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Natural convection in horizontally heated ellipsoidal cavities is considered in the low Grashof number limit. The problem is solved by matching the temperature at the interface between the fluid-filled interior and the unbounded solid exterior. The creeping flow is expressed in terms of primitive pressure-velocity variables as polynomials in Cartesian coordinates, allowing for a closed-form solution. The solution is also applicable to the two-dimensional case of a horizontal elliptical cylinder. Polynomial formulas are given for the creeping flow and the first-order correction to the temperature. The solution for the ellipse is believed to be new, and it is obtained by introducing a stream-function and solving the biharmonic equation. The pressure is computed by integrating the Stokes equation, and it is found to be proportional to xy in both the ellipse and the sphere.

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Natural convection in horizontally heated ellipsoidal cavities is considered in the low Grashof number limit.

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  • File Format: PDF
  • File Size: 154 KB
  • Pages: 4
  • Language: EN
  • Total Downloads: 94
  • Last Updated: 3 weeks ago

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