Unresolved problems in inverse radiation

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Although a considerable amount of progress has been made in developing methods for solution of inverse problems involving radiating systems, there remains significant work to be done. In specifying the conditions on the design surface, for example, the design engineer may choose conditions for which there is no acceptable physical solution, i.e. the solution might not be achievable without unacceptable heater conditions (coolers in place of heaters, excessive heater power or temperature requirements, or even imaginary absolute temperatures on the heaters). Such solutions may satisfy the conditions on the design surface mathematically, but they are not useful engineering solutions. An a priori determination of the existence of acceptable physical solutions would save a lot of fruitless calculation, but a means to do this has not yet been developed.

The predictions of the inverse solution will not be exact, since assumptions are invariably built into the forward solution which is being inverted. Such assumptions may include approximated surface properties (diffuse, gray, specular, etc.), and approximated thermophysical properties (conductivity, specific heat, etc.). Thus, to achieve specified conditions on the design surface in a real system such as a radiant furnace, feedback control is probably necessary. For feedback control, at least two additional factors must be addressed: 1) how feedback of measured temperature and/or radiative flux from the design surface can be used to adjust the inverse predictions and 2) how many feedback signals and their locations on the design surface are necessary to adequately provide feedback information. The first of these has been addressed in a preliminary way (Erturk et al., 2002) through the use of neural nets.


Ertürk, H., Ezekoye, O.A., and Howell, J.R., 2002, “The Use of Inverse Formulation in Design and Control of Transient Thermal Systems,” Heat Transfer 2002: Proc. International Heat Transfer Conf., Grenoble, pp. 729-734.

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

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