10.6. Nomenclature

Symbols	Definition	Units
$A$	Atom fraction, e.g., Eq. (10.3-7) or coefficients of the quadratic function of temperature for fuel thermal conductivity, e.g., Eq. (10.3-52) and Eq. (10.3-61).
$a$	Atomic weight
$B$	Coefficient of the quadratic function of temperature for fuel thermal conductivity, e.g., Eq. (10.7-12) to Eq. (10.7-14)
$Bu$	Fuel burnup	atom %
$C$	Plutonium alloying coefficient in thermal conductivity Eq. (10.3-102)
$C_{\text{p}}$	Specific heat	J/kg-K
$c$	Coefficient of the quadratic term in the simplified enthalpy Eq. (10.3-26)
$D$	Value of determinants in Cramer’s rule for solving a system of linear algebraic equations
$f_{\text{o}}$	Heavy-metal mass fissioned expressed as a percentage of U-Pu-Zr alloy post-irradiation mass
$H$	Enthalpy	J/mol
$h$	Enthalpy	J/kg
$K$	Thermal Conductivity	W/m-K
$K_{\text{pt}1}$	Thermal conductivity of a pore tube containing a fission gas-filled pore	W/m-K
$K_{\text{pt}2}$	Thermal conductivity of a pore tube containing a logged sodium-filled pore	W/m-K
$L$	Length, e.g., Eq. (10.3-44) or Lorenz number in Q. Eq. (10.3-68)	m or W-Ω/K2
$M$	Mass	kg
$m_{\text{a}}$	One atomic mass unit, $1.6592828 \times 10^{-27}$ kg	kg
$N$	Number of atoms, e.g., Eq. (10.3-34) or number of fissions, e.g., Eq. (10.3-35) or number of pairs of temperature and enthalpy values, e.g., Eq. (10.3-37)
$Na$	Avogadro’s number, $6.02472 \times 10^{26}$ molecules/kg-mole	/kg-mole
$P'$	Porosity fraction relative to the 100%-dense volume
$P_{\text{c}1}$	Areal fraction of a face of a unit cell that is occupied by a sodium-filled pore, e.g., Eq. (10.3-72)
$P_{\text{c}2}$	Areal fraction of a face of a unit cell that is occupied by a sodium-filled pore, e.g., Eq. (10.3-72)
$P_{\text{g}}$	Gas-filled porosity fraction relative to the swollen fuel volume
$P_{\text{I},1}$	Fraction of the side (in heat flow direction) of a unit cell that is occupied by a gas-filled pore
$P_{\text{I},2}$	Fraction of the side (in heat flow direction) of a unit cell that is occupied by a sodium-filled pore
$P_{\text{Na}}$	Sodium-filled porosity fraction relative to the swollen fuel volume
$T$	Temperature	K
$V$	Volume	m3
$v$	Characteristic volume of an atom	m3
$W$	Weight fraction
$X_{\text{i}}$	Weight fractions of the 3 database alloys to be mixed to produce the desired fuel composition
$x$	Zr weight fraction in the U-Zr binary database alloy used in enthalpy region 1 or thermal conductivity region 3
$Y_{\text{i}}$	Atom fractions of the 3 database alloys to be mixed to produce the desired fuel composition
$\alpha$	Coefficient of linear thermal expansion	per K
$\Delta L$	Linear thermal expansion from 293K	m
$\rho$	Density, e.g., Eq. (10.3-32) or electrical resistivity in Eq. (10.3-68)	kg/m3 or Ω-m
$\sigma$	Standard deviation
Subscripts:
$\text{a}$	Desired alloy or desired database alloy
$\text{c}$	Centigrade temperature scale
$\text{f}$	Fission, e.g., Eq. (10.3-38) or solid fission products, e.g., Eq. (10.3-40) or desired fuel, e.g., Eq. (10.3-61)
$\text{g}$	Fission gas
$\text{h}$	Heavy metals
$\text{i}$	Index for fuel constituents (I - U, Pu, Zr) or index for the 3 database alloys of a region of interpolation
$\text{l}$	Liquidus or molten liquid
$\text{Na}$	Sodium
$\text{o}$	Fabricated condition, e.g., Eq. (10.3-33) or 100%-dense unirradiated condition, e.g., Eq. (10.3-72) or a specified temperature, e.g., Eq. (10.3-44)
$\text{p}$	Plutonium
$\text{s}$	Solidus
$\text{sfp}$	Solid fission products
$\text{th}$	Theoretical
$\text{u}$	Uranium
$\text{uz}$	U-Zr binary alloy
$\text{u50}$	U-50 atom % Zr binary alloy
$\text{z}$	Zirconium
$\alpha$	Lowest-temperature solid-state phase (α-phase)
$\gamma$	Highest-temperature solid-state phase (γ-phase)