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.

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.

A Solution of Freezing of Liquids of Low Prandtl Number in Turbulent Flow Between Parallel Plates

1977 ◽  
Vol 99 (1) ◽  
pp. 20-24 ◽  
Author(s):  
A. A. Shibani ◽  
M. N. O¨zis¸ik
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Freezing Temperature ◽  
Axial Position ◽  
Parallel Plates ◽  
Uniform Temperature

The steady-state freezing of liquids of low Prandtl number in turbulent flow between parallel plates, the walls of which are kept at uniform temperature lower than the freezing temperature of the liquid, is solved by matched asymptotic technique. The location of the liquid-solid interface and the heat transfer rate are established as a function of the axial position along the channel.

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.

Continuum Models With Slip for the Evaporating Meniscus and Comparison With Experimental Results

2008 ◽  
Author(s):  
Arya Chatterjee ◽  
Joel L. Plawsky ◽  
Peter C. Wayner
Keyword(s):  
Experimental Data ◽  
Heat Flux ◽  
Heat Pipe ◽  
Dip Coating ◽  
Liquid Interface ◽  
Continuum Models ◽  
Experimental Investigations ◽  
Vapor Interface ◽  
Solid Liquid Interface ◽  
Solid Liquid

The evaporating meniscus is a recurring phenomenon in engineering that has relevance in diverse applications like dip-coating, pool boiling and the micro heat pipe. It is known that the evaporative heat flux at the liquid vapor interface peaks at the interline region. Recent experimental investigations have indicated a rise in the curvature in this region. To match the increased flow predicted by this curvature jump, slip may be required at the solid liquid interface. We use continuum models and experimental data on temperature and thickness to evaluate slip at the liquid solid interface.

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.

Studies on heat transfer and pressure drop in turbulent flow of silver - water nanofluids through a circular tube at constant wall heat flux

2018 ◽  
Vol 54 (7) ◽  
pp. 2089-2099 ◽  
Author(s):  
S. Iyahraja ◽  
J. Selwin Rajadurai ◽  
S. Rajesh ◽  
R. Seeni Thangaraj Pandian ◽  
M. Selva Kumaran ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Circular Tube ◽  
Wall Heat Flux ◽  
Constant Wall Heat Flux
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