## 1 Introduction  
Flow over a flat plate has many applications and is one of the basic fluid dynamics and heat-transfer topics for a better understanding of flows. It also has an important place in boundary-layer flows because it is a zero-pressure gradient flow, allowing for simplifications. Long and flat surfaces are encountered in many real flows. Examples of situations where the boundary layer forms over long and flat surfaces are flow over a ship's hull, a submarine hull, aircraft wings, textile surfaces, and atmospheric flow over flat terrain. The flow characteristics over long and flat surfaces in engineering problems are similar to the flow over a flat plate. Therefore, understanding the flow over a flat plate is important in terms of understanding the flow characteristics over flat and long surfaces in engineering problems. In addition to earlier studies [1], relatively earlier studies on flat plates have shown that inlet-turbulence intensity has a significant effect on the transition from laminar to turbulent, but that it increases heat transfer only slightly in the laminar region and that the turbulent boundary layer is only slightly affected [2, 3]. More recent studies have shown that high-inlet-turbulence values produce significant increases in heat transfer [4, 5, 6]. However, it has also been reported that inlet-turbulence intensity has no effect in the laminar region [7, 8]. The characteristics of laminar and turbulent boundary layers are different. Transition from laminar to turbulent, or relaminarization, can cause significant changes in the aerodynamic performance of the object. The aerodynamic forces and moments or heat transfer acting on the object in the fluid are directly affected by the position of the laminar to turbulent transition. In the laminar to turbulent transition region, a sudden increase in drag force and heat transfer occurs. In order to reduce the drag force in the gas turbine airfoil, it is necessary to move the transition from laminar to turbulent to a certain distance from the leading edge. Sometimes, at low Reynolds numbers, the laminar region is extended in low-inlet-turbulent flow, and flow separation occurs in the laminar region before it becomes turbulent, which is not preferred in terms of fuel economy. As a result, even a 1% saving in fuel is very important economically [9]. The transition from laminar to turbulent can occur in 80% of the blade in low-pressure turbine blades if the inlet-turbulence intensity is low [10]. Therefore, it is important to be able to correctly solve the transition from laminar to turbulent. There are many factors that affect the transition to turbulence. These are pressure gradient, Reynolds number, surface roughness, heat transfer, and inlet-turbulence intensity. These effects cannot fully represent all types of situations with the theoretical or empirical expressions presented previously [11]. Therefore, it is a subject open to study. For successful numerical computations, an accurate prediction of the laminar to turbulent transition in a flat plate is necessary. We can divide the laminar to turbulent transition mechanism into three: natural transition, bypass transition, and separated-flow transition. We encounter the first two of these transitions in the flow over a flat plate (zero-pressure gradient flow). The characteristics of all three transition mechanisms are explained by [PERSON] [12]. Natural transition occurs with the formation of Tollmien-Schlichting waves in the laminar boundary layer. It can be estimated by linear stability analysis [13]. Bypass transition occurs with the formation of direct turbulence spots in the laminar boundary layer and at high-inlet-turbulence intensities (Tu > 1%). It is also explained analytically by the turbulence spot theory [1]. Generally, in transition, predictions are encountered mainly with two concepts. The first is the use of the turbulence models, and the second is the use of experimental correlations [14].