This research work interprets the mathematical study of peristaltic flow of non-Newtonian fluid across an elliptical duct. The heat transfer mechanism for this elliptical duct problem is also considered in detail. The mathematical equations for Casson fluid model are developed and then by using appropriate transformations and long wavelength approximation, this mathematical problem is converted into its dimensionless form. After converting the problem in dimensionless form, we have obtained partial differential equations for both velocity and temperature profiles. These partial differential equations are solved subject to given boundary conditions over elliptical cross sections and exact mathematical solutions are obtained. The results are further discussed by plotting graphical results for velocity, pressure gradient, temperature, pressure rise and streamlines.

这项研究工作解释了非牛顿流体穿过椭圆形管道的蠕动流动的数学研究。该椭圆管道问题的传热机制也被详细考虑。建立了卡森流体模型的数学方程，然后通过使用适当的变换和长波长近似，将这个数学问题转化为无量纲形式。在将问题转换为无量纲形式后，我们获得了速度和温度分布的偏微分方程。这些偏微分方程在给定的椭圆截面上的边界条件下求解，并获得精确的数学解。通过绘制速度、压力梯度、温度、