Abstract
In this paper, we present a Continuous Sensitivity Equation (CSE) that describes the sensitivity of temperature with respect to shape parameters, physical properties and other parameters. We begin by introducing the notion of sensitivities using a one-dimensional, steady-state conduction problem for a composite rod. The model is extended to incorporate contact resistance at the interface between different materials. These examples illustrate some of the difficulties involved in computing sensitivities: accurate evaluation of boundary conditions for shape sensitivities and discontinuities across material interfaces. We conclude with a finite element formulation for CSE applied to phase change problems.
Published Version
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