# Document 13443981 ```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&quot; 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&quot;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
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.
MIT OpenCourseWare
http://ocw.mit.edu
22.06 Engineering of Nuclear Systems
Fall 2010