In applying nonlinear programming to optimization of temperatures in a system with radiation and conduction heat transfer, design requirements on the temperatures are translated into mathematical functions in which the design variables are the radiation surface properties, infrared emmittance and solar absorptance. Physical limitations in the surface properties and design objectives form the constraints of the nonlinear programming problem. A mathematical model of a radiative-conductive system employs a nodal analysis. Radiative heat transfer is treated under the semi-gray assumption and a total exchange factor allows surfaces to be specular-diffuse reflectors. Two types of design problems formulated consider (a) the case in which components of a system must operate within certain temperature limits and (b) a system in which uncertainty in the parameters produces uncertainty in the temperatures.

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