Gradient method for inverse heat conduction problem in nanoscale

Abstract

SUMMARYAn inverse heat conduction problem for nanoscale structures was studied. The conduction phenomenon is modelled using the Boltzmann transport equation. Phonon-mediated heat conduction in one dimension is considered. One boundary, where temperature observation takes place, is subject to a known boundary condition and the other boundary is exposed to an unknown temperature. The gradient method is employed to solve the described inverse problem. The sensitivity, adjoint and gradient equations are derived. Sample results are presented and discussed.

An iterative regularization method for inverse phonon radiative transport problem in nanoscale thin films

“…The inverse problems for EPRT system by using temperature measurements have been discussed by Kim and Daniel in References [6,13]. The estimated temperatures are not in a good agreement with the exact values.…”

An inverse problem in estimating the relaxation time for nanoscale phonon radiative transfer problem

“…It should be noted that an additional integration with respect to is considered in accordance with [19]. The result is then added to the right-hand side of Equation (6) to yield the following expression for the functional J [ ( )]:…”

“…By following the technique applied in [19], an extra integration with respect to angular variable is needed in the objective function for the original integro-differential governing equations.…”

“…To obtain the adjoint equation, Kim and Daniel [19] suggested that an extra integration with respect to angular variable is needed in the objective function for the original integro-differential governing equations. Finally, a compact form of the adjoint equations can be obtained.…”

“…The inverse problem for EPRT system by using temperature measurements to estimate the boundary temperatures has been discussed by Kim and Daniel in references [19,21]. The estimated temperatures are not in a good agreement with the exact values.…”