# Aerodynamic Drag Study of the Heat Exchange Equipment with Different Fin Geometries
## 2 Theory of the Emergence of Aerodynamic Drag  
Drag forces are caused by two different types of stress acting on the surface of the body. The first is shear stress near the surface. These stresses are caused by frictional forces and act tangentially to the surface at every point of the body and arise due to the viscosity of the fluid. The second are pressure stresses; they act perpendicular to the surface of the body and are caused by how the pressure is distributed around the object. The drag force is the result of these two stresses and acts in the direction of the flow. So, if we know exactly how the stresses are distributed over the surface of the object S, we can integrate them to obtain the resulting resistance force \(F_{D}\):  
\[F_{D}=\int\limits_{S}\left(-P_{D}\cos\theta+\tau_{W}\sin\theta\right)dS \tag{1}\]  
The drag component due to shear stresses is called friction drag \(\tau_{w}\), and the drag component due to pressure forces is called pressure drag or shape resistance \(P_{D}\). Pressure drag is more significant for bodies with poor flow (blunt front). In fact, it is caused by the difference in pressure between the front and back of the body. The pressure resistance increases significantly when a flow break occurs, that is, when the fluid boundary layer separates from the body, creating a band of recirculating flow. This creates an area of low pressure behind the body, called a separation region, and results in a large drag force. To reduce the drag force, it is necessary to minimize the zone of flow separation [17]. The reason for the separation of the flow is the following: when a liquid or gas passes along the surface of an obstacle and goes around it, it first increases its speed, because it has to travel a greater distance in the same time. At the same time, based on the Bernoulli equation, the pressure in this zone rapidly decreases in the direction of the flow--this is called a favorable pressure gradient. \[P_{f}+\frac{\rho\cdot v^{2}}{2}=const, \tag{2}\]  
where \(P_{f}\)--the pressure in the fluid flow, [Pa]; _(\(\rho\cdot v^{2}\))_/2--velocity pressure or dynamic pressure of fluid, [Pa]. After a certain point on the surface of the obstacle, the flow begins to slow down, while the pressure in the direction of the flow begins to increase--this increase is called an adverse pressure gradient. It has a great influence on the flow in the wall boundary layer of the liquid. If the increase in pressure turns out to be large enough in value, then the flow will change its direction to the opposite. In this zone, vorticity, turbulence, and separation of the flow will occur, which in turn will lead to the separation of the flow. In practice, for example, for spherical bodies, flow separation occurs during laminar motion at angles less than 90\({}^{\circ}\) and when turbulent--about 120\({}^{\circ}\)--which indicates better resistance to flow separation. Objects that move quickly in the flow, such as the wings of airplanes or submarines, have a streamlined (drop-like) shape to minimize the effect of flow separation. For very streamlined bodies with small angles of attack, the pressure drag is small because flow separation occurs with a significant delay or does not occur at all. For such bodies, the largest contribution to the total resistance force is the shear stress near the wall. The component of resistance caused by these stresses is called frictional resistance. The force of frictional resistance increases with increasing fluid viscosity and is most significant for bodies that have a large surface area aligned with the direction of flow. It was previously noted that turbulence delays flow separation and reduces drag caused by pressure. However, for frictional resistance, it has the opposite effect. Laminar and turbulent boundary layers have very different velocity profiles. The wall velocity gradient is steeper in turbulent boundary layers than in laminar boundary layers, so turbulence creates higher shear stresses.