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In this paper, homotopy perturbation method (HPM) and variational iteration method (VIM) are used to solve the large amplitude torsional oscillations equations in a nonlinearly suspension bridge. This paper compares the HPM and VIM in order to solve the equations of nonlinearly suspension bridge. A comparative study between the HPM and VIM is presented in this work. The achieved results reveal that the HPM and VIM are very effective, convenient and quite accurate to nonlinear partial differential equations. These methods can be easily extended to other strongly nonlinear oscillations and can be found widely applicable in engineering and science. The Laplace transform method is applied to obtaining the Lagrange multiplier in the VIM solution. [ABSTRACT FROM AUTHOR]

Laminar mixed convection in a cubic cavity is studied numerically using the multi-relaxation-time (MRT) lattice Boltzmann method (LBM). The sidewalls of the cavity are thermally adiabatic, while the fixed bottom and top moving walls are maintained at uniform temperatures. Simulations are performed for various values of Richardson number (Ri), sliding angle (θ), and Reynolds number (Re). It is revealed that the Nusselt number increases for different values of Reynolds number as the moving lid angle enhances. In addition, the distribution of the local Nusselt number on the bottom wall follows the direction of the moving lid. [ABSTRACT FROM AUTHOR]

In this article, Lattice Boltzmann simulation of turbulent natural convection with large-eddy simulations (LES) in a square cavity, which is filled by water/copper nanofluid, has been investigated. The present results are validated by the consequences of an experimental research at Pr = 0.71 and Ra = 1.58 × 109. Calculations are performed for high Rayleigh numbers (Ra = 107–109), low volume fractions of nanoparticles (0 ≤ ϕ ≤ 0.06), and three aspect ratios (A = 0.5, 1, and 2). In this investigation, we present that large-eddy turbulent nanofluid flow is modeled by the Lattice Boltzmann method (LBM) with a clear and simple statement. Effects of nanopartcles are displayed on streamlines, isotherm counters, local Nusselt number, and average Nusselt number. The average Nusselt number enhances with the augmentation of the nanoparticles volume fractions in the base fluid for multifarious aspect ratios and the Rayleigh numbers. Heat transfer declines with the increase in the aspect ratios in the base fluid, but the effects of nanopaticles are dissimilar for various aspect ratios at different Rayleigh numbers. [ABSTRACT FROM PUBLISHER]

This paper reports experimental studies on the performance of a natural circulation solar water heater considering the weather condition of a city in north of Iran. The tests are done on clear and partly cloudy days. The variations of storage tank temperature due to consumption from the tank, daily consumption influence on the solar water heater efficiency, and on the input temperature of the collector are studied and the delivered daily useful energy has been obtained. The results show that by withdrawing from storage tank, the system as well as its collector efficiency will increase. Considering the value of the coefficient and τα, which are obtained experimentally as 6.03 and 0.83 respectively, average monthly total load that is covered by this solar water heating system is estimated. [ABSTRACT FROM PUBLISHER]

Numerical simulation of natural convection in a nanofluids-filled partitioned square cavity is presented. Two independent solvers, an in-house LBE-BGK code and the commercially available software CFD-ACE, are used to achieve this goal. While the partitioning plates are generating heat at a uniform temperature, the vertical walls are isothermally cooled allowing for the removal of the internally generated heat with the horizontal walls being adiabatic. While the particle volume fraction is kept constant at 5%, the effective Rayleigh number, the length, and the orientation of the partition have been parametrically varied from 103-107, 0.25H-0.75H, and horizontal to vertical, respectively. [ABSTRACT FROM AUTHOR]

In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems. [ABSTRACT FROM AUTHOR]

In this article, He's energy balance method (EBM) is applied to solve Van der Pol damped nonlinear oscillators. Three examples of Van der Pol oscillators are presented and solved by this method to illustrate the effectiveness and convenience of the EBM. In this method, only one iteration leads to high accuracy of the solution. Comparisons are made between EBM results and exact solutions of the problems. The results show that the method can be easily extended to other nonlinear systems and can therefore be found widely applicable in engineering and other science. [ABSTRACT FROM AUTHOR]

In this paper, we study the Benney-Lin equation using He's homotopy perturbation method (HPM) and He's variational iteration method (VIM). We compare HPM and VIM methods and show that the results of the HPM method are in excellent agreement with the results of the VIM method and the obtained solutions are shown graphically. Several cases are considered to apply HPM and VIM, which demonstrate the reliability and efficiency of these two methods in solving such a complicated equation with various initial conditions. [ABSTRACT FROM AUTHOR]

In this research, the flow of kerosene oil with ternary hybrid nanoparticles on a stretchable exponential surface has been investigated. There is also a discussion about the entropy analysis of the flow of hydromagnetic radiation by the surface. The ternary hybrid nanofluid (THyNF) contains graphene oxide (GO), magnesium oxide (MgO), and zinc oxide (ZnO) as nanoparticles and kerosene oil as a base fluid. Using useful transformations, differential equations with partial derivatives (PDEs) were transformed into ordinary differential equations (ODEs). Then, the ODEs were solved using the RK5th method. Furthermore, the impacts of parameters like radiation parameter ($Rd$Rd), porosity parameter ($\lambda $λ), and volume fraction ($\varphi $φ) of THyNF were investigated. Magnetic field (M) and shape factor (SF) on the temperature ($\theta (\eta $θ(η)) and velocity ($f{^{\prime}}\left(\eta \right)$f ′η) profiles have been investigated. Increasing the magnetic field parameter (M) raises the Lorentz force, which produces resistance to fluid flow and reduces fluid velocity ($f{^{\prime}}\left(\eta \right)$f ′η). The temperature profile ($\theta (\eta $θ(η)) rises with increasing magnetic field because the reduced flow rate due to increasing magnetic parameter allows the nanoparticles to transfer more heat. As the nanoparticle volume fraction increases, both the velocity and temperature profiles increase. The effects of M, Rd, SF (shape factor), and $\lambda $λon entropy generation (${S_G}$SG) and Bejan number (Be) have been discussed. Also, the results show that at a fixed value of the magnetic field or the porosity parameter, with the increase in the volume fraction of nanoparticles, the $ - {C_{fx}}Re_x^{{1 \over 2}}$−CfxRex12 rises. At a constant value of the $\varphi $φ value of $N{u_x}Re_x^{ - {1 \over 2}}$NuxRex−12 rises with the increase of the radiation parameter. [ABSTRACT FROM AUTHOR]