The role of heat conduction at the leading edge of a hypersonic wing

One of the requirements of the leading edge of a hypersonic wing is that it should be able to withstand the extremely severe rates of aerodynamic heating. By taking the thermal conduction of the material into consideration, the temperature at the nose of the wing may be substantially modified as compared with the case where the boundary layer heating is balanced by radiation alone. The present investigation covering both the two-dimensional and three-dimensional wings shows that not only can the nose temperature be reduced by the inclusion of the effects of heat conduction within the material close to the leading edge but also that the temperature distribution in the leading edge region can be predicted quite accurately. Making certain simplifying assumptions, we formulate the steady state heat transfer equations within a "conducting plate". The laminar boundary layer heat transfer characteristics at high speeds are adopted here to describe the heating phenomenon over a region close to the leading edge with finite rates of heat flux at the leading edge. The effects of heat conduction are significant over lengths of the order of the "conduction length" only; further downstream the temperatures being quite close to the radiation equilibrium value. This conduction length is a function of parameters such as, the thermal conductivity and the thickness of the material, the rates of heat flux and the temperatures associated with it. For the two-dimensional plates, we have obtained solutions of the non-linear heat conduction equation by means of three independent numerical methods with the help of a high speed digital computer. A family of bodies whose streamwise cross-section of the conducting material varies trapezoidally is studied in detail. For such a distribution of the material, the nose thickness is shown to be the most important factor in the determination of the temperature distribution. The theory has been extended to three-dimensional wings to include the effects of finite span and the angle of sweep of the leading edge. The three-dimensional wings may be considered simplified versions of a caret wing which belongs to the wave-rider type of hypersonic wings. The merits of a uniformly rounded apex of a swept wing (subject to a couple of restraints) are compared with the results obtained for the sharp apex. The two-dimensional theory of conducting plates has been satisfactorily verified by experiments which cover a sufficiently wide range of possibilities represented by some non-dimensional parameter. The experimental technique has also been applied for studies of leading edge heating problems on models the solutions of which are difficult to obtain by numerical methods. In carrying out experimental studies, development of certain instruments such as radiometers and heaters became necessary. Also, property data of the material used for the models had to be acquired by separate investigations. A preliminary study has also been undertaken to investigate the two-dimensional thermal stresses that may be induced by the actual temperature distributions close to the leading edge. Thermal stability of the leading edge region of plates tapered in thickness (streamwise) is analysed with a view to relate the onset of thermal buckling with the aerodynamic heating. Since the temperature distribution near the leading edge is closely connected with the heat conducting ability of the material, the criterion used in thermal buckling must be dependent also on this ability of the material in removing heat from the nose downstream