a b s t r a c tIn this paper, thermal response of an orthotropic functionally graded coating-substrate structure with a partially insulated interface crack under heat flux supply is considered. It is assumed that there exists thermal resistance to heat conduction through the crack region. The mixed boundary value problems are reduced to a system of singular integral equations and solved numerically. Higher order asymptotic terms for the singular integral kernels are considered to improve the accuracy and the convergence efficiency of the numerical integrals. Numerical results are presented to show the effects of the orthotropy parameters, thermo-elastic nonhomogeneity parameters, and dimensionless thermal resistance on the temperature distribution and the thermal stress intensity factors (SIFs).

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The transient thermal fracture problem of a crack (perpendicular to the gradient direction) in a graded orthotropic strip is investigated. Most of the materials properties are assumed to vary as an exponential function of thickness direction. The transient two-dimensional temperature problem is analyzed by the methods of Laplace and Fourier transformations. A system of singular integral equations are obtained and solved numerically. Numerical results are figured out to show the variation of the temperature on the crack faces and extended line and stress intensity factors for different material parameters with dimensionless time.

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The ion concentration polarization (ICP) phenomenon occurs widely near nano-channel/membrane interfaces. Due to its extraordinary selective ion transport ability, ICP has been applied in many fields, such as desalination, molecular preconcentration and biomolecular separation. This paper is devoted to describing the transport mechanism of buffer ions at micro-nanochannel interfaces. Here, a multiphysics coupling model is proposed, where the boundary condition for the fixed surface voltage is introduced to describe the effect of nanochannel networks. The effectiveness of the proposed model and the calculation process is confirmed through comparative simulations. Comparing the simulations with experimental ICP results shows that the proposed model can effectively describe the nonlinear distribution of electric fields and a typical vortex pair from flow phenomena. An analytic scaling law for the propagating ion depletion zone (IDZ) is proposed, and a theoretical analysis and numerical results confirm its existence. For transient evolution, the IDZ spreads as √ t due to diffusion for t < 0.01 s and as t due to convection from 0.01 s < t < 0.1 s. Furthermore, detailed studies are performed to elucidate the ICP mechanism for desalination. The factors affecting desalination are investigated, including the buffer concentration, length and performance of the nanochannel network, height of the microchannel and the tangential electric field. Finally, the proposed research confirms that this device also has excellent potential as a micromixer pump. The rapid mixing of neutral particles can be realized using nonlinear electrokinetic flows with a mixing efficiency reaching 91%. The presented results provide some important guidance and physical insights into the design and optimization for this kind of chip and other related applications.

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