针对非牛顿幂律流体在无限大旋转圆盘上层流边界层内三维流动与传热问题,在普朗特数为常数的条件下,利用广义Karman相似变换,将连续方程、动量方程及能量方程形成的偏微分方程组化成常微分方程组,再采用多重打靶法数值求解非线性两点边值问题.分别针对剪薄型流体、牛顿流体和剪厚型流体,得到不同幂律指标下的速度和温度分布及不同普朗特数下温度场的结果.结果表明径向速度分量的峰值随幂律指标的增大而增大,轴向速度受边界层厚度的影响较突出,盘表面的传热随幂律指标和普朗特数都呈现递增趋势.最后将本文流场结果与Andersson等在不考虑传热情况下的结果进行比较表明吻合性较好.
The three-dimensional steady laminar flow of an incompressible non-Newtonian power-law fluid over a rotating infinite disk with heat transfer was studied. The governing partial differential equations, including the continuity equation, the momentum equation and the energy equation, were transformed to ordinary differential equations by utilizing the generalized Karman similarity transformation. The corresponding nonlinear two-point boundary value problem was solved by the multi-shooting method. Numerical re- sults were obtained for the shear-thinning fluid, the Newtonian fluid and the shear-thickening fluid. It is shown that the power-law character index and the Prandtl number affect the velocities in all directions and the temperature of the fluid in the boundary layer. The results are compared with those of Andersson et al. without considering heat transfer.