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Solutions of the viscous shock layer equations with mass addition are obtained. Flow-field equations include the effects of heat conduction, diffusion of reacting species, and emission and absorption of gaseous radiation for dissociated and partially ionized air in chemical equilibrium. Convective and radiative heating rates with mass addition are obtained from the solutions. Algebraic equations are derived for predicting the nose radius that minimizes total heating rates at a given flight speed and shock-layer pressure level. Values for the corresponding natural ablation rate, the effective heat of ablation, the ratio of radiative to convective heating rate, surface shear stress, and shock-wave standoff distance are given. The effects of ablated gases that radiate more strongly than air are examined. Solutions without mass addition at low Reynolds numbers where external vorticity, energy depletion, and flow energy limiting are important are compared with existing theory and experiments.