Solution to Shape Identification Problem of Unsteady Heat-Conduction Fields.

Abstract

This paper presents a numerical analysis method for shape determination problems of unsteady heat-conduction fields in which time-histories of temperature distributions on prescribed subboundaries or time-histories of gradient distributions of temperature in prescribed subdomains have prescribed distributions. The square error integrals between the actual distributions and the prescribed distributions on the prescribed subboundaries or in the prescribed subdomains during the specified period of time are used as objective functionals. Reshaping is accomplished by the traction method that was proposed as a solution to shape optimization problems of domains in which boundary velue problems are defined. The shape gradient functions of these shape determination problems are derived theoretically using the Lagrange multiplier method and the formulation of material derivative. The time-histories of temperature distributions are evaluated using the finite element method for space integral and the Crank-Nicolson method for time integral. Numerical analyses of nozzle and coolant flow passage in wing are demonstrated to confirm the validity of this presented method.