It deals with incompressible mediums, accounts for only the heat
conduction without internal heat convection, and shows no expression
for the internal heat generation per unit length q0
i. The convective
term (qcpva rT) can be added to the left hand side of the
above equation, but it is only the convective heat contribution.
We are here interested in the internal convective heat generation
depending on temperature difference as well as the external conductive
and convective heat transfer.
In this paper, we propose a systematically unified theory for the
heat transfer mechanisms of internal convection and internal equilibrium
beyond overcoming intrinsic limits on the heat diffusion
equation. In the heat transfer theory, the heat fluxes are described
as functions of temperature, time, and displacement simultaneously
under a postulate that temperature, time, and displacement
are independent and orthogonal variables in extended
phase spaces. This is the first rigorous microscopic kinetic theory
for internal equilibrium and internal convective heat transfer.
The theory unifies conduction and internal convection heat
transfer, it leads to a non-equilibrium theory beyond quasi-equilibrium
theories for the isothermal and isentropic processes, it works
on non-equilibrium and equilibrium dynamics, and it integrates
conduction and convection mechanisms. The heat transfer theory
can be applied to the internal convective thermal processes at a
solid–liquid boundary as an illustration