# Aerodynamic Drag Study of the Heat Exchange Equipment with Different Fin Geometries
## 2 Theory of the Emergence of Aerodynamic Drag
Therefore, in order to reduce the frictional resistance, it is necessary to delay the transition to the turbulent regime and maintain the laminar regime at the maximum possible distance around the object [17]. It is obvious that the value of pressure resistance and frictional resistance depends on the geometry of the body relative to the flow direction. The most obvious example of this is a flat plate. If we place it perpendicular to the direction of the oncoming flow, it will be a body with poor flow (Figure 1a). The flow will easily separate and create a separation zone behind the plate and, accordingly, a pressure drop, so the pressure resistance will be large. However, the frictional resistance will be very small because the shear stresses do not align with the direction of resistance. If we turn the body 90\({}^{\circ}\), we will achieve a very streamlined body; the pressure resistance will be small because there is no separation region, but the frictional resistance will be significant (Figure 1b). This logic can also be applied to airfoils, where the angle of attack has a large effect on the drag force. At large angles of attack, flow separation occurs, which significantly increases the drag force. When optimizing body shape to reduce aerodynamic drag, it must be understood that frictional resistance will increase as pressure resistance decreases, so these two aspects must be carefully balanced. The shape of the geometry, which has the smallest total resistance force, will not necessarily be the most streamlined [17; 18]. It was mentioned above that in order to obtain the value of the total resistance force, it is necessary to integrate Equation (1), which contains pressure stresses and shear stresses. The problem is that it is practically impossible to establish a detailed distribution of these stresses. Therefore, the total drag force is usually represented using the equation:  
\[F_{D}=C_{X}\frac{\rho\cdot v^{2}}{2}S_{e}, \tag{3}\]  
where \(C_{X}\)--coefficient of frontal drag, which takes into account all parameters that are difficult to measure, for example, the effect of the geometry of the object and the flow mode. This coefficient can be determined experimentally using a wind tunnel or by numerical simulation; \(\rho\)--fluid density, [kg/m\({}^{3}\)]; \(\
u\)--linear speed fluid flow, [m/s]; \(S_{e}\)--effective surface area, [m\({}^{2}\)]. For well-streamlined bodies, the plan area is usually taken, and for poorly streamlined bodies, it is the projected frontal area. The drag coefficient can vary significantly from the value of the Reynolds number. \[\mathrm{Re}=\frac{\rho\cdot v\cdot d}{\mu}, \tag{4}\]  
where \(v\)--linear speed of the coolant in the channel, [m/s];  
Figure 1: Model of a flat plate in a flow created by us in SolidWorks Flow Simulation. (**a**) transverse arrangement; (**b**) longitudinal location. \(d\)--characteristic length in flow, [m];  
\(\rho\)--fluid density, [kg/m\({}^{3}\)];  
\(\mu\)--dynamic viscosity of the fluid, [Pa-s]. Figure 2 shows estimated graphs of the change in the drag coefficient as a function of the Reynolds number for bodies with different shapes. This diagram was created based on the analysis of the data given in the literature source [18]. For a flat plate located perpendicular to the oncoming flow, the resistance coefficient remains unchanged (\(C_{X}=2\)) in different modes of motion because the plate is a poorly streamlined body and flow separation occurs at the edges of the plate, regardless of whether the flow is laminar or turbulent. For disk-like forms, a significant decrease in the drag coefficient is observed when transitioning between laminar and turbulent regimes (\(C_{X}=1.56\) and \(0.25\)), as flow separation is delayed when the boundary becomes turbulent, reducing drag forces. In the case of well-streamlined bodies (drop shape or flat horizontal plate), the drag coefficient gradually decreases with increasing Reynolds number because the viscous forces are smaller.