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This report develops and presents a mathematical model and a numerical-solution technique -- COMMIX-1 Computer Program -- for three-dimensional, transient, single-phase, thermal-hydraulic analysis of reactor components. A set of governing equations for the conservation of mass, momentum, and energy is solved as a boundary-value problem in space and as an initial-value problem in time. The model can treat both continuum (e.g., reactor plenum) and quasi-continuum (e.g., rod bundles or fuel assembly) sodium systems. Volume porosity, surface permeability, and distributed resistance are used in the quasi-continuum approach, which alleviates two inherent deficiencies associated with conventional subchannel analysis; one is the approximation used in the formulation of transverse momentum equations, the other is its inability to handling reverse flow or recirculatory flow.