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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.
Aiming at the three-dimensional flow and heat transfer problems of non-Newtonian power law fluid in the upper laminar boundary layer of an infinitely large rotating disc, under the conditions of Prandtl’s constant, the generalized Karman’s similarity transformation is used to convert the continuous equation, momentum equation and energy equation The differential equations are formed into ordinary differential equations, and then the multi-shot method is used to solve the nonlinear two-point boundary value problems. For the shear-thinning fluid, Newtonian fluid and shear-thick fluid respectively, the velocity and Temperature distribution and temperature field under different Prandtl numbers.The results show that the peak value of radial velocity component increases with the increase of power law index and the axial velocity is more affected by the thickness of boundary layer.The heat transfer With the power law index and Prandtl number are increasing trend.Finally, the flow field results in this paper and Andersson et al in the case of heat transfer does not consider the comparison results show good agreement.