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Transient inverse design of radiative enclosures for thermal processing of materials

This work presents a methodology to solve transient inverse design of radiative enclosures for heating processes that require refined temperature control. The proposed methodology is applied to find the heat input to a heater located at the top of a three-dimensional enclosure that can satisfy a prescribed time-dependent temperature curve on a surface located at the base of the enclosure. The process is governed by radiative exchanges between diffuse, gray surfaces. This problem is described by an ill-conditioned system of linear equations, which is regularized by the truncated singular value decomposition (TSVD) method. The inverse analysis led to a heat input in the heater that assured, within an error less than 1.0%, both uniformity and the correct magnitude of the design surface temperature in every instant of the process.