可变导热系数的颗粒复合介质传热性质的研究

Study on the thermal conduction of granular composite media with variable thermal conductivity

讨论了可变导热系数的复合介质的传热性质。当介质的导热系数是温度的函数时，热传导方程是非线性偏微分方程，作者采用基尔霍夫变换把它变成拉普拉斯方程，于是可以找到原问题的近似解析解。文中考虑一个最为简单的例子：由圆柱形的杂质构成的二维系统，杂质浓度很低，可以忽略颗粒之间的相互作用，杂质具有可变导热系数，基质的导热性质不随温度变化。在此基础上，用朗道方法导出计算可变导热系数的复合介质的有效导热系数的公式。

The thermal conduction of a composite medium with variable thermal conductivities is discussed.As the thermal conductivities of composite media depend on temperature,the heat conduction equation is a nonlinear partial differential equation.The nonlinear equation of heat conduction is transformed into a Laplace′s equation by applying the Kirchhoff transformation,and an analytic approximate solution of the equation is derived.A simplest example,i.e.,a twoˉdimensional composite systems with cylindric inclusions immersed in homogeneous host,is studied.It is supposed that the inclusions have an variable thermal conductivity;the thermal conductivity of the host does not depend on temperature and the inclusion concentration is low enough so that the effect of interactions between inclusions may be neglected.An approximate formula for effective thermal conductivity of the composite media with variable thermal conductivities is derived by using Landau′s method.