Second-order approximation for heat conduction: dissipation principle and free energies

Area of Science:

• Thermodynamics
• Continuum Mechanics
• Materials Science

Background:

• New models of heat conduction are being developed.
• The second-order approximation of Tzou's theory is equivalent to a fading memory material.

Purpose of the Study:

• To determine free energy functionals for materials with memory.
• To derive an explicit expression for the minimum free energy.

Main Methods:

• Studied the second-order approximation of Tzou's theory.
• Derived minimum, intermediate, and maximum free energy expressions.
• Focused on materials where the kernel does not satisfy traditional convexity restrictions.

Main Results:

• An explicit expression for the minimum free energy was derived.
• Simple modifications yielded intermediate and maximum free energy expressions.
• The derivations differ significantly from previous work.

Conclusions:

• The derived free energy functionals are essential for materials with fading memory.
• This work advances the understanding of heat conduction in materials with memory.