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The problem considered in this paper deal with the transient behavior of heat transfer by natural convection flow of fluid along an infinite vertical heated wavy surface. The governing equations are transformed into dimensionless form and solutions are obtained for the two dimensional flow for both pure ( α =0) and uneven surface ( α  ≠ 0). For pure vertical surface boundary layer equations are solved in the (i) upstream (small τ ) (ii) downstream (large τ ) and (iii) entire (0< τ<∞ ) regimes using analytical and numerical techniques. A very good agreement is found when results of above mentioned regimes are compared. Further, for wavy surface solutions are obtained for the entire time regime and results are discussed in terms of average Nusselt number coefficient and isotherms. Numerical results are served to reveal the influence of the physical parameters such as the Prandtl number, Pr, and wavy geometry, α , for the surface conditions.

Three-dimensional numerical simulations were conducted for lid-driven cavity phenomena around an inner circular cylinder positioned in the center of a cubic enclosure in the Reynolds number range of (100≤Re≤2000) at the Prandtl number of Pr=0.71. The numerical method is based on the finite volume method (FVM) and multigrid acceleration. In this study, the transition of the flow regime from steady state to the unsteady state and consequent three-dimensionality in the system induced by the increase of Reynolds number to (Re=1798) were investigated. By increasing further Reynolds number over the critical value, the flow in the cavity exhibits a complex behavior. Typical distributions of the transverse velocity contours and kinetic energy fields at (Re=2000) have been obtained.

In this article, we consider a class of fractional impulsive multivalued stochastic partial integrodifferential equations with state-dependent delay in a real separable Hilbert space. Sufficient conditions for the complete controllability of impulsive fractional stochastic evolution systems are established by means of the fixed-point theorem for discontinuous multivalued operators due to Dhage and properties of the α$\alpha$-resolvent operator combined with approximation techniques. Two examples are also given to illustrate the obtained theorem.

The flexible electronic structure is based on the buckling of a thin film on a compliant substrate. This paper studies the dynamic stability of this structure subjected to a uniaxial step load with damping. The equation of motion is derived by Hamilton’s principle and Euler-Lagrange equation. Through the qualitative analysis of the phase portraits of the dynamic equation, as well as the quantitative analysis of the responses according to Budiansky-Roth criterion, the critical dynamic load is determined. It is the same as that in static buckling. Affected by damping, at the stage of pre-buckling, the amplitude of the film vibrates and attenuates, where the maximum response is the initial amplitude. The structural damping can be derived by the logarithm of the ratio between two adjacent peaks of the vibration. At the stage of post-buckling, the amplitude of the film vibrates and tends to a stable response, which is the amplitude in static buckling. The upper and lower bounds of the post-buckling response are asymmetric and solved by modified Krylov-Bogoliubov method.

Abstract: In this paper, by using critical point theory and variational methods, we prove the existence of weak solutions for damped-like fractional differential equations. We given some new criteria to distinguish that the fractional boundary value problems have at least one solution. Some examples are also given to illustrate the main results.

In this paper, we propose a new method for solving two-dimensional elliptic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition. The method we used is traditional finite element method coupled with Newton’s method, it is very simple and easy to implement. The grid we used here is body-fitting grids based on the idea of semi-Cartesian grid. Numerical experiments show that this method is about second order accurate in the L∞$L^\infty$ norm.

When flow surface is higher than of a side weir crest, the overflow spilt over the crest and divert into a side channel. These structures are extensively used in urban sewage disposal networks, water supply systems, and drainage and flood diversion networks. This study simulates stream free surface, discharge over a sharp-crest side weir, and discharge coefficient of a side weir in a circular channel using FLOW-3D software. Numerical model results were compared with the experimental ones and the comparison proved an acceptable consistency between the numerical and experimental results. RNG k-ε turbulence model was used for simulating flow turbulence. The volume of fluid (VOF) method was used in this CFD analysis for predicting changes of flow free surface. Then, the numerical simulation results were examined for discharge coefficient of the side weir and flow free surface for different discharge passing through the main channel. The changes of dividing stream surface from main channel bed toward stream free surface were examined. The concluding section assessed the effect of shape of a circular channel on the pattern and intensity of a secondary flow in the main channel and the impacts of the discharge passing through the circular channel on height of stagnation point and shear stress pattern in the main channel bed.

Continuous stirred tank reactor (CSTR) is a highly nonlinear process particularly when chemical reaction takes place. The heat energy will be either liberate or absorbed by the reactor due to the reaction. The control of temperature for this process is a real challenge due to nonlinear temperature changes during reaction. In this paper a mathematical model of CSTR with its transfer function is taken for controller design and analysis. The temperature inside the reactor is controlled by altering the coolant jacket temperature. This paper compares the performances of the proportional integral derivative controller (PID) controller, PID-based nonlinear autoregressive moving average (NARMA) controller and fuzzy-based PID controller. The proposed PID-based NARMA controller shows better control of temperature than the conventional PID controller. The fuzzy-based PID controller also shows a reasonable optimal performance.

In this paper, non-polynomial spline method for solving one dimensional nonlinear Benjamin-Bona-Mahony-Burgers equation is presented. Stability analysis of the present method is analyzed by means of Von Neumann process and the method is proven to be unconditionally stable. Truncation error of the proposed method is also discussed. Few numerical evidences are given to prove the validation of the proposed method.

The super integrable system and its super Hamiltonian structure are established based on a loop super Lie algebra and super-trace identity in this paper. Then the super integrable system with self-consistent sources and conservation laws of the super integrable system are constructed. Furthermore, an explicit Bargmann symmetry constraint and the binary nonlinearization of Lax pairs for the super integrable system are established. Under the symmetry constraint,the n$n$-th flow of the super integrable system is decomposed into two super finite-dimensional integrable Hamilton systems over the supersymmetric manifold. The integrals of motion required for Liouville integrability are explicitly given.