In this paper, we extend variational iteration method (VIM) to find approximate solutions of linear and nonlinear thirteenth order differential equations in boundary value problems. The method is based on boundary valued problems. Two numerical examples are presented for the numerical illustration of the method and their results are compared with those considered by [1,2]. The results reveal that VIM is very effective and highly promising in comparison with other numerical methods.

No abstract

This work investigates the mixed convection in a Magnetohydrodynamic (MHD) flow and heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the fourth order Runge-Kutta method with shooting technique. The influence of pertinent flow parameters on velocity, temperature, surface drag force and heat transfer rate are computed and analyzed. Graphical and tabular results are given to examine the nature of the problem. The heat transfer rate at the surface increases with the mixed convection.

This work investigates the mathematical model and solution for an unsteady MHD fourth grade fluid flow over a vertical plate in a porous medium with the effects of the magnetic field and suction/injection parameters using Homotopy Perturbation Method. The flow is considered to satisfy the constitutive equations of fourth grade fluid flow model and because of the Homotopy Perturbation Method used, only the momentum equation with initial and boundary conditions are solved as governing equations. After initializing stability test, the convergence of the governing equations are observed graphically using the results of Homotopy Perturbation Method with the new analytical method used by Yurusoy in literature and there is a perfect agreement in results. The impact of dimensionless second, third and fourth grade parameters with the effects of magnetic field and suction/injection parameters on the velocity field are displayed graphically and discussed. Increase in suction parameter decreases the momentum boundary layer thickness while injection parameter enhances velocity distribution in the boundary layer. Magnetic field reduces velocity throughout the boundary layer because the Lorentz force which acts as retarding force reduces the boundary layer thickness.

This investigation addresses the influence of a buoyancy force on the flow of a couple stress hydromagnetic heat generating fluid across a porous channel with isothermal boundaries. The analytical formulations for the momentum and energy equations are derived to seek the solutions for the rate of fluid momentum, heat transfer and the rate of entropy generation with the use of a well known and efficient series solution of Adomian decomposition method (ADM). The findings are compared with earlier acquired findings for validation and hereby showed the speedy convergence of the series solution. The results showed the substantial influence of inward warmth inside the stream and buoyancy force on the motion and thermal energy of the flow system. Also, the activities of entropy generation generally occur maximally at the centreline of the flow stream with significant reduction with respect to buoyancy force and magnetic field strength.

No abstract

This work investigates the effects of radiation and Eckert number on an MHD flow with heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the sixth order Runge-Kutta method with shooting technique. Tabular and graphical results are provided to examine the physical nature of the problem. Heat transfer rate at the surface decreases with radiation, Eckert number and as radiation increases, the flow temperature also increases for velocity ratio parameters ɛ <1 and ɛ >1.

This research work examines the influence of thermal radiation on the flow of a reactive hydromagnetic couple stress fluid flowing through a passable channel under the drive of heat source. The analytical expressions for the momentum and heat transfer are obtained to find the entropy generation rate using the modified Adomian decomposition method (mADM). The results are correlated with previously obtained results in the bid to ascertain and verity the efficacy of the mADM and mostly for end users to be able to predict the safe and unsafe situations. In addition to that, the effects of thermal radiation and other thermophysical parameters on fluid motion, energy transfer and rate of entropy generation are shown and discussed in tables and graphs.