Abstract:
Research has been conducted on the exact analytical solution of the third-order hyperbolic heat conduction equation, derived with consideration of heat flux relaxation, temperature gradient, and the second-order flux term in the Fourier law formulation. The studies have shown that, depending on the values of the relaxation coefficients (temporal and spatial) and the thickness of the plate, qualitatively different variants of temperature change can be observed. And, in particular, at thicknesses significantly greater than the mean free path of microparticles, diffusion heat transfer with a time delay in establishing the boundary condition of the 1st kind is observed. At thicknesses comparable to the mean free path of microparticles (nanoscale thickness), diffusion heat exchange is replaced by wave heat exchange, which, depending on the values of the relaxation coefficients, can occur both in the ballistic heat transfer mode and in the oscillation mode with correlation in the region of negative temperature values. The conditions leading to each of the wave heat transfer variants are considered.
Keywords:locally-Nonequilibrium heat transfer, modified formula of fourier's law, hyperbolic equation, exact solution, diffusion heat transfer, wave heat transfer, relaxation time, mean free path of microparticles, second-order heat flow.
