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This study is concerned with the numerical solution of compressible Newtonian fluid flows under thermal conditions through an axisymmetric contraction channel. The numerical method employed is a modified Taylor-Galerkin pressure correction approach (TG-PC-A) finite element algorithm, which builds upon the study of previous researchers. Here, attention is paid to studying the effect of Reynolds number (Re) on the solution's behavior. Particularly, we are focused on the influence of this parameter on the solution components and the level of convergence. In addition, the behavior of the vortices generated within the contraction under the effect of the Reynolds number has been studied as well. Since temperature is considered one of the basic components in this study, a detailed analysis of the relationship between temperature and Reynolds number was carried out. Furthermore, the influence of the Reynolds number on the convergence rates of pressure, velocity, and temperature has been examined to demonstrate the high efficiency achieved in numerical convergence. This study demonstrated that the Reynolds number directly influences the flow field and acts as a key parameter in regulating both the dynamic and thermal characteristics of the system under investigation. The findings are qualitatively consistent with established scientific principles and previously published studies.
Al-Ganem et al. (Wed,) studied this question.