An inverse problem of determining two boundary heat fluxes during unsteady heat conduction in thick-walled circular cylinder

Abstract

The conjugate gradient method is used to determine two unknown temporal and spatial variations of the boundary heat fluxes, located on the inner and outer surfaces in a hollow cylinder, simultaneously, from the knowledge of transient temperature measurements taken inside the cylinder.

The advantage of the conjugate gradient method is that no a priori information is needed on the variation of the unknown quantities. The two-dimensional inverse analysis is performed by using the combination of the regular and modified conjugate gradient methods. The combined method was found to be more accurate than either of these two methods for the reasons discussed in this work.

Keywords:

• Heat conduction
• conjugate gradient
• heat fluxes