Transient Laminar Convection Induced by a Line Heat Source: A Numerical Study with Primitive Variables

The present work is addressed to the numerical study of transient laminar natural convection in an open space and induced by a line heat source. The governing equations, full Navier-Stokes and energy equations with primitive variables, are discretized in a staggered grid by a control volume approach. The equations for the fluid and solid (line heat source) phases are solved simultaneously using a segregated technique. Some of the physical and thermo-physical properties of the fluid (air), such as density, thermal conductivity and viscosity, were considered to vary with temperature. The results show that the energy equation reaches the steady state condition more rapidly than the momentum equations. Hence, at that time, the distribution of temperature does not show any change within the accuracy of the solution, while the distribution of the velocity still varies. The steady-state results obtained via the time-marching solution show good agreement with the published steady-state, self-similar results in the vicinity of the centerline of the plume. Also, the steady-state streamlines compare well with the published experimental results.