In recent years, material analysis of fluids has generated prodigious interest of researchers due to their effective role in interdisciplinary sciences. In view of its importance, the present communication is devoted to analyze the flow of power law fluid representing the features of shear thinning, shear thickening and Newtonian materials. Constitutive equations expressed in the form of tensorial representations depicting power law relation between viscosity and shear rate. The whole mathematical model is solved computationally via of finite element method by using stable $P_2-P_1$ finite element pair. A highly refined hybrid mesh is obliged for the accurate computation of results. Material properties of power law fluid are disclosed in physical configuration renowned as channel driven cavity combining various benchmark problems like cavity flow, forward and backward facing steps and channel flow. Impact of material parameters on pertinent profiles is disclosed through graphs. Verification of computed results is done by comparing the velocity, viscosity, pressure fields for power law fluid with the Newtonian case.

近年来，流体的材料分析由于其在跨学科科学中的有效作用而引起了研究人员的极大兴趣。考虑到其重要性，本通讯专门分析幂律流体的流动，这些流体代表剪切稀化，剪切增稠和牛顿材料的特征。本构方程以张量表示形式表示，描述了粘度和剪切速率之间的幂律关系。整个数学模型使用有限元方法通过有限元方法进行计算求解$P_{\mathrm{2个}}-P_{\mathrm{1个}}$有限元对。为了精确计算结果，必须使用高度精炼的混合网格。幂律流体的材料特性以称为通道驱动型腔的物理配置公开，结合了各种基准问题，例如型腔流动，向前和向后的台阶以及通道流动。通过图表公开了材料参数对相关轮廓的影响。通过将幂律流体的速度，粘度，压力场与牛顿情况进行比较，可以验证计算结果。