Theory of heat transfer to a shock-tube end-wall from an ionized monatomic gas

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Abstract
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.