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Mathematical Modelling of Strongly Non-Equilibrium Transfer Processes at Nanoscopic Scale

机译：纳米级规模强不平衡转移过程的数学建模

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Based on the concepts of local non-equilibrium thermodynamics, mathematical models for heat, mass and momentum transfer have been developed with space-time nonlocality taken into consideration. Derivation of transfer differential equations is based on taking into account both specific flows (of heat, mass and momentum) and gradients of corresponding values in diffusion laws by Fourier, Fick and Newton. The research of accurate analytical solutions of the derived models enabled us to find new change patterns of the required parameters for small and ultra small values of time and space variables, as well as for high-speed processes, the change time of which is comparable to relaxation time. Particularly, from the investigation of an accurate analytical solution, it has been found that there is a time delay for Derichlet's boundary condition acceptance, which demonstrates that due to body's resistance to heat penetration, its instant heat-up is impossible, irrespective of any heat exchange with the environment. Therefore, wall heat exchange factor depends not only on heat-exchange conditions (medium speed, viscosity, etc.), but also on the body's physical properties. So, firstly, it is a time-variant and, secondly, it can not exceed a certain limit value, established for each particular case. The conducted research of the rod oscillations with relaxation phenomena, taken into consideration, discovered bifurcation oscillations (beat) appearing under the external harmonic load in cases when the difference between the frequency of eigen-oscillations of the rod and constrained load oscillations is insufficient.
机译：基于局部非平衡热力学的概念，已经开发了用于热量，质量和动量转移的数学模型，并且考虑了时空非招聘。转移微分方程的推导是基于考虑到傅里叶，Fick和Newton扩散法中的特定流量（热量，质量和动量）和相应值的梯度。衍生模型的准确分析解决方案的研究使我们能够找到用于小和超小值的时间和空间变量所需参数的新变化模式，以及高速流程，其更改时间可与休息时间。特别地，从对准确的分析解决方案的研究来看，已经发现德里克莱希特的边界条件接受存在时间延迟，这表明由于身体对热渗透的抵抗力，其瞬间加热是不管任何热量都不可能与环境交流。因此，壁热交换因子不仅取决于热交换条件（中速，粘度等），还取决于身体的物理性质。因此，首先，它是一个时变，其次，它不能超过每个特定情况的一定的极限值。考虑到弛豫现象的杆振荡的对杆振荡的研究，发现在外部谐波载荷下出现的分叉振荡（BEAT）在杆的特征振荡频率与约束负载振荡的频率之间的差异不足时。

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