Hydrodynamic heat transfer in solids

•A local form of second law of thermodynamics demonstrates fundamental physics of superfluidity at so-called boundary of second law.•On the boundary of second law, any motion is non-dissipative. Super momentum has no shear strength and super energy flow has no thermal resistance.•At resonance, super momentum motion implies pressure waves propagating at the speed of first sound. At resonance, super energy flow is represented by temperature waves propagating at the speed of second sound.•A formula of second sound depends solely on thermos-mechanical properties has been validated against experimental data on the velocity of S waves.•Theory of hydrodynamics in solids is demonstrated by using the experimental data of transient heat transfer due to friction and interface thermal conductance. [Display omitted] In solids, hydrodynamics have been observed in both amorphous and crystalline materials under a wide range of conditions. However, its fundamental physics is still unclear. Recent advancements in nanotechnology, biomedicine and electronics have reinvigorated interest in research on hydrodynamic solids. Here, we established the hydrodynamic transport in solids from solid mechanics. We showed that isentropically, a solid becomes superfluid locally in space and time when subjected to periodic motions, and at resonance, the first and second sound are generated. We validated the speed of the second sound against the velocity of S waves, and the agreement is satisfactory. From the concept of the boundary of the second law, we established the boundary conditions for the governing equations of the supersolid and obtained the transient and steady-state solutions of the supersolid. The theory agrees well with the measured flash temperature of the bulk metallic glass (BMG), which elucidates the physics why thermocouples do not measure flash temperature accurately. The finding shall lead to the review of the adequacy of instrumentation where temperature measurement is critical. The validation of the steady-state solution was carried out by comparison to the interfacial thermal conductance (ITC) on solid-solid interfaces. The first dataset has metal-metal interfaces with variable pressures, and the second dataset has metal-dielectric interfaces with variable temperatures, whose ITC differs by 4 orders of magnitude. We discuss the physics of this difference. We believe that the theory of hydrodynamics in solids provides insights for a vast number of disciplines and that