The development and investigation of a strongly non-equilibrium model of heat transfer in fluid with allowance for the spatial and temporal non-locality and energy dissipation

Three-Dimensional Optimization Development and Regulation of Land Space Based on Spatial Equilibrium Model

“…In short, the concept of territorial balance in land use can be understood as that in a specific area, human beings are pursuing economic development [ 19 ]. The coordinated behavior between the economic activities of land use and the natural distribution of land resources enables the spatial development mode of land use to achieve territorial balance, maximizes the overall benefits of all aspects of society, and ensures that land use reaches the goal of sustainable development [ 20 ]. In short, when the territorial supply capacity is equivalent to the intensity of territorial development and utilization, regional territorial development reaches a territorial balance.…”

Heat Transport on Ultrashort Time and Space Scales in Nanosized Systems: Diffusive or Wave-like?

“…Moreover, the heat transport at ultrashort space and time scales leads to unusual non-Fourier phenomena such as wavelike temperature propagation [4][5][6]12,13], size [14,15] and distance [15] dependent thermal conductivity, and boundary temperature jumps [1,14,15], which have raised an extensive body of literature concerning different conceptual questions of these phenomena [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The problem is that when the characteristic length of the process is of the order of the mean free path (MFP) of energy carriers and/or the characteristic time scale of the process is of the order of the mean free time (MFT) of energy carriers, the thermal dynamics occur under far from local equilibrium conductions and cannot be described by classical Fourier law based on the local equilibrium assumption [31]. In this case, one needs to use an approach which is not based on the local equilibrium assumption.…”

“…In this case, one needs to use an approach which is not based on the local equilibrium assumption. The most simple and well-known generalization of the classical Fourier heat conduction equation of the parabolic type is the hyperbolic heat conduction equation (HHCE), which combines diffusive (dissipative) and wave modes of heat transport and transmits temperature discontinuity with a constant velocity without smoothing [12,25,26,[29][30][31]. To our knowledge, the HHCE was first obtained under an assumption that the energy carriers move with a well-defined finite velocity (see discussion in [29]).…”

“…To our knowledge, the HHCE was first obtained under an assumption that the energy carriers move with a well-defined finite velocity (see discussion in [29]). While the classical heat conduction equation of the parabolic type results in the infinite propagation velocity of thermal disturbances, the HHCE removes this paradox leading to a finite value of propagation [12,22,25,31]. This property of the HHCE has attracted a wide range of interest mainly in the context of heat waves in liquid helium II (the so-called "second sound") [12].…”

“…However, the HHCE cannot be used to describe heat conduction in nanosized systems where the nonlocal space effects [14][15][16][17][18]21,22,[26][27][28]31] and ballistic component of heat transport [14][15][16][17]19,23,24] lead to non-Fourier phenomena such as size-dependent thermal conductivity [1,9,[14][15][16][17] and boundary temperature jumps [14][15][16][17]19], which can be observed even in the steady-state [14][15][16][17]. Note that the HHCE in the steady-state reduces to the classical heat conduction equation of the parabolic type, and consequently, cannot describe these effects.…”