Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials （FGMs）. First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest＇s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.

Impurity effects on electrical conductivity of doped bilayer graphene in the presence of a bias voltage

We address the electrical conductivity of bilayer graphene as a function of temperature, impurity concentration, and scattering strength in the presence of a finite bias voltage at finite doping, beginning with a description of the tight-binding model using the linear response theory and Green＇s function approach. Our results show a linear behavior at high doping for the case of high bias voltage. The effects of electron doping on the electrical conductivity have been studied via changing the electronic chemical potential. We also discuss and analyze how the bias voltage affects the temperature behavior of the electrical conductivity. Finally, we study the behavior of the electrical conductivity as a function of the impurity concentration and scattering strength for different bias voltages and chemical potentials respectively. The electrical conductivity is found to be monotonically decreasing with impurity scattering strength due to the increased scattering among electrons at higher impurity scattering strength.

Ultraviolet-shielding and conductive double functional films coated on glass substrates by sol-gel process

Ultraviolet-shielding and conductive double functional films were composed of CeO2-TiO2 film and SnO2:Sb film deposited on glass substrates using sol-gel process.Ce(NO3)3·6H2O and Ti(C4H9O4),SnCl4 and SbCl3 were used as precursors of the two different functional films respectively.The CeO2-TiO2 films were deposited on glass substrates by sol-gel dip coating method,and then the SnO2:Sb films with different thickness were deposited on the pre-coated CeO2-TiO2 thin film glass substrates,finally,the substrates coated with double functional films were annealed at different temperatures.The optical and electrical properties of the CeO2-TiO2 films and the double films were measured by UV-Vis spectrometer and four probe resistance measuring instrument.The crystal structures and surface morphology of the films were characterized using XRD and optical microscope,respectively.The obtained results show that the ultraviolet-shielding rate of the glass substrates with CeO2-TiO2 films is not less than 90%,and transmittance in visible lights can reach 65%.With the thickness of the SnO2:Sb film increasing,its conductivity became better,and the surface resistance is about 260 Ω/ when the SnO2:Sb films were deposited 11 cycles of the dip on the pre-coated CeO2-TiO2 glass.The ultraviolet-shielding rate of the glass substrates with double functional films is higher than 97%,and the peak transmittance in the visible lights is 72%.Additionally,with increasing the heat treatment time,the Na+ of the glass substrates diffuses into the films,resulting in the particle size of SnO2 crystal smaller.