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The complete sets of state-to-state transition rate coefficients for both target and projectile molecules are derived from the predicted response surface designed by the ordinary Kriging model. A system of master equations is constructed for bound-bound and bound-free transitions with these designed transition rate coefficients, and the rovibrational number densities are numerically evaluated by implicitly integrating a system of master equations. In these master equation studies, relaxation of rotation and vibration modes, number density relaxation, reaction rate coefficients, and average rotational and vibrational energy losses due to dissociation are each considered in strong nonequilibrium conditions. A system of master equations are coupled with one-dimensional flow equations to analyze the relaxations of H 2 in post-normal shock and nozzle expanding flows. In post-normal shock flows, the relaxation of the rotational mode is slightly faster or almost similar to the relaxation of the vibrational mode. In nozzle expanding flows, the relaxations of both rotational and vibrational modes seem to be frozen. Nomenclature A area, cm 2 c dissociation of molecule i D dissociation energy of rovibrational state i, erg i e rovibrational energy of state i, erg r e , v e averaged rotational and vibrational energies, respectively, erg ( ) r e i , ( ) v e i rotational and vibrational energies of rovibrational state i, respectively, erg  r e ,  v e averaged rotational and vibrational energy losses, respectively, erg tr E relative translational energy, erg h enthalpy, erg/g f h formation energy, erg/mol ij m g l , ij g l , ijm g , ij g parameter to prohibit the multiple count e g statistical multiplicity of electronic state s g nuclear spin degeneracy

Master Equation Study of Hydrogen Relaxation Using Complete Sets of State-to-state Transition Rates