Conduction of heat within a body subjected to aerodynamic heating at hypersonic speeds

Rockets, Satellites and other space-craft moving at supersonic and hypersonic speeds through the atmosphere present a formidable problem of high temperature heat transfer from the boundary layer. The boundary layer temperature becomes very high and at a flight speed of Mach number 10 or more, it is of the order of 4000°C or higher. The forward tip, nose or leading edges of the moving body experience maximum heating and efforts are being made first to reduce aerodynamically the amount of boating by suitable design and second to effect cooling by suitable means. In the present work, efforts have been made to find by how much the heat conductivity of the material can help to reduce the temperature at the loading edge of the body subjected to the aerodynamic heating. Theoretical analysis of the heat balance equations indicates that the heat conductivity of material can play an important role in transferring the heat from the nose region to the downstream part of the body. The effects of the different geometry of the conducting skin on the nose temperature have also been discussed briefly. A short review of the works of many investigators indicates that the aerodynamic heating is a function of Reynolds number, Mach number, Pradtl number, ratio of specific heats of air and the ratio of the surface temperature of the body to the ambient temperature. Hence during level flight at a constant speed, the laminar boundary layer aerodynamic heating at any point on the body would be inversely proportional to the square root of its distance from the nose. With this as a guiding factor, a reflector was designed to provide a pattern of heat distribution on a piano similar to that of aerodynamic heating. It was thought that the use of a reflector with a single heating element as a heat source, would give the most convenient method of providing the required pattern of heat distribution. Necessary basic differential equations for the design of a reflector were derived. An analytical test method was also developed to find the actual heat distribution given by a reflector using a heating element of finite size. Work was carried on to find a suitable heating element to provide maximum heat energy in a high vacuum with the minimum size to suit the reflector. Materials like tungsten, pure nickel, graphite and lampblack were tasted in high vacuo. In order to obtain high accuracy in the reflector profile, a suitable method of construction was developed. Since none of the conventional heat radiation measuring instruments was suitable for measuring heat flux ∝ x[-1/2], a suitable radiometer was designed and constructed for this purpose. A water calorimeter was designed and constructed to calibrate the radiometer. Other necessary equipments such as vacuum chamber, model support tray, etc. were also designed and made. Since only a limited amount of radiant heat was available from the heating clement, high thermal conductivity materials could not be used for the conducting skin models. Models of Staybrite stainless steel (k = 3.90 ft.lb/ft/sec/°K) and Frequentite (k = 0.65 ft.lb/ft/sec/°K) were made and tested under different rates of heating in a high vacuum of the order of 10