= Solution
Continue the same-rod-number and same-height comparison from part(a), and assume unchanged pump speed, similar inlet conditions and single-phase forced flow for the normal-operation hydraulic argument.
\b[<Core power density> increases.] The active core volume decreases while total thermal power stays fixed. The fuel's own average volumetric power and the mean <fuel linear heat rate> do not increase merely from bringing the same rods closer together: fuel volume and rod count are unchanged.
\b[<Coolant> <mass flow rate> normally decreases.] Tighter passages reduce flow area and <hydraulic diameter>, increasing the core's hydraulic resistance. The unchanged <centrifugal pumps> do not enforce constant flow. The <pump operating point> moves to the intersection of the same pump curve with the steeper system-resistance curve, normally giving smaller flow at greater pump head.<Thermodynamics, Heat Transfer, and Fluid Flow, Volume 3 by the United States Department of Energy>[Module HT-03, pp.51–53, System Characteristic Curve and System Operating Point, Figure10]{ref}
\b[The core <pressure> drop normally increases for the usual pump curve.] Its resistance at any given flow is higher. At the new, smaller flow, unchanged external piping and component losses are smaller, whereas a conventional falling pump head-versus-flow curve gives greater available head. The core takes the difference. This conclusion uses the stated pump-curve assumptions; holding flow fixed or holding pump head fixed would be different models. The exact new flow and pressure drop need both system and pump characteristics.
\b[Fuel <temperature> would normally tend to rise, especially downstream, if the loss of flow increases coolant heating without a compensating improvement in film heat transfer.] At fixed inlet state,
$$
P\simeq\dot m c_p(T_{\rm out}-T_{\rm in})
$$
shows that smaller total <mass flow rate> raises the bulk coolant temperature rise. At unchanged local <fuel linear heat rate>, the fuel-to-surface conductive contribution is approximately unchanged if material properties and gap conditions are held fixed. Its boundary <temperature> and the coolant film drop can nevertheless change.
The local <coolant mass flux> is $G=\dot m/A_f$. Both total flow and flow area decrease, so the sign of the change in $G$, the <heat transfer coefficient> and the fuel <temperature> cannot be deduced from total flow alone. Changes in power peaking and inlet conditions add further qualifications to the usual hotter-fuel tendency.
\b[The <minimum departure from nucleate boiling ratio> would commonly decrease, implying reduced boiling margin, but its sign is conditional.] The defining local ratio is
$$
\mathrm{DNBR}=\frac{q''_{\rm crit}}{q''_{\rm actual}},\qquad
\mathrm{MDNBR}=\min_{\rm core}\mathrm{DNBR}.
$$
The numerator is the <critical heat flux> for the local conditions, and the denominator is actual rod-surface <heat flux>.<Reactor glossary by the United States Nuclear Regulatory Commission>[Departure from nucleate boiling ratio entry]{ref} The mean surface heat loading remains approximately unchanged for the same rods and total power. Greater coolant enthalpy rise tends to reduce margin, while changes in $G$, geometry, pressure and local power determine the actual critical heat flux. A geometry-appropriate correlation or experiment is needed for a definite MDNBR change; unchanged hardware does not supply it.
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