Thermocapillary and not thermocapillary convection around non-condensable gas bubbles

Technical Paper


The present paper reports a study of transient thermocapillary flows around non-condensable gas bubbles on heated stripes and wires through a tri-dimensional numerical model. In order to validate the numerical model, the obtained results have been satisfactory compared with experimental data obtained elsewhere. Present results coincide with previously obtained ones in confirming that thermocapillary convection is the dominant mechanism responsible for the observed jets streaming out from bubbles on heated surfaces. Temperature and flow fields have been obtained for water and isobutyl alcohol and several bubble-heated surface configurations. It has been determined that gravity tends to deviate upwards the jets streaming out from the bubbles in vertical wires and its effects are significant in the range of high Rayleigh numbers (higher than 1000), though in the neighborhood of the bubbles, thermocapillary convection is more significant. In addition, the heat transfer enhancement by thermocapillary flows is restricted to a region encompassing 2–4 bubble radii.


Convection Thermocapillary Marangoni Boiling Jet flow 

List of symbols


Acceleration due to gravity, m/s2


Heat transfer coefficient, W/(m2K)


Thermal conductivity, W/(mK)


Interface normal direction, dimensionless


Pressure, either dimensionless or Pa


Interface tangential direction, dimensionless


Time, s


Temperature, either dimensionless or °C


Velocity, either dimensionless or m/s

Greek symbols


Thermal diffusivity, m2/s


Thermal expansion coefficient, K−1


T − T ref, °C


Heat flux, W/m2


Dynamic viscosity, kg/(ms)


Kinematic viscosity, m2/s


Density, kg/m3


Temperature coefficient of surface tension, N/(mK)












Non dimensional

Dimensionless parameters


Marangoni number, Ma = |dσ| dT|ϕR 2/(kμα)


Nusselt number, \( Nu = hR/k \)


Prandtl number, Pr = ν/α


Rayleigh number, \( Ra = \beta gR^{4} \phi /(k\alpha \nu ) \)



The authors gratefully acknowledge the financial support given for the investigation by the Universidade da Coruña, Spain, through the Grant PUDC10N01, and the Centro de Supercomputación de Galicia, CESGA.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2013

Authors and Affiliations

  1. 1.Escuela Politécnica SuperiorUniversidade da CoruñaFerrolSpain

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