## 1 Introduction
The correlation is expressed as follows:  
\[Re_{\theta t}=163+\exp(6.91-Tu) \tag{1}\]  
The correlation suggested by [PERSON] (1991) [12] is as follows:  
\[Re_{\theta t}=400\;Tu^{-0.625} \tag{2}\]  
[PERSON] and [PERSON] [10] included the following expression for the transition to turbulence in their numerical model:  
\[Re_{\theta t}=120+150\;Tu^{-2/3} \tag{3}\]  
The correlations expressing the turbulent transition Reynolds number according to the inlet-turbulence intensity proposed by [PERSON] and [PERSON] [24], [PERSON] [12], and [PERSON] and [PERSON] [10], as mentioned above, are compared in Figure 1.  
[PERSON] et al. [25] experimentally investigated the laminar-to-turbulent flow on a flat plate at different inlet-turbulence intensities. The measurements were taken with a hot wire velocimetry in the range of 1.5-4.4% inlet-turbulence intensity. They stated that with the increase in inlet-turbulence intensity, the transition region becomes smaller and regresses towards lower Reynolds numbers, and they derived an empirical expression for the turbulent transition Reynolds number depending on the inlet-turbulence intensity as follows:  
\[Re_{pt}=\sum a_{i}\cdot e^{-(Tu-b_{i}/c_{i})}\;i=1,\;2,\;3 \tag{4}\]  
where: \(a_{i}\): 3346, 879.9, 419.5; \(b_{i}\): \(-0.3656\), \(-0.8927\), \(-12.93\); \(c_{i}\): 0.2825, 1.782, 18.29. Various studies on boundary-layer transition are ongoing. A solver for boundary-layer transition was developed by [PERSON] and [PERSON] [26]. [PERSON] [27] investigated the critical phenomena in the laminar-turbulent transition with a mean field model. A new turbulence model for modeling turbulent transition according to mechanical priorities was proposed by [PERSON] et al. [28]. The effects of wall heating on the boundary-layer transition on a flat plate were investigated numerically by [PERSON] and [PERSON] [29]. An evaluation of Reynolds Averaged Navier-Stokes (RANS Reynolds Averaged Navier-Stokes) turbulence models in convective heat transfer was made numerically by [PERSON] et al. [30]. A new laminar kinetic energy model for the prediction of pre-transition velocity fluctuations and the boundary-layer transition was presented by [PERSON] et al. [31]. [PERSON] [32] proposed a correlation for heat transfer in plane plate boundary layers under laminar, transitional, and turbulent flow conditions. [PERSON] et al. [33] performed large-eddy simulations (LES) for a zero-pressure gradient boundary layer developing over a flat plate to investigate the transition mechanism for variable free-stream turbulent properties. A comparative study of experiments with direct numerical simulations (DNS) of free-stream turbulence transition has been performed by [PERSON] et al. [34]. Transition under free-stream turbulence, together with large integral-length scales, has been investigated by [PERSON] et al. [35] in another DNS study. As can be understood from the above studies, the findings in some studies contradict each other, and since the effect of external turbulence on the flat plate is encountered in important application areas, studies on this subject are needed. Since the flow on the flat plate is frequently encountered in engineering problems, it is important to develop basic flow equations, such as the boundary layer for flow on the flat plate, to control the boundary layer and examine the transition to turbulence. In this study, the effects of the inlet-turbulence level on the zero-pressure gradient flow on the flat plate based on the ERCOFTAC T3A test setup were investigated by comparing various turbulence models, and it was determined that the Gamma-Theta (GT) model was the most suitable model. Then, using this model, the effect of turbulence intensity on the friction coefficient (Cf) was  
Figure 1: Relationship between the Re number and the inlet-turbulence intensity (Tu) at the transition to turbulence defined by the boundary-layer thickness [10; 12; 24].