Entropy Analysis of the Peristaltic Flow of Hybrid Nanofluid Inside an Elliptic Duct with Sinusoidally Advancing Boundaries

Peristaltic flow of hybrid nanofluid inside a duct having sinusoidally advancing boundaries and elliptic cross-section is mathematically investigated. The notable irreversibility effects are also examined in this mathematical research by considering a descriptive entropy analysis. In addition, this work provides a comparison analysis for two distinct nanofluid models: a hybrid model (Cu-Ag/water) and a phase flow model (Cu/water). A comprehensive graphical description is also provided to interpret the physical aspects of this mathematical analysis.

Geometry-Induced Rigidity in Elastic Torus from Circular to Oblique Elliptic Cross-Section

For a given material, different shapes of a built structure will be corresponding to different rigidity. In this paper, nonlinear displacement formulation is formulated and numerical simulations will be carried out for circular, normal elliptic, and oblique elliptic torus. Investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than the outer torus due to the property of their Gaussian curvature. The desired rigidity can be archived by adjusting the ratio of the minor and main radius and oblique angle.

Nonlinear vibration of a buckled/damaged BNC nanobeam transversally impacted by a high-speed C60

Nanotube can be used as a mass sensor. To design a mass sensor for evaluating a high-speed nanoparticle, in this study, we investigated the impact vibration of a cantilever nanobeam being transversally collided by a high-speed C60 at the beam's free end with an incident velocity of vIn. The capped beam contains alternately two boron nitride zones and two carbon zones on its cross section. Hence, the relaxed beam has elliptic cross section. The vibration properties were demonstrated by molecular dynamics simulation results. Beat vibration of a slim beam can be found easily. The 1st and the 2nd order natural frequencies (f1 and f2) of the beam illustrate the vibration of beam along the short and the long axes of its elliptic cross section, respectively. f2 decreases with increasing temperature. A minimal value of vIn leads to the local buckling of the beam, and a different minimal vIn leading to damage of the beam. For the same system at a specified temperature, f2 varies with vIn. When the beam bends almost uniformly, f2 decreases linearly with vIn. If vIn becomes higher, the beam has a cross section which buckles locally, and the buckling position varies during vibration. If vIn approaches the damage velocity, a fixed contraflexture point may appear on the beam due to its strong buckling. Above the damage velocity, f2 decreases sharply. These results have a potential application in design of a mass sensor.

On the stability analysis of flows in channels of elliptic cross section using the finite element method on unstructured meshes

Существующая технология численного анализа устойчивости течений вязкой несжимаемой жидкости в каналах постоянного сечения была ранее расширена на случай локальных пространственных аппроксимаций на неструктурированных сетках, приводящих к задачам с большими разреженными матрицами. Для пространственной аппроксимации при этом используется метод конечных элементов, а для решения частичных проблем собственных значений, возникающих при исследовании устойчивости течений, эффективный метод ньютоновского типа. В данной работе проводится подробное численное исследование предложенного подхода на примере двумерной конфигурации — течения Пуазейля в канале эллиптического сечения. Работоспособность подхода демонстрируется для широкого диапазона отношений длин полуосей сечения вплоть до отношения, при котором данное течение становится линейно неустойчивым. Показана сходимость ведущей части спектра по шагу сетки и совпадение результатов с результатами, полученными на основе аппроксимации спектральным методом коллокаций. The existing technique for the numerical analysis of incompressible fluid flow stability in channels of constant cross section was earlier extended to the case of local spatial approximations on unstructured meshes, which leads to large sparse matrices. The finite element method is employed for spatial approximation and a new efficient Newton-type method is used to solve partial eigenvalues problems arising in flow stability analysis. A detailed numerical study of the proposed approach is carried out in this paper by the example of Poiseuille flow in a channel of elliptic cross section. Performance ability of the approach is demonstrated for a wide range of the cross-sectional semiaxes ratio, including the case of linear instability of the flow under consideration. The convergence of the leading part of the spectrum with respect to the grid size is shown. Our results are in good agreement with those obtained via approximation by the spectral collocation method.