Numerical and experimental studies of the natural convection within a horizontal cylinder

Numerical solutions are obtained for the quasi-compressible Navier-Stokes equations governing the time-dependent natural convection within a horizontal cylinder. The early flow development and wall heat transfer are obtained after a uniformly cold wall is imposed as a boundary condition on the cylinder. Results are also obtained for a time-varying cold wall as a boundary condition with windward explicit differencing used for the numerical solutions. The viscous truncation error associated with this scheme is controlled so that first-order accuracy is maintained in time and space. Experiments within a small-scale instrumented horizontal cylinder revealed the time development of the temperature distribution across the boundary layer as well as the decay of wall heat transfer with time. Agreement between temperature distributions obtained experimentally and numerically was generally good. The time decay of the dimensionless ratio of the Nusselt number to the one-fourth power of the Grashof number is found both numerically and experimentally, and good agreement is obtained between these two results over most of the cylinder wall.