含不同形状内热源的圆管内纳米流体自然对流及换热数值研究

采用格子玻尔兹曼方法对有三种恒温热源（圆形、三角形、方形）参与的圆管内纳米流体（铜-水）自然对流进行数值研究。主要研究瑞利（Ra）数，纳米颗粒体积分数以及热源几何形状等控制参数对纳米流体的流动与传热的影响。结果发现纳米颗粒体积分数的增加有利于强化传热，且在Ra数较小时，平均努塞尔（Nu）数增加的幅度要优于Ra数较大的情况。在所研究的控制参数范围内，方形热源的平均Nu数最大。根据数值结果给出不同热源表面的平均Nu数、纳米颗粒体积分数、Ra数三者之间的函数关系式，该函数关系可为此类工程的设计提供理论指导。

Numerical Study on Natural Convective Flow and Heat Transfer of Nanofluids in a Circular Tube Containing Heat Source with Different Shape

Natural convection of copper(Cu)-water nanofluids in a circular tube containing heat source with different shape (circular, triangular, and square) is numerically simulated with lattice Boltzmann method. Effects of Rayleigh number, nanoparticle volume fraction, and geometric shape of heat source on flow and heat transfer characteristics of the nanofluid are studied. It shows that heat transfer can be enhanced with increasing volume fraction of nanoparticles. And the increase of average Nusselt number in the case with small Rayleigh numbers is faster than those with large Rayleigh numbers. The largest average Nusselt number could be obtained in the square heat source case for all Rayleigh numbers considered. Finally, empirical prediction functions among average Nusselt number of the heat source surface, volume fraction of nanoparticles, and the Rayleigh number are presented. These relations provide predictions for engineering problems.