Sharif Digital Repository

The analytical approximate solution of a non-linear jet impingement flow model will be demonstrated. We will show that this is an improvement over the series approximation obtained via the Adomian decomposition method, which is itself, a powerful method for analysing non-linear differential equations. The results of these approximations will be compared to the Runge-Kutta approximation in order to demonstrate their validity  

This paper considers a repair-replacement strategy for a special class of discretely degrading and repairable products under renewing free replacement warranty. Each product may experience N different working states with different exponential hazard functions, before the warranty contract expires. Once the item enters working state i (i = 1,2, ⋯ ,N), it can either fail or move to any of the subsequent working states with different probabilities, given that a transition has been made. In the former case, the best rectification action, replacement or minimal repair, regarding the failure status, i.e., the product degradation level at the failure time and the remaining warranty time, should be... 

In this paper a replacement-repair model is developed to study a renewing free replacement warranty (RFRW) for a class of multi-state deteriorating repairable products. After a replacement, the product warranty is renewed. Two parameters affect the manufacturer's decision to minimally repair or replace a failed item: the product deterioration level at the time of failure and the remaining warranty time. We derive an optimal replacement-repair policy to minimise the expected warranty servicing cost per item sold. In the case of a product with two different working states, we are able to explicitly find the optimal values of the replacement-repair parameters using the Adomian decomposition... 

In this paper, modified Adomian decomposition (MAD) is introduced to investigate the effect of the Casimir attraction on pull-in instability of beam-type NEMS theoretically. Two engineering cases including cantilever and double cantilever nano-beam are considered. The proposed MAD method is employed to solve the nonlinear constitutive equation of nano-beams. The basic engineering parameters such as critical deflection and pull-in voltage of nano-beams are computed. It is found that the Casimir forces decrease the pull-in deflection and voltage of nano-beams. On the other hand, the fringing field increases the pull-in deflection while decreases the pull-in voltage of the actuators. As a... 

The Adomian Decomposition Method is employed in the solution of the two dimensional laminar boundary layer of Falkner-Skan equation for wedge. This work aims at the solution of momentum equation in the case of accelerated flow and decelerated flow with separation. The Adomian Decomposition Method is provided an analytical solution in the form of an infinite power series. The effect of Adomian polynomials terms is considered on accuracy of the results. The velocity profiles in boundary layer are obtained. Results show a good accuracy compared to the exact solution. © 2007 Elsevier B.V. All rights reserved  

The Adomian Decomposition Method (ADM) for solving the highly non-linear vorticity-stream function formulation of 2D incompressible Navier-Stokes equations has been implemented. The analysis is accompanied by numerical boundary conditions. Also, numerical simulation, using finite difference method (FDM), is performed for comparison purposes. The obtained results only for few terms of the expansion are presented. Because present software such as Mathematica/Maple can not calculate many terms (for example: up to 10 terms) of solution and then ADM approach of this problem is an open problem case  

Adomian decomposition method has been applied to evaluate the conduction-convection heat transfer through a straight fin, property distribution due to convection-diffusion, and conduction heat transfer through a slab with temperature dependent thermal conductivity. The Adomian decomposition method (ADM), provides the closed form solution of the non-linear problems without applying any non-realistic simplifications and/or approximations. The obtained analytical solutions are compared with exact and numerical solutions, using finite volume method. It is shown that the numerical simulation has some limitations and may not always produce correct results. However, the Adomian decomposition method... 

The Adomian decomposition method (ADM) can provide analytical approximation or approximated solution to a rather wide class of nonlinear (and stochastic) equations without linearization, perturbation, closure approximation, or discretization methods. In the present work, ADM is employed to solve the momentum and energy equations for laminar boundary layer flow over flat plate at zero incidences with neglecting the frictional heating. A trial and error strategy has been used to obtain the constant coefficient in the approximated solution. ADM provides an analytical solution in the form of an infinite power series. The effect of Adomian polynomial terms is considered and shows that the... 

This paper investigates the effect of dispersion (van der Waals and Casimir) forces on the pull-in instability of cantilever nano-actuators by considering their range of application. Adomian decomposition is introduced to obtain an analytical solution of the distributed parameter model. Dispersion forces decrease the pull-in deflection and voltage of a nano-actuator. However, the fringing field increases the pull-in deflection while decreasing the pull-in voltage of the actuator. The minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to van der Waals and Casimir attractions were determined. Furthermore, the proposed approach is capable of...