Buoyancy-Induced Flow Due to Isolated Thermal Sources on a Vertical Surface

The natural convection flow due to multiple isolated heated elements located on a vertical adiabatic surface has been studied analytically. The problem, which is of particular relevance to electronic circuitry cooling and to the question of locating sources in manufacturing systems, is considered for a Prandtl number of 0.7, which applies for air. Of particular interest were the temperature and velocity fields that arise and the dependence of these on the heat input and on the distance between the heated elements. The flow is treated as a boundary layer problem and the governing equations are solved numerically. The results obtained indicate the general nature of the flow and the dependence of the heat-transfer coefficient for an element, located in the wake of another, on the energy input and location. The downstream variation of the surface temperature, the velocity level, and the resulting velocity and temperature profiles are studied in detail. The results obtained are also compared with those for a single source, bringing out several interesting features.