CONSERVATION EQUATIONS Lumped-parameter formulation M cv   m i t i    (MV ) cv   (m V ) i   F j t i j (mass) (momentum)    E cv V2  Q  W   m  h   gz  2 t i   i  (energy)  Q  S cv       (m s) i  S gen t j T j i (entropy) 1D formulation G   z t   G 2  P  w p w G   g cos     A z    z t  (mass) (momentum) h h q" p h P G P  w p w   G    (  ) t z A A   t  z (energy) Differential (3D) formulation      ( V )  0 t     V  [  V  V ]  P   2V  g t  T  DP c p [  V  T ]    q"q    T  t Dt Symbols: A c E F g G h m M p P Q S, s t T V W z (mass) (momentum, for incompressible fluid) (energy) Subscripts: Flow Area Specific Heat Internal Energy Force Gravitational Acceleration Mass Flux Enthalpy Mass Flow Rate Mass Perimeter Pressure Rate of Heat Transfer Entropy Time Temperature Velocity Rate of Energy Transfer as Work Elevation cv gen h P r w Control Volume Generation heated Pressure Radial Wall or Wetted Greek Symbols     Therm. Expansion Coeff. Dissipation function Viscosity Density  Shear Stress REACTOR THERMAL PERFORMANCE PARAMETERS Parameter Name Typical values PWR BWR 67 77 Units q Power of fuel rod q′ 18 20 kW/m (BTU/hr-ft) q Linear heat generation rate (or linear power) Heat flux 600 530 kW/m2 (BTU/hr-ft2) q′″ Volumetric heat generation rate 350 240 MW/m3 (BTU/hr-ft3)  Q Core power * * MW kW (BTU/hr) * It varies much from plant to plant For a fuel rod operating at steady-state conditions, the parameters are related as follows: q  q L  q 2 Rco L  q  R 2f L  Q / N Where Rf is the fuel pellet radius, Rco is the fuel rod outer radius, L is the fuel rod active (heated) length and N is the total number of fuel rods in the core.

Thermal Parameters + Conservation Equations

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