Heat and Mass Transfer

, Volume 46, Issue 4, pp 421–429 | Cite as

Onset of unsteady axi-symmetric laminar natural convection in a vertical cylindrical enclosure heated at the wall

  • Amitesh Kumar
  • Mitesh Vegad
  • Subhransu RoyEmail author


In the present study laminar transition to oscillatory convection of fluids having different Prandtl numbers in a laterally heated vertical cylindrical enclosure for different aspect ratios (melt height to crucible radius) of 2–4 is investigated numerically for 0.01 ≤ Pr ≤ 10. Numerical solution to two-dimensional axisymmetric transient Navier Stokes equations and energy equation were solved by finite volume method using SIMPLE algorithm. Numerical results illustrate that there exists a critical Rayleigh number for each Prandtl number beyond which sustained laminar oscillatory flow sets in. The oscillatory regime was characterised by the oscillation of the average kinetic energy and average thermal energy of the melt. For a given aspect ratio, critical Rayleigh number increases with Pr upto 1 and then flattens. It was observed that for low Prandtl number fluids, Pr < 1.0, critical Rayleigh number is found to increase with increase in aspect ratio while for high Prandtl number fluids, Pr ≥ 1.0, it is found to decrease with increase in aspect ratio. The influence of aspect ratio on the transient behaviour of the melt volume below and above the critical Rayleigh number was studied.


Aspect Ratio Prandtl Number Rayleigh Number Critical Rayleigh Number Sustained Oscillation 
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List of symbols


Melt height


Thermal conductivity


Average kinetic energy


Dynamic pressure


Prandtl number


Heat flux at side wall


Radial, axial coordinates in cylindrical coordinate system


Aspect ratio (melt height/crucible radius)


Rayleigh number


Radius of crucible


Crystal radius






Average thermal energy


Reference melt temperature

vr, vz

Radial and axial velocity


Thermal diffusivity


Coefficient of thermal expansion


Kinematic viscosity


Stream function


Fluid density


Density at melt temperature


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of TechnologyKharagpurIndia

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