  We report design details of the whole assembly of a compact and continuous
nuclear demagnetization refrigerator (CNDR) with two PrNi$_5$ nuclear stages,
which can keep temperature below 1 mK continuously, and test results of a new
thermal contact method for the PrNi$_5$ stage using Zn soldering rather than Cd
soldering. By measuring a residual electrical resistance of a short test piece,
the thermal contact resistivity between the PrNi$_5$ rod and an Ag wires
thermal link was estimated as $1.8\pm0.1 \times 10^{-4}
T^{-1}~\rm{Km^2W^{-1}}$. Based on this value and 2D numerical and 1D analytical
thermal simulations, the largest possible temperature gradient throughout the
nuclear stage was calculated to be negligibly small ($\leq$ 2 %) at 1 mK under
a 10 nW heat leak, the expected cooling power of the CNDR.
