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Wärme - und Stoffübertragung

, Volume 16, Issue 2, pp 105–111 | Cite as

Planar solidification of a warm flowing-liquid under different boundary conditions

  • R. V. Seeniraj
  • T. K. Bose
Article

Abstract

Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resulted in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy.

Keywords

Heat Transfer Heat Flux Convective Heat Transfer Phase Change Material Problem Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

a

thickness of wall, m

Bi

Biot Number

Cp

specific heat, J/kg/K

g

freezing-front speed, m/sec

h

convective heat transfer coefficient, W/m2/K

k

thermal conductivity of solid, W/m2/K

L

latent heat of fusion, W/kg

q″

heat flux, case (b), W/m2

S

dimensionless frozen layer thickness

S*

modified Stefan Number, case (b)

T

temperature, K

t

time, s

U

dimensionless temperature

X

position coordinate in frozen layer measured from wall, m

Xs

thickness of frozen layer at steady state, m

x

dimensionless coordinate

In

natural logarithm

Greek symbols

α

thermal diffusivity of solid, m2/s

β

flux parameter, case (b)

ε

Stefan number

\(\bar \varepsilon \)

dimensionless thickness of solid layer, case (b)

ϱ

density of solid, kg/m3

τ

dimensionless time

Subscripts

c

coolant

f

freezing front

O

overall

s

steady state

w

wall

1

liquid phase of solidifying substance

Gefrieren einer warmen, strömenden Flüssigkeit in ebener Front unter verschiedenen Bedingungen

Zusammenfassung

Der Gefriervorgang einer warmen, strömenden Flüssigkeit mit konvektivem Wärmeübergang zur ebenen wachsenden Phasengrenze wurde mit den Randbedingungen konstante Temperatur, konstanter Wärmestrom und konvektiver Wärmestrom an der Oberfläche untersucht. Man erhält zwei gekoppelte Differentialgleichungen für die Temperatur und die Dicke der festen Schicht als Funktion des Ortes, der Zeit und der Problemparameter. So gelangt man zu analytischen Ausdrücken für die Temperaturverteilung in der festen Schicht, der Geschwindigkeit und die Zeit der Erstarrung. Die hier angewandte Störungsrechnung ist einfach und, im Gegensatz zu älteren Verfahren, explizit. Für konvektive Übertragung als Randbedingung erhält man gute Übereinstimmung zwischen Experiment und Theorie. Diese Ergebnisse sind wichtig für Entwurf und Auswertung von experimentellen Resultaten mit Frieren und Schmelzen in einer Ebene. Der Einfluß der Stefan-Zahl, die für in Frage kommende Stoffe klein ist, wird im Zusammenhang mit Wärmespeicherung untersucht.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • R. V. Seeniraj
    • 1
  • T. K. Bose
    • 1
  1. 1.Department of Aeronautical EngineeringIndian Institute of TechnologyMadrasIndia

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