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We prove some coupled fixed point theorems for mappings satisfying different contractive conditions on complete cone metric spaces.

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SUMMARYElectric energy storage systems are used considerably in industries and daily applications. The demand for batteries with high energy content has increased because of their use in hybrid vehicles. Lead-acid batteries have wide applications because of their advantages such as high safety factor and low cost of production. The major shortcoming of lead-acid batteries is low energy content and high dimension and weight. Nowadays, a common method to increase the energy content of lead-acid battery is the experimental method with trial and error, which is time consuming and expensive. In this paper, non-isothermal one-dimensional numerical simulation of lead-acid battery with finite volume method is performed. In addition, a cell with higher energy content and lower thickness is designed by using particle swarm optimization algorithm based on developed simulation code. The results of single objective optimization show that an optimal battery that has 27.6% higher energy can be made with the same cell dimension. The results also show that an optimum cell battery can be obtained with a decrease of 24% in thickness while keeping the energy the same. Moreover, a multi-objective optimization algorithm is utilized to find Pareto optimal solutions while considering the energy content and thickness objectives simultaneously.

Wind turbines are of the most promising devices to cut down carbon emissions. However, some phenomena that adversely affect their performance are inevitable. The aim of the present paper is to investigate flow separation prevention exploiting leading edge (LE) single dielectric barrier discharge plasma actuator (SDBD-PA) on an airfoil belonging to a section of a locally developed wind turbine. The numerical results of the surface pressure distribution over the airfoil were compared with the experimental measurements carried out by the authors on the same blade section, and good agreement was found between numerical and experimental data for both plasma-OFF and plasma-ON cases. An in-depth parametric numerical investigation was then carried out to provide a better understanding of the flow behavior affected by the activation of PA over the same airfoil at post stall angle of attacks (AOAs). According to the results, the frequency and voltage of actuation, AOA, and free stream velocity are shown to have strong impacts on separation delay and actuation effectiveness. In Reynolds number of 2.85 × 105, the maximum PA effectiveness takes place at 21° which is approximately 312%, 307%, and 256% corresponding to the PA location of LE, 0.02 chord, and 0.15 chord, respectively. Also, maximum velocity of the domain is increased three times of the free stream velocity on average for three investigated Reynolds numbers at the frequency and voltage of 12 kHz and 12 kV, respectively. Furthermore, the size of the wake area noticeably contracts due to the presence of the SDBD-PA. The results clearly indicate that the lift and drag coefficients as well as the lift-to-drag ratio fit a linear variation pattern with the frequency of actuation. The variation rate of the aforementioned parameters becomes steeper as the peak voltage of actuation increases. Highly nonlinear aerodynamic responses and significant interactions were demonstrated between the investigated parameters.

A highly accurate finite-difference PSE code has been developed to investigate the stability analysis of incompressible boundary layers over a flat plate. The PSE equations are derived in terms of primitive variables and are solved numerically by using compact method. In these formulations, both nonparallel as well as nonlinear effects are accounted for. The validity of present numerical scheme is demonstrated using spatial simulations of two cases; two-dimensional (linear and nonlinear) Tollmien-Schlichting wave propagation and three-dimensional subharmonic instability breakdown. The PSE solutions have been compared with previous numerical investigations and experimental results and show good agreement.

Matthews [12] introduced a new distance P on a nonempty set X, which he called a partial metric. The purpose of this paper is to present some fixed point results for weakly contractive type mappings in ordered partial metric space. An application to nonlinear fractional boundary value problem is also presented.

A new simulation method for solving fluid-structure two-way coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A new definition of velocity-vorticity formulation aids us to introduce an immersed boundary method that does not require a force term to impose the no-slip condition on the solid boundaries. The proposed method is easy to implement and apply for two-way fluid-structure interaction problems. The dynamics of a falling and rising circular cylinder in a quiescent fluid as well as the motion of a circular cylinder in a lid-driven cavity are considered to evaluate the capabilities of the presented method.