A silicone oil layer deep sits between two rigid

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Convection, rotation and geophysical flows · Convection, rotation and geophysical flows

Fluid Dynamics, Ch Thermal convection and the Rayleigh-Benard problem

Problem

100\,\mathrm{cSt}

silicone oil layer

4.0\,\mathrm{mm}

deep sits between two rigid, perfectly conducting plates. For this oil a

1\,\mathrm{cm}

layer has

Ra = 856\,\mathrm{K^{-1}}

. Use

Ra \propto d^3

at fixed fluid and temperature difference, and the rigid-plate values

Ra_c = 1707.8

k_c = 3.117

. ((a)) Find the Rayleigh number of the

4.0\,\mathrm{mm}

layer per kelvin. ((b)) Find the onset temperature difference. ((c)) Find the wavelength of the convection rolls at onset.

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