Analytical investigation of laminar flow through expanding or contracting gaps with porous walls

AbstractLaminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is investigated analytically using optimal homotopy asymptotic method (OHAM). OHAM is a powerful method for solving nonlinear problems without depending to the small parameter. The concept of this method is briefly introduced, and it׳s application for this problem is studied. Then, the results are compared with numerical results and the validity of these methods is shown. After this verification, we analyze the effects of some physical applicable parameters to show the efficiency of OHAM for this type of problems. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate (α) and permeation Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels

Optimal homotopy asymptotic and homotopy perturbation methods for linear mixed volterra-fredholm ıntegral equations

Bu çalışmada, karma Volterra-Fredholm integral denklemleri optimal homotopi asimptotik metod (OHAM) ve Homotopi Perturbasyon metodu (HPM) vasıtasıyla irdelenmiştir. Yaklaşımımız zamandan bağımsız ve basit hesaplamalar yolu ile tam çözüme oldukça yaklaşık çözümler veren bir yöntemdir. Bu iki yöntemin karşılaştırılması tartışılmıştır. OHAM yaklaşımının doğruluğu ve etkinliği HPM çözümleri ile dört örnek kullanılarak karşılaştırılmıştır. Sonuçlar OHAM ın HPM ye göre daha verimli ve esnek bir yöntem olduğunu göstermektedir.In this paper, we study the mixed Volterra-Fredholm integral equations of the second kind by means of optimal homotopy asymptotic method (OHAM) and Homotopy Perturbation method (HPM).Our approach is independent of time and contains simple computations with quite acceptable approximate solutions in which approximate solutions obtained by these methods are close to exact solutions. Comparison of these methods have been discussed. The accuracy and efficiency of OHAM approach with respect to Homotopy Perturbation method (HPM) is illustrated by presenting four test examples. The results indicate that the OHAM is very effective and flexible to use with respect to HPM

Multistage optimal homotopy asymptotic method for solving initial-value problems

In this paper, a new approximate analytical algorithm namely multistage optimal homotopy asymptotic method (MOHAM) is presented for the first time to obtain approximate analytical solutions for linear, nonlinear and system of initial value problems (IVPs).This algorithm depends on the standard optimal homotopy asymptotic method (OHAM), in which it is treated as an algorithm in a sequence of subinterval. The main advantage of this study is to obtain continuous approximate analytical solutions for a long time span.Numerical examples are tested to highlight the important features of the new algorithm.Comparison of the MOHAM results, standard OHAM, available exact solution and the fourth-order Runge Kutta (RK4) reveale that this algorithm is effective, simple and more impressive than the standard OHAM for solving IVPs