Search

A linear stability analysis has been carried out to examine the effect of internal heat source on the onset of Rayleigh–Bénard convection in a rotating nanofluid layer with double diffusive coefficients, namely, Soret and Dufour, in the presence of feedback control. The system is heated from below and the model used for the nanofluid layer incorporates the effects of thermophoresis and Brownian motion. Three types of bounding systems of the model have been considered which are as follows: both the lower and upper bounding surfaces are free, the lower is rigid and the upper is free, and both of them are rigid. The eigenvalue equations of the perturbed state were obtained from a normal mode analysis and solved using the Galerkin method. It is found that the effect of internal heat source and Soret parameter destabilizes the nanofluid layer system while increasing the Coriolis force, feedback control, and Dufour parameter helps to postpone the onset of convection. Elevating the modified density ratio hastens the instability in the system and there is no significant effect of modified particle density in a nanofluid system. [ABSTRACT FROM AUTHOR]

The buoyant Marangoni convection heat transfer in a differentially heated cavity is numerically studied. The cavity is filled with water-Ag, water-Cu, water-AlO, and water-TiO nanofluids. The governing equations are based on the equations involving the stream function, vorticity, and temperature. The dimensionless forms of the governing equations are solved by the finite difference (FD) scheme consisting of the alternating direction implicit (ADI) method and the tri-diagonal matrix algorithm (TDMA). It is found that the increase in the nanoparticle concentration leads to the decrease in the flow rates in the secondary cells when the convective thermocapillary and the buoyancy force have similar strength. A critical Marangoni number exists, below which increasing the Marangoni number decreases the average Nusselt number, and above which increasing the Marangoni number increases the average Nusselt number. The nanoparticles play a crucial role in the critical Marangoni number. [ABSTRACT FROM AUTHOR]

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper. The rotating enclosure is filled with water-Ag, water-Cu, water-Al2O3, or water-TiO2 nanofluids. The governing equations are in velocity, pressure, and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the solid volume fraction, 0.0 = ɸ = 0.05, and the rotational speeds, 3.5 = Ω = 17.5 rpm, and the centrifugal force is smaller than the Coriolis force and both forces were kept below the buoyancy force. It is found that the angular locations of the local maximums heat transfer were sensitive to rotational speeds and nanoparticles concentration. The global quantity of heat transfer rate increases about 1.5%, 1.1%, 0.8%, and 0.6% by increasing 1% ɸ of the nanoparticles Ag, Cu, Al2O3, and TiO2, respectively, for the considered rotational speeds. [ABSTRACT FROM AUTHOR]

This investigation reports the magnetic field effect on natural convection heat transfer in a curved-shape enclosure. The numerical investigation is carried out using the control volume-based-finite element method (CVFEM). The numerical investigations are performed for various values of Hartmann number and Rayleigh number. The obtained results are depicted in terms of streamlines and isotherms which show the significant effects of Hartmann number on the fluid flow and temperature distribution inside the enclosure. Also, it was found that the Nusselt number decreases with an increase in the Hartmann number. [ABSTRACT FROM AUTHOR]

Abstract: An adaptive Legendre–Gauss–Radau collocation method is presented for solving time-varying delay systems. By dividing the domain of the problem into a uniform mesh, the delay system is replaced with a sequence of initial value problems. The method developed in this paper adjusts both the mesh spacing and the degree of the polynomial on each mesh interval in order a specified error tolerance is satisfied. We investigate some error estimates on the whole domain of interest. Some numerical examples are given and comparisons with other methods are made to demonstrate the efficiency and accuracy of the proposed method. [Copyright &y& Elsevier]

Effects of a conductive wall on natural convection in a square porous enclosure having internal heating at a rate proportional to a power of temperature difference is studied numerically in this article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (0 ≤ Ra ≤ 1000), the internal heating and the local exponent parameters (0 ≤ γ ≤ 5), (1 ≤ λ ≤ 3), the wall to porous thermal conductivity ratio (0.44 ≤ Kr ≤ 9.9) and the ratio of wall thickness to its width (0.02 ≤ D ≤ 0.5). The results are presented to show the effect of these parameters on the fluid flow and heat transfer characteristics. It is found a strong internal heating can generate significant maximum fluid temperature more than the conductive solid wall. Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. It is also found that at very low Rayleigh number, the heat transfer across the porous enclosure remain stable for any values of the thermal conductivity ratio. [ABSTRACT FROM AUTHOR]

