Inverse Design of Thermal Systems with Predominant Radiation

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Design of equipment for high-temperature thermal processes is very complex when multiple modes of heat transfer (radiation, convection and/or conduction) are present. When the modes are present and coupled, the equations describing energy transfer are very nonlinear, and may be integro-differential in form. Very sophisticated programs have been developed to model such systems. These programs are expensive to run and require large memory and storage capacity . They are based on forward design; that is, the geometry and boundary conditions are specified, and the resulting temperatures and rates of heat transfer are computed. If these are unsatisfactory, then the geometry or other conditions are altered, and the program is rerun. This process is repeated until the desired outcome is reached and the design is then fixed. An inverse design method specifies the desired outcome, and directly finds the conditions necessary to achieve this outcome without iteration. However, the mathematics of inverse techniques is less developed than is the case for forward problems, because the equations describing inverse design are ill-behaved (near-singular). Based on successful methods we have previously applied to inverse design of radiating systems, we propose to extend inverse design techniques to the much more complex case of multimode heat transfer with significant radiative transfer including combustion sources, where the mathematics becomes not only inverse, but non-linear. The results, if successful, will lead to much more efficient practical design of high-temperature equipment such as turbine engines and industrial/utility furnaces and boilers.