Humboldt State University
Arcata, California, U. S. A.
Natural convection of fluid between two horizontal concentric cylinders which are maintained at a constant different temperature is investigated using the finite Fourier series expansion. The flow is governed by the Boussinesq approximation to the full Navier Stokes, thermal energy and continuity equations. Under the assumptions that the flow is two-dimensional and laminar across the vertical centerline, the stream and temperature functions are represented by infinite cosine and sine series. The direct spectral method then replaces the original system of coupled, nonlinear partial differential equations in time and two spatial dimensions which an equivalent system in time and one spatial dimension. This equivalent system is solved for the coefficients in the above expansions using forward, Hermitian, and modified Crank-Nicholson finite-differencing schemes.
For fluid of low Prandtl number (Pr=0.002) in a system with a wide range of gap width is investigated. For lower Ra (Rayleigh number), different initial conditions lead to unicellular as well as multicellular flows. With increase of Ra, the multicellular oscillatory convection sets in.