Gradient method for inverse heat conduction problem in nanoscale

An 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