Transient Freezing of Liquids in Forced Flow Inside Circular Tubes

1969 ◽  
Vol 91 (3) ◽  
pp. 385-389 ◽  
Author(s):  
M. N. O¨zis¸ik ◽  
J. C. Mulligan
Keyword(s):  
Solid Phase ◽  
Freezing Temperature ◽  
Local Heat ◽  
Liquid Interface ◽  
Forced Flow ◽  
Transfer Rates ◽  
Tube Wall Temperature ◽  
Temperature Constant ◽  
Solid Liquid Interface ◽  
Solid Liquid

The transient freezing of a liquid flowing inside a circular tube is investigated analytically under the assumption of a constant tube wall temperature which is lower than the freezing temperature, constant properties, a slug-flow velocity profile and quasisteady state heat conduction in the solid phase. The variation of the local heat flux and the profile of the solid-liquid interface during freezing has been determined as a function of time and position along the tube. The analysis produced steadystate heat transfer rates and profiles for the solid-liquid interface which agreed well with experiments.

Crystallization of liquids in the vicinity of a solid

1981 ◽  
Vol 34 (1) ◽  
pp. 1
Author(s):  
JE Lane ◽  
TH Spurling
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Solid Phase ◽  
Adsorbed Layer ◽  
Liquid Interface ◽  
Spherically Symmetric ◽  
Present Evidence ◽  
Ensemble Monte Carlo ◽  
Solid Liquid Interface ◽  
Solid Liquid

We present evidence, gained from grand ensemble Monte Carlo simulations of the solid/liquid interface, that an adsorbed layer of spherically symmetric liquid particles can have a crystal-like structure even if the solid phase is structureless.

Transient Freezing of Liquids in Turbulent Flow inside Tubes

1979 ◽  
Vol 101 (3) ◽  
pp. 465-468 ◽  
Author(s):  
Chul Cho ◽  
M. N. O¨zis¸ik
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Circular Tube ◽  
Freezing Temperature ◽  
Liquid Interface ◽  
Wall Heat Flux ◽  
Uniform Temperature ◽  
Solid Liquid Interface ◽  
Solid Liquid

The problem of freezing of a liquid in turbulent flow inside a circular tube whose wall is kept at a uniform temperature lower than the freezing temperature of the liquid is solved. The radius of the solid-liquid interface and the local wall heat flux are determined as a function of time and position along the tube for several different values of the Prandtl number and the freezing parameter.

Numerical and Experimental Investigation of Phase Change Heat Transfer in the Presence of Rayleigh–Benard Convection

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Mohammad Parsazadeh ◽  
Xili Duan
Keyword(s):  
Nusselt Number ◽  
Phase Change ◽  
Local Heat ◽  
Liquid Interface ◽  
Interface Location ◽  
Local Heat Flux ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract This research investigates the melting rate of a phase change material (PCM) in the presence of Rayleigh–Benard convection. A scaling analysis is conducted for the first time for such a problem, which is useful to identify the parameters affecting the phase change rate and to develop correlations for the solid–liquid interface location and the Nusselt number. The solid–liquid interface and flow patterns in the liquid region are analyzed for PCM in a rectangular enclosure heated from bottom. Numerical and experimental results both reveal that the number of Benard cells is proportional to the ratio of the length of the rectangular enclosure over the solid–liquid interface location (i.e.,, the liquified region aspect ratio). Their effect on the local heat flux is also analyzed as the local heat flux profile changes with the solid–liquid interface moving upward. The variations of average Nusselt number are obtained in terms of the Stefan number, Fourier number, and Rayleigh number. Eventually, the experimental and numerical data are used to develop correlations for the solid–liquid interface location and average Nusselt number for this type of melting problems.

The Solution of a Heat Transfer Problem With Change of State Inside a Spherical Shell

2012 ◽  
Author(s):  
Danillo Silva de Oliveira ◽  
Fernando Brenha Ribeiro
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Spherical Shell ◽  
Outer Surface ◽  
Transfer Problem ◽  
Freezing Temperature ◽  
Liquid Interface ◽  
Inner Surface ◽  
Solid Liquid Interface ◽  
Solid Liquid

The heat transfer problem is solved for the case of cooling, below the freezing temperature, an initially liquid material inside a spherical shell. The shell is limited by a fixed inner surface and by an outer surface, free to radially expand or contract. As boundary conditions it is imposed that the inner surface is kept constant below the freezing temperature of the liquid and the outer surface is maintained constant above it. The solution represents the formation of a solidified layer that expands outward, separated from the liquid by a spherical surface kept constant at the freezing temperature. The problem is solved in the form of two closed form solutions, written in non-dimensional variables: one for the heat conduction equation in the solid layer and the second for the heat conduction – advection equation in the liquid layer. The solutions formally depend of and are linked by the time dependent radius of the spherical solid–liquid interface and its time derivate, which are, at first, unknown. A differential equation describing the solid–liquid interface radius as function of time is obtained imposing the conservation of energy through the interface during the heat exchange process. This equation is non-linear and has to be numerically solved. Substitution of the interface radius and its time derivate for a particular instant in the heat transfer equations solutions furnishes the temperature distribution inside the spherical shell at that moment. The solution is illustrated with numerical examples.