In this paper, a non-standard finite difference scheme is proposed for solving a steady finite Rayleigh number convection in a porous cavity with an inclined magnetic field and non-uniform internal heating. Numerical results are compared with the classical finite difference scheme. [ABSTRACT FROM AUTHOR]

Transient natural convection in a square cavity filled with a porous medium is studied numerically. The cavity is assumed heated from one vertical wall and cooled at the top, while the other walls are kept adiabatic. The governing equations are solved numerically by a finite difference method. The effects of Rayleigh number on the initial transient state up to the steady state are investigated for Rayleigh number ranging from 10 to 2 x 10². The evolutions of flow patterns and temperature distributions were presented for Rayleigh numbers, Ra = 10² and 10³. It is observed that the time taken to reach the steady state is longer for low Rayleigh number and shorter for high Rayleigh number. [ABSTRACT FROM AUTHOR]

Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method MHPM is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method HPM. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta RK4 solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations. [ABSTRACT FROM AUTHOR]

The natural convection in an inclined porous square cavity is investigated numerically. The left wall is assumed to have spatial sinusoidal temperature variations about a constant mean value, while the right wall is cooled. The horizontal walls are considered adiabatic. A finite difference method is used to solve numerically the nondimensional governing equations. The effects of the inclination angle of the cavity, the amplitude and wave numbers of the heated sidewall temperature variation on the natural convection in the cavity are studied. The maximum average Nusselt number occurs at different wave number. It also found that the inclination could influence the Nusselt number. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the non-standard finite difference method (for short NSFD) is implemented to study the dynamic behaviors in the fractional-order Rössler chaotic and hyperchaotic systems. The Grünwald–Letnikov method is used to approximate the fractional derivatives. We found that the lowest value to have chaos in this system is 2.1 and hyperchaos exists in the fractional-order Rössler system of order as low as 3.8. Numerical results show that the NSFD approach is easy to implement and accurate when applied to differential equations of fractional order. [Copyright &y& Elsevier]

Abstract: Features of nonlinear dynamics of thermal convection in an electrically conducting fluid layer heated from below and cooled from above subjected to a constant magnetic field are studied theoretically. The Galerkin truncated approximation is employed to derive a low dimensional Lorenz-like model. Numerical analysis was performed to examine the influence of magnetic field on the phase space trajectory of various chaotic regimes. The result indicates that it is possible to suppress or enhance the chaotic convection. [Copyright &y& Elsevier]

Abstract: In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chen system. We shall call this technique as the multistage HPM (for short MHPM). In particular we look at the accuracy of the HPM as the Chen system changes from a nonchaotic system to a chaotic one. Numerical comparisons between the MHPM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear chaotic and nonchaotic systems of ODEs. [Copyright &y& Elsevier]

The aim of this paper is to investigate the accuracy of the Adomian decomposition method (ADM) for solving the hyperchaotic Chen system, which is a four-dimensional system of ODEs with quadratic nonlinearities. Comparisons between the decomposition solutions and the fourth order Runge–Kutta (RK4) solutions are made. We look particularly at the accuracy of the ADM as the hyperchaotic Chen system has higher Lyapunov exponents than the hyperchaotic Rössler system. A comparison with the hyperchaotic Rössler system is given. [ABSTRACT FROM AUTHOR]

Abstract: The problem of unsteady natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner circular cylinder is studied in this paper. The cylinder temperature is assumed to vary sinusoidally with time about a fixed mean temperature. The coupled momentum and energy equations have been solved numerically over a wide range of values of the amplitude and the frequency of the source temperature signal, as well as the source radius. It is found that the heat transfer rate tends to increase by oscillating the source temperature signal. The maximum heat transfer augmentation was obtained for frequency between 25π and 30π for a high amplitude and a moderate source radius. [Copyright &y& Elsevier]

