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Updated: Jul 27, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Thermal diffusion in a sinusoidal temperature field
Walter L Craig1, Sorasak Danworaphong, Gerald J Diebold
1Department of Mathematics, McMaster University, Hamilton, Ontario, Canada.
Abstract:
Separation of liquid mixtures in a thermal gradient, known as the Ludwig-Soret effect or thermal diffusion, is governed by a nonlinear, partial differential equation. It is shown here that the nonlinear differential equation for a binary mixture can be reduced to a Hamiltonian system of equations and that a solution can be obtained for the linear problem. The calculation gives a closed form expression for the space and time dependence of the concentration profile of the mixture, valid at short times.
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