Deconinck Bernard, Pelloni Beatrice, Sheils Natalie E
Department of Applied Mathematics , University of Washington , Seattle, WA 98195-2420, USA.
Department of Mathematics , University of Reading , Reading RG6 6AX, UK.
Proc Math Phys Eng Sci. 2014 May 8;470(2165):20130605. doi: 10.1098/rspa.2013.0605.
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.
通过给出一维热方程在每个区域的显式解，研究了一维分段均匀复合材料中的热传导问题。界面位置已知，但在界面处既未规定温度也未规定热通量。相反，在界面处它们连续性的物理假设是唯一施加的条件。详细研究了两个半无限区域的问题和两个有限尺寸区域的问题。我们还指出了如何将求解方法扩展到一侧由半无限区域包围的一个有限尺寸区域以及三个有限尺寸区域的情况。
