The present paper investigates the effects of a vertical magnetic field on the double diffusive nanofluid convection. The effects of the Brownian motion and thermophoresis due to the presence of nanoparticles and the effects of the Dufour and Soret parameters due to the presence of solute are included in the investigated model. The normal mode technique is used to solve the conservation equations. For the analytical study, valid approximations are made in the complex expression for the Rayleigh number to get useful and interesting results. The bottom heavy binary nanofluids are more stable than the regular binary fluids, while the top heavy binary nanofluids are less stable than the regular binary fluids. The critical wave number and the critical Rayleigh number increase whereas the frequency of oscillation (for the bottom heavy configuration) decreases when the Chandrasekhar number increases. The numerical results for the alumina-water nanofluid are studied by use of the MATHEMATICA software.
A simple but applicable analytical model is presented to predict the lateral distribution of the depth-averaged velocity in meandering compound channels. The governing equation with curvilinear coordinates is derived from the momentum equation and the flow continuity equation under the condition of quasi-uniform flow. A series of experiments are conducted in a large-scale meandering compound channel. Based on the experimental data, a magnitude analysis is carried out for the governing equation, and two lower-order shear stress terms are ignored. Four groups of experimental data from different sources are used to verify the predictive capability of this model, and good predictions are obtained. Finally, the determination of the velocity parameter and the limitation of this model are discussed.
A new view of the spatial relation between fluctuating wall pressure and near-wall streamwise vortices (NWSV) is proposed for wall bounded turbulent flow by use of the direct numerical simulation (DNS) database. The results show that the wall region with low pressure forms just below the strong NWSV, which is mostly associated with the overhead NWSV. The wall region with high pressure forms downstream of the NWSV, which has a good correspondence with the downwash of the fluids induced by the upstream NWSV. The results provide a significant basis for the detection of NWSV.
The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system (H-S) and standing system (S-S) are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.
The present research explores the three-dimensional boundary layer flow of the Maxwell nanofluid. The flow is generated by a bidirectional stretching surface. The mathematical formulation is carried out through a boundary layer approach with the heat source/sink, the Brownian motion, and the thermophoresis effects. The newly developed boundary conditions requiring zero nanoparticle mass flux at the boundary are employed in the flow analysis for the Maxwell fluid. The governing nonlinear boundary layer equations through appropriate transformations are reduced to the coupled nonlinear ordinary differential system. The resulting nonlinear system is solved. Graphs are plotted to examine the effects of various interesting parameters on the non-dimensional velocities, temperature, and concentration fields. The values of the local Nusselt number are computed and examined numerically.
The frequency effects on the velocities and attenuations of the bulk waves in a saturated porous medium are numerically studied in the cases of considering and neglecting the compressibility of solid grain, respectively. The results show that the whole frequency can be divided into three parts, i.e., low frequency band, medium frequency band, and high frequency band, according to the variation curves and the characteristic frequency. The compressibility of the solid grain affects the P1 wave distinctively, the S wave tiny, and the P2 wave little. The effects of the porosity and Poisson's ratio on the bulk waves are numerically analyzed. It is found that both the porosity and Poisson's ratio have obvious effects on the bulk waves. Compared with the results in the case of neglecting the porosity-moduli relation, the results in the case of considering the porosity-moduli relation are more reasonable. The results in the case of considering the porosity-moduli relation can be degenerated into the results of elastic solid and pure fluid, while the results in the case of neglecting the porosity-moduli relation cannot be degenerated into the results of elastic solid and pure fluid. Therefore, the porosity-moduli relation must be considered in the parametric study for a certain porous medium.
The dynamic behaviors of several moving cracks in a functionally graded piezoelectric (FGP) strip subjected to anti-plane mechanical loading and in-plane electrical loading are investigated. For the first time, the distributed dislocation technique is used to construct the integral equations for FGP materials, in which the unknown variables are the dislocation densities. With the dislocation densities, the field intensity factors are determined. Moreover, the effects of the speed of the crack propagation on the field intensity factors are studied. Several examples are solved, and the numerical results for the stress intensity factor and the electric displacement intensity factor are presented graphically finally.
Based on the fundamental equations of piezoelasticity of quasicrystals (QCs), with the symmetry operations of point groups, the plane piezoelasticity theory of onedimensional (1D) QCs with all point groups is investigated systematically. The governing equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the operator method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form solutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.
For the better use of composites and a deeper insight into the fracture propagation and stress transfer of the interface between fiber and matrix, a theoretical solution of closed form is presented with the assumed bilinear local bond-slip law and a parabolic shear stress distribution along the thickness of the matrix. The load-displacement relationship and interfacial shear stress are obtained for four loading stages. Finally, the effects of Young's modulus of fiber (matrix) and bond length on the performance of the interface are illustrated.
Duplication and divergence have been widely recognized as the two dominant evolutionary forces in shaping biological networks, e.g., gene regulatory networks and protein-protein interaction (PPI) networks. It has been shown that the network growth models constructed on the principle of duplication and divergence can recapture the topological properties of real PPI networks. However, such network models only consider the evolution processes. How to select the model parameters with the real biological experimental data has not been presented. Therefore, based on the real PPI network statistical data, a yeast PPI network model is constructed. The simulation results indicate that the topological characteristics of the constructed network model are well consistent with those of real PPI networks, especially on sparseness, scale-free, small-world, hierarchical modularity, and disassortativity.