三维球、柱坐标系下导热微分方程的离散求解  

Numerical Method for Three-dimensional Heat Conduction in Cylindrical and Spherical Coordinates

作　　者：贾欣鑫[1] 徐明海[1] 胡国华[1] 刘娟[1] 路辉[1] 梁卓[1] 

机构地区：[1]中国石油大学(华东)储运与建筑工程学院,山东青岛266555

出　　处：《重庆理工大学学报（自然科学）》2014年第1期33-37,48,共6页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(512761 99);国家科技重大专项(2011ZX05017-004)

摘　　要：根据柱坐标系与球坐标系的导热微分方程式推出了导热微分方程在球坐标系、柱坐标系上的三维高精度数值求解离散公式,并与解析解进行对比,验证了该离散公式有较高的精确度。在球坐标系下离散θ扩散项时,运用积分第一中值定理成功处理了复杂的θ扩散项的离散系数。该离散格式为三维柱坐标与球坐标下导热微分方程的数值求解提供了良好的借鉴作用。同时为导热微分方程在工程计算中的应用提供了精确的数值离散格式与理论依据。According to the differential equations of heat conduction on cylindrical and spherical coor- dinate system, numerical solution of the discrete formulation on cylindrical and spherical coordinate system with high accuracy has been derived. Compared with the analytical solution, this discrete for- mula has been verified with a high degree of accuracy. To make the complex dispersion coefficient of diffusion term θ more concrete in spherical coordinates, this paper derived the discretion coefficient of diffusion term θ by the first mean value theorem of integral. The accurate schemes provides a good ref- erence for researchers whom work in solving the equation of heat conduction of three-dimensional cy- lindrical coordinates and spherical coordinates, and it will provide accurate numerical schemes and the theoretical basis for solving practical engineering problems.

关 键 词：导热微分方程 球坐标系 数值传热 积分第一中值定理 

分 类 号：TK121[动力工程及工程热物理—工程热物理]