We present the evaluation of two different design configurations of a two-stage PrNi$_5$ continuous nuclear demagnetization refrigerator. Serial and parallel configurations of the two stages are considered, with emphasis on the attainable cooling power at sub-mK temperatures and the impact of the design choices on the operation of the refrigerator. Numerical simulations of heat transfer in the setup are used to evaluate the performance of the refrigerator as well as the technological requirements for the essential thermal links. In accord with similar findings for adiabatic demagnetization refrigerators [Shirron, emph{Cryogenics} textbf{62}, 2014], our simulations show that the performance of both configurations improves as the thermal links improve, and that the parallel configuration yields a higher cooling power than the series design for a given thermal link resistance and sample temperature.
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