Numerical simulation of buoyant plumes using a fixed point iterative method

Abstract

A numerical simulation of unsteady plumes for driven thermal high convection dominated flows is presented in this work. The problem is of practical interest for example in the cooling of electronic devices and heat transfer from pipes in heat exchange systems. This kind of thermal flows may be modeled using the unsteady Boussinesq approximation in the Stream function-vorticity formulation. Results are obtained with a simple numerical method previously reported for isothermal/natural and mixed convection flows. The numerical method is based on a fixed point iterative process to solve the non-linear elliptic system that results after an appropriate discretization in time. The iterative process leads us to the solution of uncoupled, well-conditioned and symmetric linear elliptic problems for which very efficient solvers are known to exist regardless of the space discretization.