Transient Heat Transfer Phenomenon of a Two-Dimensional Anisotropic Medium Using Thermal Wave Theory
Chu., H. S.
q ( r, t+tau ) = - k defT( r, t)
本論文的主題是藉著應用熱波理論來討論二維暫態的熱傳導現象。本論文分別討論兩種邊界條件：等溫邊界及絕熱邊界。此外也探討物質的非等向性對熱傳之影響，討論的例子包括傳導係數比 (K= 1, 4 )及時間延遲常數比 (tau = 1, 2, 4 )。本文使用格林函數 (Green function)方法解答上述邊界值問題。由研究結果顯示二維熱波傳播時熱波波前溫度將會急驟變化及於尾端產生相反方向之波，同時波受到有限區之熱及邊界情況等交互作用及反射現象將更為複雜。|
In classical Fourier heat conduction theory, heat flux is postulated to be directly proportional to temperature gradient. That implies an infinite speed of propagation of the thermal wave, indicting that a local change in temperature cause an instantaneous perturbation in the temperature at each point in the medium, even if the intervening distances are infinitely large. Although an infinite speed of heat propagation is nonphysical, for most engineering applications, this approximation is quite acceptable. However, in situations dealings with very low temperature near absolute zero, an extremely short transient duration, and an extremely high rate change of temperature or heat flux. The Fourier equation breaks down because the heat propagation velocity in such situations becomes finite and dominant. To consider the finite speed of wave propagation, a damped-wave model has been proposed that uses a variety of reasoning and derivations. Researcher suggested a modified heat flux model of the form q ( r, t+tau ) = - k defT ( r, t) This means that the heat wave model allows a time lag between the heat flux and the temperature gradient. In fact, the relaxation time is associated with the communication ‘time’ between phonons (phonon-phonon collisions) necessary for commencement of heat flow and is a measurement of the thermal inertia of a medium. The objective of this work is to discuss the two-dimensional heat conduction phenomenon by applying the thermal wave theory. Two kinds of boundary conditions; either a constant wall temperature or adiabatic boundary condition, were considered. In addition, the influence of thermal conductivity ratio K and the relaxation time ratio(tau) on the heat transfer phenomenon were examined in detail. In this work, the Green’s function technique is adopted to solve the above boundary value problem. The results show that the disturbance induces a severe thermal wave front that traverses the medium with a sharp peak at the leading edge and generated a negative trailer that follows behind the wave front. Moreover, the reflection and interaction of thermal waves are complicated by two factors, the finite area of the thermal disturbance and the boundary conditions.
|Appears in Collections:||Thesis|