A New Algorithm For Solving Thermal Newtonian Flow In Axisymmetric Straight Channel

Abstract

In this study, three main problems in fluid flow have been discussed. First, the derivation of the energy equation is conducted within cylindrical coordinates, which has not been addressed by the researchers before. Secondly, we develop a new algorithm for solving the governing equations that describe incompressible Newtonian flows under thermal condition. This algorithm is constructed based on the so-called Taylor-Galerkin/Pressure-Correction finite element method with the help of the two-step Lax-Wendroff scheme. Finally, we study the effect of non-dimensional numbers, such as the Reynolds number (Re) and the Prandtl number (Pr), on the velocity, pressure, and temperature. The results show that the developed method is consistent with established physical phenomena and other studies