Shao-Shu Chu

Thermally induced optical effects in optical fibers by inverse methodology

A conjugate gradient method based on an inverse algorithm is applied in this study to estimate the unknown time-dependent convection heat transfer coefficient and microbending loss in carbon-coated optical fibers by reading the transient temperature measurement data at the fiber surface, when the optical fibers are subjected to transient thermal loading. No prior information is available on the functional form of the unknown convection heat transfer coefficient in the present study; thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact temperature measurements. Results show that an excellent estimation on time-dependent convection heat transfer coefficient, temperature distributions, and thermally induced microbending loss can be obtained for all the test cases considered in this study. The individual effect of the thickness, Young’s modulus, Poisson’s ratio, and thermal expansion coefficient of t...

Transient thermoelastic analysis of an annular fin with coupling effect and variable heat transfer coefficient

A hybrid numerical method of the Laplace transformation and the finite difference method is applied to solve the transient thermoelastic problem of an annular fin, in which the thermomechanical coupling effect is taken into account in the governing equation of heat conduction and the heat transfer coefficient is a function of the radius of the fin. The general solutions of the governing equations are first solved in the transform domain. Then the inversion to the real domain is completed via the method of matrix similarity transformation and Fourier series technique. The transient distributions of temperature increment and thermal stresses of the fin in the real domain are calculated numerically. The presented method is more efficient in computing time and is applicable to other types of boundary conditions.

Analytical solution of flexural vibration responses on taped atomic force microscope cantilevers

Abstract An analytical solution of flexural vibration responses on taped atomic force microscope (AFM) cantilevers has been derived and a closed-form expression obtained. The results coincide with previously published analytical solutions for two special cases that are used with the rectangular AFM cantilever. The analytical solution derived in this Letter, can easily assist in obtaining the resonance frequency at arbitrary dimensions and tip radii. It is useful for the design of the AFM cantilever, including the solid or hollow circular and rectangular cross-section, and can serve to evaluate the accuracy of the approximate or numerical solutions for the AFM cantilever with a complicated cross-section. Furthermore, the solution was confirmed and can also be applied to obtain the resonant frequency of a conical cantilever with an elongated tip which is used for imaging the deep trenches and complex structures.

Thermal Stresses in Multilayer Gun Barrel with Interlayer Thermal Contact Resistance

A hybrid numerical method of the Laplace transformation and the finite difference is applied to solve the transient heat transfer problem of a gun barrel, in which the interlayer thermal contact resistance between the steel cylinder and the chrome coating is taken into account in the boundary conditions. The general solutions of the governing equations are first solved in the transform domain. Then the inversion to the real domain is completed by the method of Fourier series technique. The transient distributions of temperature and thermal stresses for the gun barrel in the real domain are calculated numerically.

Hybrid numerical method for transient analysis of two-dimensional pin fins with variable heat transfer coefficients

A hybrid numerical technique is used to investigate a two-dimensional cylindrical pin fin with arbitrary variable Biot numbers on the pin fin lateral and tip surfaces. By taking the Laplace transform with respect to time, the governing equation and boundary conditions are discretized by central finite difference then general solutions for dimensionless transient responses are obtained in the transform domain. A Laplace inverse technique is taken to achieve the inversion to the real domain. The transient distributions of temperature in the real domain are presented numerically. It is found that the variable Biot number can lead to an obvious temperature lagging effect base on the function of Biot numbers when pin fin immerses in variety physical environments. Moreover, the present method also can be applied to cases with different types of boundary conditions, such as time-dependent changes in boundary temperatures.

Effect of Interactive Damping on Vibration Sensitivities of V-Shaped Atomic Force Microscope Cantilevers

This article analyzes the interactive damping effect on the sensitivity of flexural and torsional vibration modes of a V-shaped atomic force microscope (AFM) cantilever. The interaction of the cantilever with the sample surface is modeled by a combination of a spring parallel to a dashpot in the normal direction and a similar combination in the lateral direction. An approximate form for the sensitivities of both modes was derived based on the method of Rayleigh–Ritz. Using the approximate formula, predictions of modal sensitivity may be made to design cantilevers with optimum sensitivity for specified uses. The results show that the effect of interactive damping is significant and should not be disregarded in the design of V-shaped AFM cantilevers. Interactive damping decreases the sensitivities of both flexural and torsional vibration modes when the contact stiffness is low.

INVERSE PROBLEMS IN AN AXISYMMETRIC MULTILAYER ANNULAR CLINDER WITH AN INTERLAYER THERMAL RESISTANCE

A numerical approach to estimate an unknown heat flux for axisymmetric multilayer annular cylinder with an interlayer thermal resistance is presented. The effects of interlayer thermal resistance upon temperature response to predict the subjected heat flux are investigated and discussed. The conjugate gradient method of minimization with an adjoint equation is successfully used to solve the inverse problem in estimating the unknown inner heat flux of multi-layer annular cylinder with an interlayer thermal resistance. While knowing the temperature history at any point of the annular cylinder, the inner boundary time-varying heat flux can be computed. In the analysis, the thermal resistance effect between interlayer is taken into account in the governing equation of heat conduction and the convection heat transfer. No prior information is available on the functional form of the unknown heat flux in the present study: thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using simulated and inexact measurements obtained within the medium

Modelling of coupled heat and moisture transfer in porous construction materials

In this paper, a mathematical model is proposed for predicting air temperature and humidity in a two-room region. The model contains a coupled relationship between temperature and humidity within the constructions and can be solved by using the numerical method. However, the two-room region can be reduced to a single region when the region with no ventilation is considered, and then the room temperature and relative humidity can be obtained analytically. The solution obtained in this paper is verified by comparing with the result of the analytical method. It shows that the two results are in agreement. In addition, the proposed model can also be applied to simultaneously obtain the transient temperature and humidity of a two-room region for different porous construction materials.

Inverse estimated transient thermal responses of multicoated optical fiber under time-dependent heat transfer environments

A conjugate gradient method based on an inverse algorithm is applied in this study to estimate the unknown time-dependent convection heat transfer coefficient under the varying ambient temperatures in multicoated optical fibers by reading the transient temperature measurement data at the fiber surface, when the optical fibers are subjected to transient thermal loading. No prior information is available on the functional form of the unknown convection heat transfer coefficient in the present study; thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact temperature measurements. Results show that the estimation of time-dependent convection heat transfer coefficient and transient temperature distributions can be obtained and are even effected by the varying ambient temperatures for all the test cases considered in this study.