Application of differential transformation method (DTM) for heat and mass transfer in a porous channel

Reddy

et al. 2018

Heat Trans. Asian Res.

In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non‐Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non‐Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The nondimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter (β), unsteadiness parameter (A), Prandtl number (Pr), buoyancy parameter (λ). The semi‐analytical differential transform method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built‐in solver “bvp4c” to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter, whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter, whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid), whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness, and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach.

Section: Solution Of the Problemmentioning

confidence: 99%

Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet

Reddy

et al. 2018

Heat Trans. Asian Res.

International Journal of Applied Mechanics and Engineering

“…In [34], authors used the DTM for finding analytical solutions of governing equations of a non-Newtonian fluid flow using an axisymmetric channel and porous wall on turbine disk. The approach was adopted for a cooling application.…”

Section: Dtm In Fluid Mechanics and Heat Transfermentioning

confidence: 99%

A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations

Rashidi

Rabiei

Nia

et al. 2020

In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.

Arab Journal of Basic and Applied Sciences

“…Numerous influential methods have been proposed to investigate the exact travelling wave solutions to nonlinear partial differential equations (NPDEs) of fractional order as well as integer order, as for instance the symmetry group method (El-Shiekh, 2018), the expðÀUðnÞÞ-expansion method (Kaplan & Akbulut, 2018), the direct algebraic method (Seadawy, 2012), the fractional sub-equation method (Alzaidy, 2013;Mohyud-Din, Nawaz, Azhar, & Akbar, 2017;Zhang & Zhang, 2011), the extended direct algebraic method (Seadawy, 2014;Seadawy, 2016a;Seadawy, 2016b), the Adomian decomposition method (El-Sayed, Behiry, & Raslan, 2010;Hu and He, 2016), the variational iteration method (Singh and Kumar, 2017;Tang, Fan, Zhao, & Wang, 2016), the modified extended direct algebraic mapping (Seadawy, 2016c), the auxiliary equation mapping method and direct algebraic mapping method (Seadawy & Lu 2016), the ðG 0 =GÞ-expansion method and its various modifications (Alam & Akbar, 2014;Feng, Li, & Wan, 2011;Islam, Akbar, & Azad, 2017), the amplitude ansatz method (Seadawy & Lu 2017;Seadawy, 2017a), multiple scales methods (Seadawy, 2017b), the homotopy perturbation method (Cherif, Belghaba, & Ziane, 2016;He, 1999), the extended auxiliary equation method (Seadawy, 2017c), the mathematical methods (Seadawy, 2017d). the differential transformation method (Sepasgozar, Faraji, & Valipour, 2017), the extended modified mapping method (Seadawy, 2018), auxiliary equation method (Tariq and Seadawy, 2018), the finite element method (Gao, Sun, & Zhang, 2012;Huang, Huang, & Zhan, 2008), the finite difference method (Li, Chen, & Ye, 2011), the exp-...…”

Section: Introductionmentioning

confidence: 99%

Closed-form travelling wave solutions to the nonlinear space-time fractional coupled Burgers’ equation

Islam

Akbar

Azad

2018

Fractional order nonlinear evolution equations play important roles to give a depiction of the complex physical phenomena of real world. The main aim of this article is to extract exact analytic solutions to the space-time fractional coupled Burgers' equation in the sense of conformable fractional derivative. A suitable composite transformation is implemented to reduce the considered equation into an ordinary differential equation of fractional order. Then a new approach, called the rational fractional ðD a n G=GÞ-expansion method, the Exp-function method and the extended tanh method, is employed to construct the closed-form solutions. This effort makes available the travelling wave solutions in terms of hyperbolic function, trigonometric function and rational function, which are found to be newer and more general than the existing results in the literature. The proposed method is highly efficient and may further be used to invstigate entirely new solutions to many other fractional evolution equations.