New applications of approximate methods in fluid mechanics

Abstract

In this paper, we have modeled boundary layer flows induced by continuous stretched surfaces by implementing one of the newest analytical methods of solving nonlinear differential equations called homotopy analysis method (HAM), which gives us a vast freedom to choose the answer type. We have used an iterating analytical method to cope with the nonlinearity. A new adapting boundary condition is proposed in this work that is based on an initial guess and then it is developed to the solution expression. The analytic results are compared with the numerical solution (NS) and the comparison reveals that a good agreement exists between the NS and HAM solution. Also the convergence of the obtained HAM solution is discussed explicitly. The obtained approximate solutions are valid for all values of the dimensionless parameter β, as it is shown later in the paper. 

The flow of a micropolar fluid through a porous channel with expanding or contracting walls

“…When α = 0, this is the special case discussed by Ziabakhsh and Domairry [28], Joneidi et al [29], Takhar et al [30].…”

“…Kelson and Farrell [27] analyzed the flow of a micropolar fluid over a stretching sheet with strong suction or injection. Ziabakhsh and Domairry [28], Joneidi et al [29] discussed the micropolar fluid in a porous channel by homotopy analysis method (HAM). However, very little reports were found in literature for micropolar fluids with expanding or contracting walls.…”

A Novel Approximation Approach for the Analytical Solution of the Flow of Micropolar Fluid Through a Permeable Channel

“…Similarly, Abdulaziz et al (2009) used the homotopy analysis method to study a fully developed micropolar fluid flow between vertical plates under the influence of a magnetic field. A homotopy analysis approach solution has been applied by Ziabakhsh and Domairry (2008) to micropolar fluid flow in a porous channel with mass transfer in a permeable channel separated by parallel plates. A comparative study of the acquired results and those found in the literature revealed very good agreement.…”

Magnetohydrodynamic flow of linear visco-elastic fluid model above a shrinking/stretching sheet: A series solution

“…It has been shown by many authors that this method provides improvements to the existing numerical techniques. Considerable research [23][24][25][26][27][28][29][30] has been recently conducted on applying this method to a wide class of linear and nonlinear equations. However, to the best of the author's knowledge, no one has studied the MHD ow of a linear visco-elastic uid above a shrinking/stretching sheet by means of homotopy perturbation method.…”