This paper presents a mathematical method for analyzing transient flow and enthalpy transport in rod-bundle nuclear fuel elements during both boiling and nonboiling conditions. A mathematical model is formulated by dividing the bundle flow area into flow subchannels that are assumed to contain one-dimensional flow and are coupled to each other by turbulent and diversion crossflow mixing. The mathematical model neglects sonic velocity propagation and neglects temporal and spatial acceleration in the transverse momentum equation. A semiexplicit finite-difference scheme is used to perform a boundary-value solution where the boundary conditions are the inlet enthalpy, inlet flow rate, and exit pressure. Calculations are presented to show the effect of rapid changes in heat flux, inlet enthalpy, and inlet flow rate on the subchannel flow and enthalpy distribution in rod bundles.