理想流体对流传热问题的理论解

Analytical solutions to convective heat transfer of ideal fluid

研究理想流体受迫对流传热和自然对流传热问题的理论解。采用流体无垂直于壁面法线方向运动 (即无穿透 )的条件取代黏性流体在壁面无滑移条件 ,解决了流体在边界上有滑移时计算对流传热系数的困难 ,给出了理想流体与平壁受迫对流传热、理想流体与竖直壁面自然对流传热和理想流体在管内受迫对流传热的理论解。结果表明 :理想流体的对流传热与黏性流体同样存在着热边界层。在外部流动的情况下 ,无论受迫对流传热还是自然对流传热 ,对流传热系数都与流体的导热系数、密度和比热三者乘积的二分之一次方成正比。在管内受迫对流的情况下 ,当无因次长度大于 0 .0 5时 ,局部 N u和界面无因次温度分布都不再变化 ,对于恒热流边界条件 ,N u等于 8,截面无因次平均温度等于 2 ;对于恒壁温边界条件 ,N u等于 5 .782 ,截面无因次平均温度等于 2 .3 1

Analytical solutions to the forced and natural convetive heat transfer of ideal fluids were studied in order to obtain theoretical bounds under typical geometries. The difficulties encountered, in the computation of heat transfer coefficient with sliding between fluid and solid wall using existing theories, were eliminated with a generalized no-penetration boundary condition. Analytical solutions to the forced convective heat transfer of ideal fluid with plane wall of constant temperature, natural convective heat transfer with vertical wall maintaind constant temperature and forced convection in pipe with either constant wall temperature or constant heat flux are presented. It is shown that there exists a thermal boundary layer for the convective heat transfer of ideal fluids also, similar to that for viscous fluid. In both case of forced and natural convection of external flow, the heat transfer coefficient is proportional to the square root of the product of thermal conductivity, density and spccific heat capacity of the fluid. For pipe flow, when the dimensionless length, x/D, exceeds 0.05, both the local Nu and the heat transfer coefficient keep constant. Numerical results show that, the Nu is egnal to 8 while the dimensionless mean temperature is 2 for the case of constant wall heat flux and the Nu is 5.782 and the dimensionless mean temperature is 2.316 for the case of constant wall temperature.