Computer Vision Analysis of a Melting Interface Problem with Natural Convection

  • Gisele Maria R. VieiraEmail author
  • Fabiana R. Leta
  • Pedro B. Costa
  • Sergio L. Braga
  • Dominique Gobin
Part of the Augmented Vision and Reality book series (Augment Vis Real, volume 4)


This study presents some Computer Vision techniques to analyze a phase change problem with natural convection. The analysis and interpretation of images are important to understand the phenomenon under study. Methods of image processing and analysis are used to validate the mathematical model and to automate the process of extracting information from the experimental model. The images produced by the experiment show the melting of a vertical ice layer into a heated rectangular cavity in the presence of natural convection and maximum density.


Computer vision analysis Natural convection Melting interface Image segmentation Digital filter 

List of nomenclature


Acrylic wall


Copper wall


Specific heat

c*(z*,t*), c(z,t)

Dimensional and dimensionless positions of the interface


Heat exchanger


Fourier number


Modified Grashof number


Height of the enclosure




Thermal conductivity


Liquid cavity maximum width


Latent heat

P* and P

Dimensional and dimensionless pressures


Prandtl number

\({{\partial c} \mathord{\left/ {\vphantom {{\partial c} {\partial \tau }}} \right. \kern-0pt} {\partial \tau }}\)

Velocity of the interface in the \(\bar{n}\) direction




Stefan number

t* and t

Dimensional and dimensionless times


Average temperature


Fusion temperature of the material

TH and T0

Temperatures of the hot and the cold walls




Temperature of the maximum density


Dimensionless velocity vector


Removable window

y* and y

Horizontal dimensional and dimensionless coordinates

z* and z

Vertical dimensional and dimensionless coordinates

Z and Y

Computational dimensionless coordinates


Thermal diffusivity

\(\varDelta T = T_{H} - T_{\text{Fus}}\)

Temperature difference

\(\varDelta T_{\hbox{max} }\)

Maximum temperature interval considered


Phenomenological coefficient


Kinematic viscosity


Dimensionless temperature


Maximum density


Reference density


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Gisele Maria R. Vieira
    • 1
    Email author
  • Fabiana R. Leta
    • 2
  • Pedro B. Costa
    • 3
  • Sergio L. Braga
    • 4
  • Dominique Gobin
    • 5
  1. 1.Mechanical Engineering DepartmentFederal Center of Technological Education Celso Suckow da Fonseca—CEFET/RJRio de JaneiroBrazil
  2. 2.Mechanical Engineering DepartmentUniversidade Federal Fluminense—UFFNiteróiBrazil
  3. 3.National Institute of Metrology, Quality and TechnologyDuque de CaxiasBrazil
  4. 4.Mechanical Engineering DepartmentCatholic University of Rio de Janeiro—PUC-RJRio de JaneiroBrazil
  5. 5.FAST—CNRS—Université Paris VI, Campus UniversitaireOrsayFrance

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