Vortices and Backflow in Hydrodynamic Heat Transport

Area of Science:

• Condensed matter physics
• Mesoscopic physics
• Fluid dynamics

Background:

• Recent experiments have renewed interest in phonon hydrodynamics, a regime distinct from diffusive heat transport.
• Phonon hydrodynamics is governed by momentum-conserving phonon collisions, described by viscous heat equations (VHEs) at the mesoscopic scale.

Purpose of the Study:

• To analytically solve the viscous heat equations for phonon hydrodynamics.
• To explore the conditions for observing thermal vortices and negative thermal resistance in microscale devices.
• To provide a foundational framework for designing hydrodynamic phonon and electron flows.

Main Methods:

• Separating and recasting VHEs into modified biharmonic equations for velocity potential and stream function.
• Analytical solutions for irrotational and incompressible limits of VHEs.
• Examination of thermal flow in a 2D graphite strip device.

Main Results:

• VHEs are analytically solvable via modified biharmonic equations, yielding a complex potential for flow streamlines.
• Two distinct temperature contributions related to thermal compressibility and vorticity are identified.
• The analysis extends to the electron compressible regime and identifies conditions for thermal vortices and negative thermal resistance.

Conclusions:

• The study provides analytical tools to design and understand hydrodynamic phonon and electron flows.
• This work offers a foundational framework for experiments on nonstandard transport, plasmonics, and collective excitations.
• The findings are crucial for advancing microscale systems exhibiting collective excitations.