The growth of a deposited layer on a cold surface

doi:10.1016/0017-9310(65)90002-5

International Journal of Heat and Mass Transfer

Volume 8, Issue 3, March 1965, Pages 395-402

https://doi.org/10.1016/0017-9310(65)90002-5 Get rights and content

Abstract

An approximate analysis of the growth of, and the temperature within, a deposit which may occur in a cold surface in a gas stream is developed with the convective heat transfer to the surface of the deposit taken into account. Simple “short time” and “long time” solutions are obtained. A numerical example which may be of interest in connection with cryogenic surfaces in a hypersonic wind tunnel is presented.

Résumé

Une analyse approchée de la croissance et du champ de température intérieur d'un dépôt qui peut se produire sur une surface dans un écoulement gazeux, est étudiée en tenant compte du transport de chaleur par convection à la surface du dépôt. Des solutions simples pour un “temps court” et pour un “temps long” sont obtenues. Un exemple numérique est présenté qui peut avoir de l'intérêt en connection avec les surfaces cryogéniques dans une soufflerie hypersonique.

Zusammenfassung

Das Anwachsen und die Temperatur einer Ablagerung, die an einer kalten Oberfläche in einem Gasstrom auftreten kann, wird näherungsweise untersucht, wobei der konvektive Wärmeübergang an die Oberfläche der Ablagerung miteinbezogen wird. Man erhält einfache “Kurzzeit-” und “Langzeit-” -Lösungen. Ein Zahlenbeispiel, das in Verbindung mit sehr tiefen Oberflächentemperaturen in einem Hyperschallwindkanal interessieren dürfte, wird angegeben.

References (13)

R.J. Cresci et al.
Use of a supersonic compressor for a high enthalpy test facility
R.V. Smith et al.
Analysis of the frost phenomena on a cryo-surface
D.B. Chelton et al.
Solid formation in flowing cryogenic fluids Advanc
Cryogenic Engng
(1963)
R.L. Chuan et al.
Principle and application of the two-phase wind-tunnel system
University of Southern California Engineering Center, Report 42-101
(1955)
R.L. Chuan
A study of the condensation of nitrogen below the triple point
University of Southern California Engineering Center, Report No. 56-201
(1957)
K. Karamcheti
A note on the thermal conductivity of solid nitrogen and the direct condensation of nitrogen gas into a solid
University of Southern California Engineering Center Report No. 56-206
(1959)

There are more references available in the full text version of this article.

Cited by (24)

