This work aimed to investigate the boundary design problem for uniform thermal conditions, when multiple three-dimensional (3-D) design objects (DOs) are placed inside the radiant furnace, and to explore the suitable configuration of DOs located inside the radiant furnace. Also the objective includes ascertaining the limit of maximum numbers of DOs that can be accommodated to get the uniform thermal conditions. To accomplish this task, 19 cases are evaluated, consisting of the different number of DOs with various configurations, located on the bottom surface of the furnace enclosure. Each case is treated as an inverse boundary design problem separately. The radiative information is calculated using the radiation element method by ray emission model (REM2). The microgenetic algorithm (MGA) is used as an optimization tool. The specularity effect of the surfaces of heaters, of surfaces of radiant enclosure, and of the DOs is taken into account. The suitability of the configuration of DOs is shown by comparing the estimated heat flux distribution on DOs. The effect of different heater power ranges on the uniformity of the heat flux distribution on DOs is discussed. With a sample case, the optimal heater power setting that produces the desired uniform thermal conditions on DOs is also given. In the present boundary design problems, to obtain the uniform thermal conditions, a pronounced effect of the configuration of DOs and the numbers of DOs is observed.
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