Solution of the Boundary Layer Equation of the Power-Law Pseudoplastic Fluid Using Differential Transform Method

Abstract

The boundary layer equation of the pseudoplastic fluid over a flat plate is considered. This equation is a boundary value problem (BVP) with the high nonlinearity and a boundary condition at infinity. To solve such problems, powerful numerical techniques are usually used. Here, through using differential transform method (DTM), the BVP is replaced by two initial value problems (IVP) and then multi-step differential transform method (MDTM) is applied to solve them. The differential equation and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated in every sub domain. In this solution, there is no need for restrictive assumptions or linearization. Finally, DTM results are compared with the numerical solution of the problem, and a good accuracy of the proposed method is observed.

Investigation of the viscoelastic flow and species diffusion in a porous channel with high permeability

“…The components of the Jacobian matrix in Eq. (21) can be computed by differentiating analytically with respect to a 1 to a 3 and then substituting (a 1 , a 2 , a 3 ) n in that equation. …”

“…He used this method to derive the semi analytical solution for the electrical circuit analysis. A considerable amount of researches have been done using DTM to investigate the solution of linear differential algebraic equations [19], nonlinear ordinary differential equations [20][21][22][23][24], partial differential equations [25], fractional differential equations [26] and integral equations [27]. DTM is a powerful and simple technique which is well known as a high accurate technique for solving the differential equations.…”

A numerical solution of a singular boundary value problem arising in boundary layer theory

“…This problem arises in the study of laminar boundary layers exhibiting similarity in fluid mechanics. The solutions of the one-dimensional third-order boundary-value problem described by the Falkner–Skan equation are the similarity solutions of the two-dimensional incompressible laminar boundary layer equations (Cheng 1977 ; Merkin 1980 ; Salama 2004 ; Postelnicu and Pop 2011 ; Mosayebidorcheh 2013 ).…”

A new algorithm based on differential transform method for solving multi-point boundary value problems

“…Secondly, those works [22,37,45] which aim to improve the accuracy of the DTM have extended the applications of this method. Actually, in the past 40 years, the DTM and its modifications have been successfully applied to solve various differential equations [6,14,17,22,37,38,40,45,51], difference equations [3], differential-difference equations [4], integral equations [5,44,50] and integrodifferential equations [2,5]. The DTM has also been successfully applied to a large number of practical problems.…”