Abstract
In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.
Highlights
A number of industrially important fluids such as molten plastics, polymer solutions, pulps, foods and slurries, fossil fuels, special soap solutions, blood, paints, certain oils and greases display a rheologically-complex non-Newtonian fluid behavior
It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable
The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM)
Summary
A number of industrially important fluids such as molten plastics, polymer solutions, pulps, foods and slurries, fossil fuels, special soap solutions, blood, paints, certain oils and greases display a rheologically-complex non-Newtonian fluid behavior. The non-linearity nature of the equations comes from the constitutive equations which represents the material properties of rheological fluids. Boundary-layer flows of non-Newtonian fluids have been of great interest to researchers during the past three decades. Non-linear initial-value problems in electric circuit analysis This method constructs, for differential equations, an analytical solution in the form of a polynomial. Not like the traditional high-order Taylor series method that requires symbolic computation, the DTM is an iterative procedure for obtaining Taylor series solutions [12,13] Against these advantages, the DTM solutions diverge for some highly non-linear differential equations that have boundary conditions at infinity [14].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
