Thermal modeling of isothermal cuboids and rectangular heat sinks cooled by natural convection

Thermally-induced buoyancy effects are not always sufficient to adequately cool high density microelectronic packages found in modern circuit boards. In many instances thermal enhancement techniques, such as heat sinks, must be used to increase the effective surface area for heat transfer and lower the thermal resistance between source and sink. The irregular surfaces of heat sinks present a formidable challenge for designers in determining the boundary conditions along the fluid-solid interface. A simple yet accurate method for calculating the thermal performance of rectangular heat sinks using a flat plate boundary layer model is presented. Several heat sink geometries are examined over a range of Rayleigh number between 10³ and 10¹⁰. The heat-transfer performance of the heat sinks, as given by the Nusselt number, is determined for each test based on the isothermal body temperature and the square root of the wetted surface area. Results obtained using a conjugate model, META, are compared against an analytically-based correlation and experimental data. In addition to the rectangular heat sinks, isothermal cuboids of various sizes are modeled using META, where the cuboid is approximated as a thin uniformly-heated base plate with an attached extended surface. The cuboid results are compared with experimental data and an analytically based correlation