Thermal Analysis of Electronics in a Missile System

    Thermal analysis of electronics in a  missile system presents particular problems. The enclosure is cylindrical in  shape, but the heat sources (the electronic components) are rectangular. The  use of a cylindrical coordinate system would make it easier to model the  tube, but very difficult to model the electronics, and vice-versa. In  FLOTHERM the entire problem is represented on a simple Cartesian grid system.

    The cylindrical tube wall is represented  by a series of overlapping cuboid elements (see figures 1 and 3). The area of  overlap between the cuboid elements provides the correct conduction path in  the tube wall. This stairstep approach is obviously not appropriate for  calculating the heat transfer on the outside of the tube, where high-speed  aerodynamic effects are important. However, this simple approach correctly  accounts for all the important heat-transfer mechanisms inside the tube,  which are of primary concern in this case. The use of a Cartesian grid  simplifies detailed modeling near the heat sources. The same approach can be  used for any situation where electronic components are housed in cylindrical  or curvilinear shaped enclosures (e.g. periscope tubes, handheld devices,  etc.).

    Figure 1 shows the main elements of the  problem. The outer tube is 1mm thick stainless steel. The PCBs in the Control  Module are modeled as two connected blocks with thermal properties of 96%  Alumina and Epoxy. Each layer is 0.04 inches thick. The heat sources from the  components within the Control Module are represented as planar sources  directed into the surface of the board. An interface resistance is added  between the blocks to represent a thin layer of die-attach epoxy. The Signal  Processing Module is modeled in an equivalent manner, except that the Alumina  substrate is 0.025 inches thick.

    The Thermal Battery is modeled as an  octagonal volume with a fixed temperature of 60. The lens filter module  provides no thermal contribution and is simply modeled as an adiabatic block.

    The effects of radiation between adjacent board surfaces and from the  board surfaces to the tube wall are included. The external ambient  temperatue is set to 60C. The heat transfer from the tube wall to the  environment is represented by a fixed heat transfer coefficient.

    In this case, the analysis is for  steady-state conditions. However, the analysis is easily extended to  transient to include:

    changes in the external temperature and heat transfer  coefficient as a function of time, and internal power dissipation profiles which change as a  function of time.

    Figure 3 shows very small air velocities in the order of 3-4mm/s produced by  natural convection in the open spaces inside the tube. This convection  assists the heat transfer between the electronics and the tube wall, although  the dominant heat transfer modes are conduction and radiation.

    This example illustrates how thermal  models of complex geometries consisting of cylindrical or curvilinear  enclosures containing rectilinear heat sources can be produced in a simple  and efficient way using FLOTHERM.