Reconstruction of the heat transfer coefficient at the interface of a bi-material

Abstract

The knowledge of heat transfer behaviour of composite thermal systems requires the characterization of the heat transfer coefficient at the contact interfaces between the constituent materials. The present work is devoted to investigating an inverse problem with generalized interface condition containing an unknown space-and time-varying interface coefficient from non-invasive temperature measurements on an accessible boundary. The uniqueness of the solution holds, but the problem does not depend continuously on the input measured temperature data. A new preconditioned conjugate gradient method (CGM) is utilized to address the ill-posedness of the inverse problem. In comparison with the standard CGM with no preconditioning, this method has the merit that the gradient of the objective functional does not vanish at the final time, which restores accuracy and stability when the input data is contaminated with noise and when the initial guess is not close to the true solution. Several numerical examples corresponding to linear thermal contact and nonlinear Stefan-Boltzmann radiation condition are tested for determining thermal contact conductance and Stefan-Boltzmann coefficient, respectively.The numerical results in both one-and two-dimensions illustrate that the reconstructions are robust and stable.

Models of recrystallization activated by a diffusion flow of impurities from a thin-film coating with a convection term at the crystal surface: exact solutions

“…where we introduce indicators  1,2 . In the case of  1 = 1 and  2 = 0 condition (9) transforms into boundary condition of the first type (7); in the case of  1 = 0 and  2 = 1 condition (9) transforms into boundary condition of the second type (8); in the case of  1 = 1 and  2 = 1 condition (9) transforms into boundary condition of the third type (6).…”

“…The solution (29) and equation (30) of general problem allows to write: i) the solution of the firs type problem, which satisfies the boundary condition of the first type (7) at the surface, as follows…”

“…Even though such problems have become widely used to simulate processes caused by heat transfer [6,7,8], the formulation of problems for describing diffusion-controlled processes in polycrystalline solids can be considered insufficiently studied [9,10].…”

Reconstruction of time-dependent right-hand side in parabolic equations on disjoint domains

“…A large number of processes in mechanics, physics, heat-mass transfer, biology and mathematical finance can be formulated as inverse differential equations problems, see e.g. [17,21,22]. The inverse problems also have a fundamental mathematical significance.…”

“…For problems with unknown coefficients and right-hand side of equations, a number of results are obtained, see e.g. [10,11,12,13,17,20,21,22]. These are challenging and interesting inverse problems, which has many applications in various fields of physics and mechanics.…”