中文摘要：

基于分形几何定量描述了多尺度自仿射的粗糙表面形貌，建立了微通道内层流流动换热的理论模型并对表面形貌的影响进行了数值模拟。研究表明，自仿射分形维数直接反映了表面轮廓的不规则度，对于两个具有相同统计粗糙度的轮廓，可能存在不同的分形维数；与常规尺度通道不同，雷诺数、粗糙高度和粗糙表面分形维数都对微通道内层流流动换热有着重要影响。

英文摘要：

The multi-scale self-affine topography of rough surfaces is characterized by using fractal geometry. Based on such characterization, a model of laminar heat transfer in rough microchannels is proposed to investigate the effects of rough surface topography on laminar convective heat transfer. The results indicate that, the self-afflne fractal dimension can directly exhibit the frequency variation of the surface profile, and the fractal dimension may be different for two profiles with the same average roughness height. Differing from the conventional channel, the Reynolds number, roughness height and fractal dimension of the surface roughness all play considerable roles in the mieroscale laminar convective heat transfer.