Natural Convection Heat Transfer of Non-Newtonian Power-Law Fluids Within an Array of Elliptic Cylinders

In this study, natural convection of non-Newtonian power-law fluids around an array of elliptic cylinders has been investigated numerically. The governing equations have been solved using an in-house computational fluid dynamics code based on the well-known finite volume method. It is assumed that the flow and temperature fields are laminar, steady, and two-dimensional. Furthermore, due to the low-temperature difference between the tube walls and the surrounding fluid, the changes in the physical properties of the fluids are neglected. The numerical results are validated against the available experimental and numerical results. The results show that by increasing the non-Newtonian fluid power-law index, the ratio of average Nusselt number of the ith cylinder to the average Nusselt number of a single cylinder under identical thermal conditions decreases. Moreover, it is found that the increase in the ratio of the distance between elliptic centers and the elliptic vertical diameter increases the ratio of the average Nusselt number of ith cylinder to the average Nusselt number for a single cylinder. Finally, a mathematical expression is given for the array averaged Nusselt number.