Interaction of Natural Convection Wakes Arising From Thermal Sources on a Vertical Surface

A numerical study of the interacting natural convection flows generated by isolated thermal energy sources, such as electronic components, located on a vertical adiabatic surface is carried out. Of particular interest were the effects of the wake on the heat transfer from and the flow over a downstream heat source and the nature of the wall plume far from the sources. This consideration is related to the positioning of finite-sized electronic components and the relevant heat removal process. A two-dimensional flow is considered, without making the boundary-layer assumptions. The full elliptic equations governing the flow are solved numerically, employing finite-difference methods. The results are compared with the boundary layer solutions, obtained in earlier studies, in order to determine the nonboundary-layer effects. This is an important consideration in several practical circumstances that involve small heat inputs, sources of relatively small heights, and small separation distances between the sources. It is found that the flow downstream rapidly approaches the characteristics of an idealized wall plume due to a line source. A boundary-layer flow arises far from the heat sources and this flow provides the boundary conditions for the elliptic problem. The nature of the velocity and temperature fields is studied in detail for a wide range of governing parameters and the heat transfer coefficients for the heated elements determined. The relevance of the results obtained to practical systems is outlined, particularly for small Grashof numbers which necessitate a solution of the full equations.