# Calculation of Heat Transfer and Drag Coefficients for Aircraft Geometric Models
## 5 Conclusions  
Of all the above problems, the following two were singled out and this work was devoted to these problems: the calculation of viscous shear stresses (and friction coefficient \(C_{f}\)) on the surface of a streamlined body, and the calculation of convective flow \(q_{w,L}\) to the surface of a streamlined body.  
The direct way to quickly estimate the friction coefficient and heat fluxes by numerically integrating the complete system of Navier-Stokes equations is problematic and is accompanied by serious difficulties and computer computing resources. This is because the characteristic size of the streamlined body (about ten meters) is much larger than the characteristic size of the boundary layer (boundary layer thickness: \(\delta\approx 5\cdot(\mu\varepsilon/\rho U)^{0.5}\approx 1\) mm, where \(\mu\) is the dynamic viscosity of the gas; \(\varepsilon\) is the characteristic length of the streamlined object; is the characteristic density of the gas; \(U\) is the characteristic velocity of the incoming flow), and the need to resolve the boundary layer near the surface of the streamlined body leads to the fact that the computational grid will require large amounts of random access memory and high-performance processors.  
Therefore, one of the goals of the work was to develop a simplified (operational) method for estimating convective heat fluxes and drag coefficients for the bodies of simple and complex spatial shapes moving in the Earth's atmosphere. Thus, the method for assessing heat transfer near the HSA surface was formulated based on two physical and mathematical models: a 2D engineering-physical-mathematical model using bodies of simple geometric shapes, and a 3D numerical technique designed to calculate the complex geometric shapes of HSA using unstructured meshes [34].  
An approximate mathematical model for calculating the friction coefficient and convective flux in the boundary layer [35; 36; 37; 38; 39; 40] was built in this study. A novel computational method for the evaluation of the effective length effects was presented. Calculations based on the proposed mathematical model were carried out and compared with the experiments. Based on both experiments and calculations, the proposed mathematical model was Successful validation and verification of the proposed mathematical model was carried out on the basis of experiments and calculations carried out earlier. Successfully validated and verified. The heat flux \(q_{w}\) and the aerodynamic coefficients, \(C_{px}\) and \(C_{py}\), are given for the geometric X-33 and X-43 models.  
Conceptualization, S.V.R. and A.Y.V.; software, V.V.K.; validation, V.V.K.; writing--original draft preparation, S.V.R. and V.V.K.; writing--review and editing, V.V.K., S.V.R. and A.Y.V.; project administration, S.V.R. All authors have read and agreed to the published version of the manuscript.  
The results were obtained as part of the implementation of the Priority 2030 Program and the Federal Project of the Ministry of Science and Higher Education of the Russian Federation \"Advanced Engineering Schools\" (PISH).  
Not applicable.  
No new data were created or analyzed in this study. Data sharing does not apply to this article.  
The authors declare no conflict of interest.