Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

The boundary condition design of a three-dimensional furnace that heats an object mov-ing along a conveyor belt of an assembly line is considered. A furnace of this type can beused by the manufacturing industry for applications such as industrial baking, curing ofpaint, annealing or manufacturing through chemical deposition. The object that is to beheated moves along the furnace as it is heated following a specified temperature history.The spatial temperature distribution on the object is kept isothermal through the wholeprocess. The temperature distribution of the heaters of the furnace should be changed asthe object moves so that the specified temperature history can be satisfied. The designproblem is transient where a series of inverse problems are solved. The process furnaceconsidered is in the shape of a rectangular tunnel where the heaters are located on the topand the design object moves along the bottom. The inverse design approach is used for thesolution, which is advantageous over a traditional trial-and-error solution where an it-erative solution is required for every position as the object moves. The inverse formula-tion of the design problem is ill-posed and involves a set of Fredholm equations of the firstkind. The use of advanced solvers that are able to regularize the resulting system isessential. These include the conjugate gradient method, the truncated singular valuedecomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination. @DOI: 10.1115/1.1763179#

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