Kinetics of melt crystallization of organic eutectic forming binary mixtures in non-flow systems
2001, Chemical and Engineering Processing
The kinetics of melt crystallization of binary eutectic forming organic mixtures in non-flow systems with cooling from below for the preferential crystallization of one component alone have been studied experimentally. The effect of subcooling, superheating and the initial concentration of the melt on the crystallization kinetics have been studied. Based on the experimental data, a correlation for the instantaneous height of the crystal (volume fraction of the solidified mass) has been proposed. The experimental results were also analyzed based on a model from the literature, which considered simultaneous heat and mass transport. The analysis shows that in the present experiments, the melt crystal interface was very close to the initial melt composition, i.e. concentration equilibrium was maintained. This is attributed to the very low cooling rates used, even though the thermal diffusivity is much greater than the mass diffusivity of the melt.
A note on the contact temperature during high-Peclet-number flow over a flat substrate
1998, International Journal of Heat and Mass Transfer
Knowledge of the temperature at the interface between a hot liquid spreading over a cold solid substrate is important in determining the nature and extent of any freezing of the spreading liquid and/or melting of the substrate. In this paper, a simple model is studied to assess the influence of convection on the spatial and temporal variation of the interface temperature. New solutions are determined by both analytical and approximate numerical techniques. The theoretical and numerical results are compared in the case of slug flow and shown to be in good agreement Shear flow and axisymmetric flow are also considered.
Mathematical modelling of the desublimation of phthalic anhydride
1990, Chemical Engineering and Processing
The paper presents a mathematical model of desublimation of phthalic anhydride (PA), taking into account the possibility of the formation of mist in the vapour—air mixture. Solid PA, depositing on the external surface of finned condenser tubes, has a porous structure. The equation obtained defines porosity of the deposit as a function of time and location within the apparatus. It has been shown that in an industrial condenser only heterogeneous condensation may occur (formation of mist), leading to a decrease in the overall efficiency of the process. The predicted temperature and concentration profiles have been compared with the experimental data.
Es wird ein mathematisches Modell des Sublimationsprozesses von Phthalsäureanhydrid (PSA) entwickelt, bei dem auch die Kondensation in der Dampf — Luft-Mischung in Form von Nebel berücksichtigt ist. Das PSA, das sich auf der Außenfläche der Rippenrohre eines Kondensators absetzt, hat eine poröse Struktur. Eine Gleichung beschreibt, wie sich die Porosität des Niederschlags in Abhängigkeit von der Zeit und dem Ort im Kondensator ändert. Es wurde festgestellt, daß in industriell verwendeten Kondensatoren nur heterogene Kondensation in Form von Nebel auftreten kann, was zu einer Abnahme des Gesamtwirkungsgrades des Desublimations-prozesses in Kondensator führt. Die berechneten Temperatur- und Konzentrationsverläufe werden mit den experimentell bestimmten verglichen.
A theoretical and experimental study on solidification dynamics of a flowing fluid through a vertical cooled channel from a reservoir
1989, International Communications in Heat and Mass Transfer
A theoretical and experimental work on solidification dynamics of a flowing molten fluid through a vertical cooled channel from a constant pressure reservoir is presented. An explicit theoretical model for the channel plugging time is developed along with simple methods for the transient mass displacement. Experimental results of channel plugging times, transient mass displacement, and the total mass displaced prior to complete channel plugging are obtained using paraffin wax and Wood's metal as molten fluids. These experimental results are compared with the predictions of theory. In addition, the applicable range of theory is presented in terms of dimensionless parametric values.
The steady state ice layer profile on a constant temperature plate in a forced convection flow-I. Laminar regime
1979, International Journal of Heat and Mass Transfer
The shape of the steady state ice layer that forms on a constant temperature horizontal plate in a parallel forced convection flow was analyzed. This paper, part I of a two part series, will examine phenomena that effect the shape of the ice layer in the laminar flow regime. Of particular interest are the effects of curvature of the ice surface on the free stream flow and of streamwise heat conduction in the ice layer. A two-dimensional theory developed to account for these effects suggests that a modified Reynolds number of the form Re_x/θ²_c where θ_c is a temperature ratio parameter should be used to correlate the ice profiles. It was found that measurements could be correlated over a wide range of plate temperatures, free stream temperatures and free stream velocities using this parameter. Also in the laminar regime thermal instabilities of the boundary layer were observed which produced longitudinal grooves in the ice surface.
On étudie la forme de la couche de glace qui apparait en régime permanent sur une plaque horizontale à température constante, dans un écoulement parallèle forcé. Dans cette première partie, on examine les phénomènes qui affectent la forme pour le régime laminaire. Les effets de courbure de la surface de la glace et de la conduction thermique longitudinale dans la couche de glace sont particulièrement intéressants. Un modèle bidimensionnel développé pour tenir compte d'eux, suggère l'utilisation d'un nombre de Reynolds modifié Re_x/θ²_c où θ_c est un paramètre de température. On trouve que les mesures peuvent être unifiées par ce paramètre, pour un large domaine de température de plaque, de température d'écoulement libre et de vitesse d'écoulement. Dans le régime laminaire, des instabilités thermiques de la couche limite sont observées, lesquelles produisent des rainures longitudinales sur la surface de la glace.
Die Form einer stationären Eisschicht, die sich auf einer horizontalen Platte konstanter Temperatur bei paralleler erzwungener Strömung bildet, wurde analysiert. Diese Arbeit, Teil I einer zweiteiligen Folge, wird die Phänomene, welche die Form der Eisschicht im Bereich der laminaren Strömung beeinflussen, untersuchen. Von besonderem Interesse sind die Einflüsse der Krümmung der Eisoberfläche auf die freie Strömung und die der Wärmeleitung der Eisschicht in Strömungsrichtung. Eine zweidimensionale Theorie, in der diese Einflüsse berücksichtigt werden, legt es nahe, eine modifizierte Reynolds-Zahl der Form Re_x/θ_c zur Darstellung der Eisprofile zu verwenden, wobei θ_c ein Temperaturverhältnisparameter ist. Es wurde gefunden, daβ bei Verwendung dieses Parameters die Messungen in einem weiten Bereich von Plattentemperaturen sowie Temperaturen und Geschwindigkeiten der freien Strömung gut korreliert werden konnten. Auch im laminaren Bereich wurden thermische Instabilitäten der Grenzschicht beobachtet, die Längsrillen in der Eisoberfläche hervorriefen.
ANaлизиpyeтcя кoNфигypaция cтaциoNapNoгo cлoя льдa, oбpaзyючeгocя Na гopизoNтaльNoй плacтиNe, Naчoдячeйcя в пapaллeльNoм пoтoкe. B дaNNoй cтaтьe, пpeдcтaвляючeй coбoй пepвyю чacть paбoты, иccлeдyютcя явлeNия, oкaзывaючиe влияNиe Na кoNфигypaцию cлoя льдa пpи лaмиNapNoм peжимe тeчeNия. Ocoбoe вNимaNиe oбpaчeNo Na влияNиe кpивизNы пoвepчNocти льдa Na cвoбoдNый пoтoк и тeплoпpoвoдNocть cлoя льдa в NaпpaвлeNии тeчeNия. Для yчëтa этич эффeктoв paзpaбoтaNa двyмepNaя мoдeль, в кoтopoй для oбoбчeNия пpoфилeй cлoя льдa иcпoльзyeтcя мoдифициpoвaNNoe чиcлo peйNoльдca видa $Re_{x} 0^{2}_{c}$ , гдe 0_c — пapaмeтp oтNoшeNия тeмпepaтyp. NaйдeNo, чтo c пoмoчью дaNNoгo пapaмeтpa peзyльтaты измepeNий мoжNo oбoбчить для шиpoкoгo диaпaзoNa тeмпepaтyp плacтиNы, тeмпepaтyp и cкopocтeй cвoбoдNoгo пoтoкa. cлeдyeт oтмeтить, чтo пpи лaмиNapNoм peжимe тeчeNия Naблюдaлиcь тepмичecкиe Neycтoйчивocти пoгpaNичNoгo cлoя, кoтopыe пpивoдили к oбpaзoвaNию пpoдoльNыч кaNaвoк Na пoвepчNocти льдa.
An assessment of fuel freezing and drainage phenomena in a reactor shield plug following a core disruptive accident
1978, Nuclear Engineering and Design
An important problem related to the assessment of the recriticality potential for an LMFBR following a core disruptive accident is an understanding of the freezing phenomena of molten fuel on a cold structure which may prevent fuel dispersal and subsequent shutdown. Transient analytical freezing and drainage calculations have been applied to molten UO₂ travel through the rather cold lower shield plug of the Clinch River Breeder Reactor (CRBR). The successive approximation technique is used to obtain a solution to the non-linear freezing problem, where such effects or heat generation, viscous heat dissipation, temperature dependent thermophysical properties and a convective boundary condition at the solidification front have been incorporated into the present analytical formulation. Results indicate that previous steady-state analysis overestimate the rate of frozen layer build-up by a bout a factor of two. However, of primary importance is the driving force for drainage and the diameter of the shield plug flow channel.

