Bi	Biot number
cp	specific heat (J/kgK)
∆H	latent heat (kJ/kg)
h	heat transfer coefficient (W/m2K)
k	thermal conductivity of the billet (W/mK)
L	billet width (m)
q	heat flux (W/m2)
R	heating rate (K/s)
S	objective function
T	temperature (K)
t	time (s)
x, y	space coordinates (m)
Greek symbols
φ	emission factor
ρ	density (kg/m3)
σ	Stefan–Boltzmann constant (5.56 × 10−8 (W/m2K4))
ε	emissivity
Subscript
C	center
Co	corner
cv	convection
i	initial
f	final
g	gas in the reheating furnace
m	measured
p	predicted
Q	quarter
r	radiation
S	surface
t	total