spray cooling on a smooth silicon surface and nano- and hybrid micro/nano-structured surfaces. The spray cooling experiments show that the heat transfer rates were best for the nano-structured surface, followed by the smooth surface coated with the SiO2 film and the pure silicon surface since the contact angle was smallest on the nano-structured surface and increased on the other two surfaces. The Critical Heat Flux (CHF) was largest for the 25G×25S surface coated with four Carbon Nano Tube (CNT) films with a 75.3% increase over the smooth surface.Copyright