S = Eq. (8) T = absolute temoerature u = x-component of velocity v = y component of velocity x = distance along meridian profile of body y = distance normal to body surface V = Eq. (6) 0 = Eq. (8) \x = absolute viscosity * = Eq. (5) p = mass density a = Prandtl Number c p fx/kA method of predicting laminar heat-transfer rates to blunt, highly cooled bodies with constant wall temperature in dissociated air flow is developed. Attention is restricted to the case of axisymmetric bodies at zero incidence, although two-dimensional bodies could be treated the same way. The method is based on the use of the "local similarity" concept and an extension of the ideas used by Fay and Riddell. 1 A simple formula is given for predicting the ratio of local heat-transfer rate to stagnation-point rate. It depends on wall conditions and pressure distribution, but not on the thermodynamic or transport properties of the hot external flow, except at the stagnation point.Experimental heat-transfer rates obtained with correct stagnation-point simulation and high wall cooling in shock tubes are also presented and compared with the theoretical predictions. On the whole, the agreement is good, although in regions of rapidly varying pressure there is evidence that the local similarity assumption breaks down, and the theory underestimates the actual heat-transfer rate by up to 25 per cent. SYMBOLS Ci Cp D DT f g h h hi 0 h D H k I Li U T L M 8 P Pi = = = = = = = = = = = = = = = = = = = mass fraction of ith component Vd(dhi/dT) diffusion coefficient thermal diffusion coefficient Eq.(7) Eq.(8) enthalpy per unit mass of ith component enthalpy per unit mass of the mixture, including dissociation energy, Xci(hi -hi 0 ) heat evolved in the formation of component i at 0°K., per unit mass average atomic dissociation energy times atom mass fraction in external flow h + (l/2)u 2 thermal conductivity PM/' PwP y = differentiation with respect to indicated variable oo = free-stream conditions o = local similarity solution E = equilibrium (1) INTRODUCTION T HE THEORY of heat transfer at a stagnation point in a dissociating gas has been discussed by Fay and Riddell. 1 They considered the mechanism of heat transfer, with the pertinent physical and chemical effects which arise because of gas dissociation. It was shown ...

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Stagnation-point heat transfer in a partially ionized diatomic gas is considered. The concept of frozen thermal conductivity is used, and a simplified "binary diffusion" model of the gas is proposed. In this model the charge-exchange cross-section for atom-ion collisions is taken t,-be infinite so there is no relative diffusion of the atoms and the ionelectron pairs. This permits the diffusion effects to be dealt with as if there were only two components, molecules and atom-ion-electron particles, and thus greatly simplifies the calculations. However, the thermodynamic and transport properties are evaluated using all four components, molecules, atoms, ions, and electrons. With this model, calculations are made for both frozen and equilibrium boundary layers in nitrogen up to about 60, 000 ft/sec, and arguments are presented for applying the resalts to air. The results show the equilibrium heat transfer rate to be progressively smaller than the frozen rate as the velocity increases above 30, 000 ft/sec, the ratio reaching Z/3 at 50, 000 ft/sec.Simple correlation formulas for the results are given.

This paper deals with the calculation of the convective heat transfer rate to the end-wall of a shock tube from a monatomic gas heated by a reflected shock. We consider a range of shock strengths for which the equilibrium thermodynamic state is one of appreciable ionization. The resulting boundary-layer problem involves the thermal conductivity and ambipolar diffusion coefficient for a partially ionized monatomic gas. The formulation here is restricted to the case of a catalytic wall and equal temperatures for all species. We ignore the effect of the plasma sheath at the wall. Consideration is given to three limiting cases for which similarity-type solutions of the boundary-layer equations may be found: (1) complete thermodynamic equilibrium behind the reflected shock and within the boundary layer; (2) equilibrium behind the reflected shock, but no gas-phase recombination in the boundary layer; (3) no ionization in either region. Numerical calculations are carried out for argon using estimated values of thermal conductivity and ambipolar diffusion, and compared with shock-tube experiments of Camac & Feinberg (1965). For no ionization, calculations were made with thermal conductivity varying as the ¾ power of the temperature, which fits the estimates of Amdur & Mason (1958) up to 15,000°K. Excellent agreement with experiment is obtained confirming an extrapolation of this power law up to 75,000°K. For ionized cases, based on estimates of Fay (1964), the theory predicts heating rates 20–40% lower than measured values. Some possible reasons for this discrepancy are discussed.