The thermal aspects of non-Newtonian flow field manifested with the buoyant convection effect in a closed cavities is not abundantly investigated as yet due to complexity of boundary constraints. Therefore the present work is the key attempt in this direction to offer the untapped computational findings on the trapezium enclosure equipped with the buoyantly convective non-Newtonian fluid and rooted with the partially heated T-shaped fin. The relative velocity of the non-Newtonian fluid and the walls of trapezium enclosure is taken zero. Both left and right walls of cavity are taken uniformly heated. The top wall is insulated and bottom wall is taken cold. The tips of T-shaped fin are taken case-wise: cold, heated and adiabatic. The problem is mathematically controlled by way of system of coupled partial differential equations. For solution purpose the numerical method named finite element method is utilized. The grid accuracy is debated by considering sex different hybrid meshing levels. The impacts of non-Newtonian flow controlling parameters namely the Rayleigh number and the Casson fluid parameter are examined. The outcomes subject to dimensionless horizontal velocity, dimensionless vertical velocity, stream-function, and temperature distribution are shared by means of contour plots. The line graph study is executed to report the Nusselt number variations for T-shaped fin having heated tips and along left/right walls of trapezium enclosure.

由于边界约束的复杂性，尚未对封闭腔中浮力对流效应所表现出的非牛顿流场的热学方面进行大量研究。因此，目前的工作是在这个方向上的主要尝试，以便为配备有对流非牛顿流体并以部分加热的T形翅片为根的梯形罩提供未开发的计算结果。非牛顿流体与梯形罩壁的相对速度为零。腔体的左壁和右壁均被均匀加热。顶壁是绝缘的，而底壁是冷的。T形翅片的尖端视情况而定：冷，加热和绝热。该问题是通过耦合的偏微分方程组进行数学控制的。为了解决问题，使用了一种称为有限元法的数值方法。通过考虑性别不同的混合网格划分级别，对网格精度进行了辩论。研究了非牛顿流控制参数（即瑞利数和卡森流体参数）的影响。通过等高线图可以共享无量纲水平速度，无量纲垂直速度，流函数和温度分布的结果。执行线图研究以报告具有加热尖端并沿着梯形外壳的左/右壁的T形鳍的Nusselt数变化。研究了非牛顿流控制参数（即瑞利数和卡森流体参数）的影响。通过等高线图可以共享无量纲水平速度，无量纲垂直速度，流函数和温度分布的结果。执行线图研究以报告具有加热尖端并沿着梯形外壳的左/右壁的T形鳍的Nusselt数变化。研究了非牛顿流控制参数（即瑞利数和卡森流体参数）的影响。通过等高线图可以共享无量纲水平速度，无量纲垂直速度，流函数和温度分布的结果。执行线图研究以报告具有加热尖端并沿着梯形外壳的左/右壁的T形鳍的Nusselt数变化。