Equilibrium heat transfer is the reversible process of (nonzero a,
b, and k; T = t = r = 0). The equilibrium process takes place at a nonzero
T0 ¼ Tp
0 Tr
0
while the temperatures between reactants and
products are the same, Tp = Tr; T = 0 in (11). Note that T0 is a variable
depending on the temperature difference between Tp
0 and Tr
0
while T0 is the equilibrium temperature. Similarly, the spatial
and temporal equilibriums are attained at t = r = 0 in (11), but t0
and r0 are nonzero variables.
During the equilibrium process, the independent temperature,
time, and displacement variables are parameterized as