Operator splitting techniques for the numerical analysis of natural convection heat transfer

Natural convection heat transfer in rectangular enclosures is an active research area, due to its significance for both fundamental interest and engineering applications such as thermal management of electronic components. In this present numerical study, combined conduction and natural convection have been analysed for one or two heat sources mounted on substrates in an enclosure. For one heat source, the substrate is mounted on a vertical wall, and for the case of two heat sources, the substrates are mounted vertically and horizontally. Buoyancy forces drive the fluid flow. The Picard method with a hybrid grid system is utilized to decouple between pressure and velocity components, resulting in componentwise splitting. Linear systems obtained via the Picard method have been solved by the ADI method, resulting in directional splitting. Effects of different parameters such as Prandtl number, Rayleigh number, and boundary conditions on the temperature and flow field have been analysed.