# Forced Convection Heat Transfer for Stratospheric Airship Involved Flight State
## 1 Introduction  
A stratospheric airship is a type of aircraft that takes off by buoyancy. Compared with other aerostats, the stratospheric airship has its unique advantages and is widely used in civil fields such as satellite communications, meteorological measurements, and military fields such as surveillance and defense [1; 2; 3].  
Convection heat transfer process, including natural convection and forced convection, is one of the most common natural phenomena, which is widely used in almost all of the engineering fields, such as heat exchanger [4; 5], aircraft [6; 7; 8; 9], electronics [10], airship [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22], and so on.  
Thermal performance is one of the most important factors affecting the flight state of a stratospheric airship. The stratospheric airship is filled with a large amount of gas, and it experiences a rough external environment during flight, as the change in temperature affects the buoyancy to a large extent [23]. In the past decades, many research activities have been held on the forced convection heat transfer of a stratospheric airship. In their researches, [PERSON] and [PERSON] [11] established a simple numerical model to simulate the average temperature of balloon envelope and lifting gas. [PERSON] [12] proposed a multi-node thermal transient model of stratospheric airship and verified the model using high-altitude flight experiments. [PERSON] [15] built a two-node thermal model to analyze heatsource and heat transfer patterns that affect thermal balance and thermal performance of airships flying in stratospheric environment. However, the most existing forced convection heat transfer correlations are only applicable in the case of low Reynolds number, so [PERSON] [17] investigated the steady forced convection heat transfer of an isothermal spherical aerostat with the Reynolds number range from 20 to 10\({}^{8}\), and a new piecewise correlation was proposed. Later, [PERSON] [21,22] proposed a new fixed-point adjustment method of an airship to solve the problem of height instability due to dramatic daily-temperature swings. The airship membrane was discretized into a triangular element to enhance the computing accuracy, and a multi-node thermodynamic model of the airship was established.  
In summary, despite the attainment of considerable knowledge on the forced convection heat transfer of a stratospheric airship (through experimental or numerical work), the most relevant empirical correlations are only applicable to spherical airships or airships flying under horizontal state. So many conclusions are not universal because the consistency of study object and correlation equations geometric model is often neglected. And, no specific correlation is available on the external forced convection heat transfer of an ellipsoidal airship flying with a certain angle of attack, although the literature has pointed out that the efficiency of heat transfer is increased by 7 percent considering the angle of attack [24]. The heat transfer criterion equations need to be improved. The present study investigates the effects of Reynolds number, length to diameter ratio, and angle of attack on the thermal characteristics of an ellipsoidal airship to answer this demand. A new correlation of the average Nusselt number is built based on the data obtained from computational fluid dynamic (CFD) calculations. Moreover, a correction factor \(K\) considering angle of attack is proposed to modify this formula.