Abstract
The inverse design of a three-dimensional furnace that is built to heat an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history while the spatial temperature distribution is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is a transient design problem where a series of inverse solutions is utilized. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located at top and the design object moves at the bottom.
The inverse formulation of such a system is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem involves ill-posed Fredholm equation of the first kind and the use of a regularized solver rather than an ordinary one such as Gauss-Seidel or Gauss elimination is essential. The radiative transfer is formulated utilizing the Monte Carlo method that enables including further realistic characteristics like specularly reflecting walls.