Abstract: Heat transfer enhancement utilizing nanofluids in a trapezoidal enclosure is investigated for various pertinent parameters. Transport equations are modelled by a stream-vorticity formulation and solved numerically by finite difference approach. The inclined sloping boundaries is treated by adopting staircase-like zigzag lines. Based upon the numerical predictions, the effects of Grashof number, inclination angle of the sloping wall, volume fraction of nanoparticles on flow and temperature patterns as well as the heat transfer rate within the enclosure are presented. Water–Cu and water–Al2O3 nanofluids were tested. We found that acute sloping wall and Cu nanoparticles with high concentration are effective to enhance the rate of heat transfer. We also developed a new correlation for the average Nusselt number as a function of the angle of the sloping wall, effective thermal conductivity and viscosity as well as Grashof number. [ABSTRACT FROM AUTHOR]

Abstract: A basic enzyme kinetics is used to test the effectiveness of an analytical method, called the variational iteration method (VIM). This enzyme–substrate reaction is formed by a system of nonlinear ordinary differential equations. We shall compare the classical VIM against a modified version called the multistage VIM (MVIM). Additional comparison will be made against the conventional numerical method, Runge–Kutta (RK4)(fourth-order). Numerical results were obtained for these three methods and we found that MVIM and RK4 are in excellent conformance. [Copyright &y& Elsevier]

Abstract: This article discusses the effectiveness of a fresh analytical method in solving a prey–predator problem, which is described as a system of two nonlinear ordinary differential equations. The method of interest is the multistage variational iteration method (MVIM), which provides a slight modification of the classical variational iteration method (VIM). We shall compare solutions of the classical VIM along with MVIM and match them against the conventional numerical method, Runge–Kutta (RK4) (fourth-order). [Copyright &y& Elsevier]

Abstract: In this Letter, variational iteration method (VIM) is applied to obtain approximate analytical solution of the sine-Gordon equation without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient. [Copyright &y& Elsevier]

Abstract: This paper applies the variational iteration method to multispecies Lotka–Volterra equations. Comparisons with the Adomian decomposition and the fourth-order Runge–Kutta methods show that the variational iteration method is a powerful method for nonlinear equations. [Copyright &y& Elsevier]

Abstract: By means of variational iteration method the solution of generalized Huxley equation are obtained, comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, He’s variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials. [Copyright &y& Elsevier]

Abstract: In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald–Letnikov discretization process which is easily implemented and reliably accurate. [Copyright &y& Elsevier]

• Galerkin weighted residual finite-element method was applied to solve the dimensionless governing equations subject to the boundary conditions. • The two-phase nanofluid model is utilized for modelling the nanofluid heat transfer within the wavy-walled cavity. • Comparisons with previously experimental and numerical published works verify good agreement with the proposed method. • The effects of central solid cylinder, uniform magnetic field, Brownian diffusion of nanoparticles and thermophoresis were explained. Control of energy transport and convective liquid circulation is a challenge in various engineering devices. Solution to this major problem can be obtained by different techniques such as magnetic field impact, irregular shape of the walls, internal solid obstacles, nanoliquids, moving walls and so on. The current study is devoted to a numerical analysis of nanoliquid mixed convective circulation and thermal transmission within a lid-driven wavy chamber with a central solid cylinder in the presence of a uniform magnetic influence, Brownian diffusion of nanoparticles and thermophoresis effects. The governing equations are formulated by employing the conservation laws in dimensionless form and the results are calculated by the finite-element method. Validations with experimental/numerical data are accomplished which lend confidence in the numerical data of the existing code. Analysis of the nanoliquid circulation and energy transport is conducted for a wide range of control parameters. It has been revealed that the augmentation of nano-sized particles enhances the overall energy transport in the case of low Reynolds number. [ABSTRACT FROM AUTHOR]