Inverse Radiation Design Problem in a Two-Dimensional Radiatively Active Cylindrical Medium Using Automatic Differentiation and Broyden Combined Update

Abstract

Inverse radiation design analysis in a two-dimensional, concentric, cylindrical, absorbing, emitting and scattering medium has been conducted, given desired boundary conditions on the design surface. The finite-volume method was adopted to solve the radiative transfer equation and the energy conservation equation in the direct problem, while the Levenberg-Marquardt method was used to solve a set of equations, which are expressed by errors between estimated and desired radiative heat fluxes on the design surface. In order to diminish the computational time required for calculating sensitivity matrix, automatic differentiation as well as the Broyden combined update were utilized.

Acknowledgments

The financial assistance by the Combustion Engineering Research Center at the Korea Advanced Institute of Science and Technology is gratefully acknowledged.