CONSERVATION EQUATIONS Lumped-parameter formulation M cv m i (mass) ti  (MV )cv (m V  )i F  j (momentum) ti j Ecv   2   Q W m h  V  gz  (energy) ti  2 i cv St  j  QT   j  i (m s)i  S gen (entropy) 1D formulation  G  (mass) t z  Gt   z  G  2    Pz  wApw g cos (momentum) h  G h  q" ph  P  G (P  w pw ) (energy) t z A t z A  Differential (3D) formulation     (V )  0 (mass) t  [V  V  V  ]  P  2V  g  (momentum, for incompressible fluid) t cp [T  V  T ]    q "q T DP  (energy) t Dt Symbols: Subscripts: A Flow Area cv Control Volume c Specific Heat gen Generation E Internal Energy h heated F Force P Pressure g Gravitational Acceleration r Radial G Mass Flux w Wall or Wetted h Enthalpy m Mass Flow Rate Greek Symbols M Mass  Therm. Expansion Coeff. p Perimeter  Dissipation function P Pressure  Viscosity Q Rate of Heat Transfer  Density S, s Entropy  Shear Stress t Time T Temperature V Velocity W Rate of Energy Transfer as Work z ElevationREACTOR THERMAL PERFORMANCE PARAMETERS Parameter Name Typical values PWR BWR Units q q′ q q′″ Q Power of fuel rod Linear heat generation rate (or linear power) Heat flux Volumetric heat generation rate Core power 67 18 600 350 * 77 20 530 240 * kW (BTU/hr) kW/m (BTU/hr-ft) kW/m2 (BTU/hr-ft2) MW/m3 (BTU/hr-ft3) MW * 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 2 fL  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.MIT OpenCourseWarehttp://ocw.mit.edu 22.06 Engineering of Nuclear Systems Fall 2010 For information about citing these materials or our Terms of Use, visit: