A partial differential equation for non-equilibrium heat transfer depending on space, time, and temperature is given by where the heat flux includes the internal convection and external
conduction heat transfer. The above equation is the extension of the conduction heat equation The thermal particle number constant in Eq. (5) is connected to the entropy change by a = ln X = S/kB, where X is the number of microstates in the microcanonical ensembles. kr = b/s = 1/s0 in Eq. (6) stands for the rate constant in heat transfer and is the inverse of the mean reaction time s0. k= (b2 a2)1/2 = k/k in Eq. (7) is connected to the reaction cross section rc = V/kk0, and n0 = k/V is the particle number per unit volume. It is worth noting that the particle
number constants can be utilized to classify heat transfer
mechanisms