Study on the Micro-Scale Thermal Wave Propagation

• Main Authors: Chin-Shan Tsai, 蔡錦山
• Other Authors: Chen-I Hung
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/09273503105768228366

博士 === 國立成功大學 === 機械工程學系碩博士班 === 93 === 　The analytical-numerical technique, which is based on the Laplace transformation and the Riemann-sum approximation, is employed to predict the temperature and heat flux histories in the materials of Fourier, non-Fourier, and modified non-Fourier heat conduction problems. The whole solution processes for solving temperature or heat flux histories in the materials are set and nondimensionalized the appropriate governing equations, initial conditions, and boundary conditions for the analyzed problems first of all. Then the Laplace transform technique is employed to deal with the dimensionless time-derivative terms in the governing equations, initial conditions, and boundary conditions. When using numerical method to solve hyperbolic heat conduction equation, how to suppress the numerical oscillation in the vicinity of the wavefront is the major difficulty. In the present study, the convergence criterion is set as to avoid the numerical oscillation. 　The dynamic thermal behavior of a micro-spherical particle due to pulsed laser heating source is investigated and compared with the experimental data. According to the values of thermal diffusivity and absorptivity of the micro-spherical particle, the spatially uniform heating and non-uniform heating of the surface model are used to predict the surface temperature histories of the micro-spherical particles, respectively. The effects of different parameters such as the Biot number, the intensities of the incident laser beams, the radii of micro-spherical particles, and the polar angles are studied and presented. Good agreements are found between the analytical-numerical solutions and experimental data. 　In the classical theory of diffusion, Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient and assumed that the heat propagation speeds are infinite. When the heat transfer situations include extremely high temperature gradients, temperatures near absolute zero, extremely large heat fluxes, and extremely short transient duration, the heat propagation speeds are finite, and the Fourier law should be modified, the modified models include the thermal wave model (or hyperbolic heat conduction equation, HHCE), the phase-lag concept, the dual-phase-lag (DPL), and modified parabolic thermal wave equation (MPTWE). The results obtained using the hyperbolic heat conduction equation, and modified parabolic thermal wave equation are compared with the classical Fourier law, which is the parabolic heat conduction equation. Although the thermal waves can be split into two waves, transmitted and reflected waves, respectively, and travel in the opposing direction under hyperbolic heat conduction equation, but the modified parabolic thermal wave equation rejects interference and reflection of thermal wave. The speeds of heat propagation are finite, as revealed in the temperature and heat flux calculated by using the hyperbolic heat conduction equation and modified parabolic thermal wave equation. The smaller the dimensionless relaxation time is or the larger the thermal diffusivity is, the larger the thermal wave propagation speed is. The effect of thermal conductivity on thermal wave propagation speed is negligible. 　The results obtained using modified parabolic thermal wave equation and hyperbolic heat conduction equation, the heat propagation speeds are finite, while using Fourier law the heat propagation speeds are infinite. The solutions obtained by modified parabolic thermal wave equation and Fourier law are always consistent with the second law of thermodynamics, while by hyperbolic heat conduction equation violate the second law of thermodynamics sometimes. When the relaxation time is close to zero or the system reaches steady state, all the solutions obtained under modified parabolic thermal wave equation, hyperbolic heat conduction equation, and Fourier law are the same. 　The lasers are widely used as a welding, cutting, surface treatment, surface cleaning, or heating biological tissues tool. The lasers can be considered as continuous or pulsed, stationary or moving, and point, line or surface heat sources. The affections of heat conduction in the rod with finite thermal wave propagation speed on the dimensionless temperatures distribution predicted using hyperbolic heat conduction equation, and modified parabolic thermal wave equation are investigated and presented in the present paper. The effects of different parameters such as the dimensionless relaxation time , moving heat source speeds , dimensionless heat convective losses , and the dimensionless strength of the heating source term are also analyzed and presented. The temperature profiles in the rod predicted by modified parabolic thermal wave equation and Fourier law are smooth than by hyperbolic heat conduction equation. The temperature profiles obtained using hyperbolic heat conduction equation are significantly steep in the vicinity of the thermal wave front. The temperature profiles reveal the wave nature of heat propagation under hyperbolic heat conduction equation and modified parabolic thermal wave equation, and the thermal wave propagation speeds are finite.