Effects of the Flow Speed on Dendritic Growth in Phase-Field Simulation of Binary Alloy with Convection

2012 ◽  
Vol 217-219 ◽  
pp. 1516-1519 ◽  
Author(s):  
Wen Yuan Long ◽  
Wei Dong Wang ◽  
Jun Ping Yao
Keyword(s):  
Binary Alloy ◽  
Phase Field ◽  
Flow Speed ◽  
Liquid Interface ◽  
Forced Flow ◽  
Solute Boundary Layer ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Solute Gradient ◽  
Theoretical Results

A phase-field approach which incorporates mass and momentum and solute conservation equations for simulation of Al-Si binary alloy solidification is studied. The effect of force flow on the dendrite growth and solute profile during the solidification of binary alloy were investigated. The results indicate that dendritic grows unsymmetrically under a forced flow, the growth velocity of the upstream tip is faster than the downstream tip. With the force flow, the upstream tip grows faster due the thinner solute boundary layer. The solute gradient in the solid/liquid interface regions of the upstream tip is higher than that of the downstream tip. The faster the flow velocity, the greater the solute gradients in the solid/liquid interface regions of the upstream tip, the thinner the diffusion layer before the upstream tip. The downstream tip is opposed to the upstream tip. The simulations agree qualitatively with the solidification theoretical results.

scholarly journals Numerical Simulation of Solidification of Colloids Inside a Differentially Heated Cavity

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Yousef M. F. EL Hasadi ◽  
J. M. Khodadadi
Keyword(s):  
Solid Phase ◽  
Colloidal Suspension ◽  
Concentration Field ◽  
Liquid Interface ◽  
Thermosolutal Convection ◽  
Alumina Nanoparticles ◽  
Convection Cell ◽  
Fluid Mixture ◽  
Solid Liquid Interface ◽  
Solid Liquid

Development of the solid–liquid interface, distribution of the particle concentration field, as well as the development of thermosolutal convection during solidification of colloidal suspensions in a differentially heated cavity are investigated. The numerical model is based on the one-fluid mixture approach combined with the single-domain enthalpy porosity model for phase change, and it is implemented in fluent software package. The linear dependence of the liquidus and solidus temperatures with the concentration of the nanoparticles was assumed. A colloidal suspension consisting of water and copper or alumina nanoparticles were considered. In the current investigation, the nanoparticle size selected was 5 and 2 nm. The suspension was solidified unidirectionally inside a square differentially heated cavity that was cooled from the left side. It was found that the solid–liquid interface changed its morphology from a planar shape to a dendritic one as the solidification process proceeds in time, due to the constitutional supercooling that resulted from the increased concentration of particles at the solid–liquid interface rejected from the crystalline phase. Initially, the flow consisted of two vortices rotating in opposite directions. However, at later times, only one counter clockwise rotating cell survived. Changing the material of the particle to alumina resulted in crystallized phase with a higher concentration of particles. If it is compared to that of the solid phase resulted from freezing the copper–water colloidal suspension. Decreasing the segregation coefficient destabilizes the solid–liquid interface and increases the intensity of the convection cell with respect to that of the case of no particle rejection. At slow freezing rates, the resulting crystal phase consisted of lower particle content compared to the case of higher freezing rate.

scholarly journals The combined effects of shear and buoyancy on phase boundary stability

2019 ◽  
Vol 868 ◽  
pp. 648-665 ◽  
Author(s):  
S. Toppaladoddi ◽  
J. S. Wettlaufer
Keyword(s):  
Shear Flow ◽  
Solid Phase ◽  
Liquid Interface ◽  
Flow Instabilities ◽  
Flow Strength ◽  
Buoyancy Driven Flows ◽  
The Stability ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Boundary Stability

We study the effects of externally imposed shear and buoyancy driven flows on the stability of a solid–liquid interface. A linear stability analysis of shear and buoyancy-driven flow of a melt over its solid phase shows that buoyancy is the only destabilizing factor and that the regime of shear flow here, by inhibiting vertical motions and hence the upward heat flux, stabilizes the system. It is also shown that all perturbations to the solid–liquid interface decay at a very modest shear flow strength. However, at much larger shear-flow strength, where flow instabilities coupled with buoyancy might enhance vertical motions, a re-entrant instability may arise.

GROWTH CONDITIONS FOR STABILITY OF A CELLULAR SOLID-LIQUID INTERFACE

1957 ◽  
Vol 35 (10) ◽  
pp. 1223-1227 ◽  
Author(s):  
E. L. Holmes ◽  
J. W. Rutter ◽  
W. C. Winegard
Keyword(s):  
Freezing Temperature ◽  
Growth Conditions ◽  
Solute Concentration ◽  
Critical Value ◽  
Liquid Interface ◽  
Cellular Solid ◽  
First Approximation ◽  
Comparison Of The Results ◽  
Solid Liquid Interface ◽  
Solid Liquid

Samples of zone-refined lead containing various amounts of silver as solute were solidified under well-controlled conditions to study the transition from cellular to dendritic freezing as a function of composition, speed of freezing, temperature gradient in the melt during freezing, and crystallographic orientation of the solidifying crystal. A comparison of the results of this investigation with those of Tiller and Rutter (1956) on alloys of tin in lead shows that to a first approximation the onset of dendritic freezing under any given growth conditions occurs at a critical value of the average solute concentration in the liquid at the solid–liquid interface, independent of whether the solute present is tin or silver.

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