By using four different frozen-convection approximations, we investigate nonadiabatic radial pulsations for a 9 M☉ and a 2 M☉ stellar model, which represent, respectively, the Cepheid and δ Scuti variables, and we compare the characteristics of the pulsations. We find that the periods of the pulsation modes can differ as much as 6% for the 9 M☉ model and a small amount for the 2 M☉ model. The locations of the pulsation instability strips produced by the four frozen-convection approximations are significantly different from each other, as well as the eigenfunctions and work integrals. It is found that the approximation L = 0 restrains the driving feature at the bottom of the convection zone in the quasi-adiabatic stellar interior and then gives rise to the red edge of the instability strip, while the approximations δFC = 0 and δLC = 0 result in the correct locations of the blue edges of the instability strips that are in good agreement with the observations. We conclude that each of the four frozen-convection approximations may describe some aspects of the convection-pulsation interaction, but none of them can be a complete solution of the problem. Based on considerations of the timescales of the pulsation and response time of the convection, we suggest that a combination of proper frozen-convection approximations may be a good measure of the nonadiabatic stellar pulsations.
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