View all citing articles on Scopus

^☆: This research was sponsored by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, under Contract AF 33(657)-8286.

^‡: Professor of Aerospace Engineering; presently Professor, Department of Aerospace and Mechanical Engineering Sciences, University of California San Diego.

^§: Research Fellow.

View full text

Article preview

International Journal of Heat and Mass Transfer

Abstract

Résumé

Zusammenfassung

References (13)

Use of a supersonic compressor for a high enthalpy test facility

Analysis of the frost phenomena on a cryo-surface

Solid formation in flowing cryogenic fluids Advanc

Cryogenic Engng

Principle and application of the two-phase wind-tunnel system

University of Southern California Engineering Center, Report 42-101

A study of the condensation of nitrogen below the triple point

University of Southern California Engineering Center, Report No. 56-201

A note on the thermal conductivity of solid nitrogen and the direct condensation of nitrogen gas into a solid

University of Southern California Engineering Center Report No. 56-206

Cited by (24)

Kinetics of melt crystallization of organic eutectic forming binary mixtures in non-flow systems

A note on the contact temperature during high-Peclet-number flow over a flat substrate

Mathematical modelling of the desublimation of phthalic anhydride

A theoretical and experimental study on solidification dynamics of a flowing fluid through a vertical cooled channel from a reservoir

The steady state ice layer profile on a constant temperature plate in a forced convection flow-I. Laminar regime

An assessment of fuel freezing and drainage phenomena in a reactor shield plug following a core disruptive accident

The growth of a deposited layer on a cold surface☆

Abstract

Résumé

Zusammenfassung

Use of a supersonic compressor for a high enthalpy test facility

Analysis of the frost phenomena on a cryo-surface

Solid formation in flowing cryogenic fluids Advanc

Cryogenic Engng

Principle and application of the two-phase wind-tunnel system

University of Southern California Engineering Center, Report 42-101

A study of the condensation of nitrogen below the triple point

University of Southern California Engineering Center, Report No. 56-201

A note on the thermal conductivity of solid nitrogen and the direct condensation of nitrogen gas into a solid

University of Southern California Engineering Center Report No. 56-206