State functions/quantities in thermodynamics and heat transfer

In thermodynamics, it is essential to distinguish between state functions and process functions. The reason is that the simple compressible thermodynamic system is a bivariate-process system, and the change of internal energy, a state function, corresponds to two process functions, heat and work. Among the state functions in thermodynamics, entropy is a special one because it has to be defined through a process function, exchanged heat $$ , and a unique factor of integration, 1/T. In heat transfer, it is shown that Fourier's law and the differential equation of heat conduction are both relations of state quantities alone, and process quantities appear when an integration with respect to time is applied. Moreover, an incompressible heat conduction medium element without conversion between heat and work is a univariate-process system governed by a single variable, temperature. In this case, the change of the thermal energy ("heat content") stored in the system, a state quantity as a function of T alone, corresponds to only one process quantity, the transferred heat. Therefore, on the one hand, it is unnecessary to strictly distinguish between state quantities and process quantities in heat transfer, and on the other hand, there is no need to use a factor of integration to prove entransy a state quantity in heat transfer. Thermodynamics and heat transfer are two parallel sub-disciplines in thermal science. It is incorrect to deny entransy as a state quantity in heat transfer by the uniqueness of the factor of integration for entropy in thermodynamics, and entransy has significant physical meaning in the analysis and optimization of heat transfer processes.