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The paper presents an application of the semi‐analytical differential transform method (DTM) to thermofluidics of generalized Couette flow of couple stress fluid inside a composite channel. The channel comprises a fluid‐saturated porous layer and a clear fluid region. The flow is caused by a uniformly favorable pressure gradient applied at the mouth of the channel and the shear of the moving upper wall of the channel. The matching conditions are taken such that the velocity, temperature, and respective gradients are continuous at a clear fluid–porous medium. The problem is novel because this is the first mathematical endeavor to treat fluidic systems involving composite channels. Besides the mathematical rigor, it presents an analysis of thermodynamic irreversibility and other quantities of interest, viz, skin friction and Nusselt number. The results derived from DTM are compared with those obtained by exact solution showing excellent agreement. The plots and tables are drawn and discussed. [ABSTRACT FROM AUTHOR]

The present investigation is intended to follow the characteristics of thermal as well as solutal buoyancy on the flow of non‐Newtonian–Casson nanofluid flow over the exponential stretching sheet embedding with the permeable medium. The interaction of thermal radiation along with the chemical reaction enriches the flow phenomena significantly. These properties are useful due to their recent applications in various industries as well as the biomedical area. The blood flow phenomenon described in the human body is characterized by the use of Casson nanofluid which is helpful for the drug delivery system. The suitable transformation rules are employed for the transformation of the proposed governing equation into ordinary and nonlinear. Furthermore, an approximate analytical approach such as Differential Transform Method is used for the solution of transformed governing equations. The illustration of the physical behavior of the contributing parameters involved in the flow phenomena is presented via graphs and tabular form. [ABSTRACT FROM AUTHOR]

This article focuses on analytic solutions for Newtonian fluid flow with slip and mass transpiration on a porous stretching sheet using the differential transform method and Pade approximants of an exceptionally nonlinear differential equation. The impacts of different parameters including mass transpiration (suction/injection), Navier's slip, and Darcy number parameters on the velocity of the liquid and tangential stress are discussed. A comprehensive comparison of our results with the previous one in the literature is made, and the results showed good agreement. An investigation is conducted of a combination of magnetic liquids that are conceivably pertinent for wound medicines, skin repair, and astute coatings for natural gadgets. It is found that there is a decrease in the velocity profiles and the boundary layer thickness for the case of suction. [ABSTRACT FROM AUTHOR]

A porous fin of longitudinal geometry with different profiles like rectangular, triangular, and convex shapes is considered in the present investigation. The totally wet condition under the existence of natural convection and radiation has been examined. In addition, the generation of thermal‐dependent internal heat is studied. The analysis also concentrates on the material of the fin. Here, the fin made up of aluminum and copper metal is taken for scrutinization. The derived ordinary differential equation was solved by the differential transform method. The obtained consequences have been graphically interpreted. It is determined that the fin made up of aluminum material dissipates more heat than the copper material fin. [ABSTRACT FROM AUTHOR]

In this study, a deterministic mathematical model involving the transmission dynamics of Japanese encephalitis (JE) is presented and studied. The biologically feasible equilibria and their stability properties have been discussed. This study investigates a series of solutions to the system of ordinary differential equations (ODEs) in the transmission dynamics of JE. To get approximate series solutions of the JE model, we employed the differential transform method (DTM) and variational iteration method (VIM). DTM utilizes the transformed function of the original JE model, while VIM uses the general Lagrange multiplier to develop the correction functional for the JE model. The results show that the VIM solution is more accurate than the DTM solution for short intervals of time. In addition, the fractional compartmental model of JE is briefly discussed. We illustrated the profiles of the solutions of each of the compartments, from which we found that the fourth‐order Runge–Kutta method solutions are more accurate than the DTM and VIM solutions for long intervals of time. [ABSTRACT FROM AUTHOR]

Multilayer fluid flow models are significant in various applications, namely, cooling electronic systems, solar thermal systems, and nuclear reactors. The density of a fluid fluctuates nonlinearly due to large temperature difference circumstances in thermal systems. Thus, the linear Boussinesq approximation is no longer relevant. Therefore, this article describes a multilayer flow of nanoliquids in the presence of nonlinear Boussinesq approximation. The hybrid nanoliquid layer is sandwiched between two nanoliquid layers. The single‐phase khanafer‐vafai‐lightstone model is implemented to simulate the nanoliquids. The quadratic density temperature fluctuation and viscous heating are taken into account. The temperature and velocity across the interface are assumed to be continuous. The equations that govern the problem are solved analytically by using the differential transformation method. The results show that the presence of a hybrid nanoliquid layer affects the velocity and heat transfer properties of the nanofluid flow. Hybrid nanofluid can be used to achieve the desired multilayer flow properties of a nanofluid and its heat transfer properties. Further, the quadratic convection aspect increases the velocity distributions. [ABSTRACT FROM AUTHOR]

The differential transform method (DTM) is a simple technique based on the Taylor series. Applying the DTM, a given linear boundary eigenvalue problem (BEVP) involving ordinary differential equations is converted into a recurrence relation or a system of recurrence relations for the Taylor coefficients. This ultimately leads to the solution of the problem in the form of an infinite power series with an appropriate region of convergence. The present paper aims to apply the DTM in solving a BEVP arising from the Darcy–Brinkman convection in a rectangular box subject to general boundary conditions whose vertical sidewalls are assumed to be impermeable and adiabatic. The non‐dimensional temperature difference between the plates represented by the Darcy–Rayleigh number, the eigenvalue of the problem, is obtained as a function of the width of the Bénard cell (2πb : b is the horizontal wave number) and other parameters using the DTM. The work includes investigation on the convergence of the series solution. The solution by the DTM is compared with that obtained by the MATLAB bvp4c routine and excellent agreement is found thereby establishing the accuracy of the DTM. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic (MHD) materials processing is becoming increasingly popular in the 21st century as it offers significant advantages over conventional systems, including improved manipulation of working fluids, reduction in wear, and enhanced sustainability. Motivated by these developments, the present work develops a mathematical model for Hall and ion‐slip effects on non‐Newtonian Casson fluid dynamics and heat transfer toward a stretching sheet with a convective heating boundary condition under a transverse magnetic field. The governing conservation equations for mass, linear momentum, and thermal (energy) are simplified with the aid of similarity variables and Ohm’s law. The emerging nonlinear‐coupled ordinary differential equations are solved with an analytical technique known as the differential transform method. The impact of different emerging parameters is presented and discussed with the help of graphs and tables. Generally, aqueous electroconductive polymers are considered, for which a Prandtl number of 6.2 is employed. With increasing Hall parameter and ion‐slip parameter, the flow is accelerated, whereas it is decelerated with greater magnetic parameter and rheological (Casson) fluid parameter. Skin friction is also decreased with greater magnetic field effect, whereas it is increased with stronger Hall parameter and ion‐slip parameter values. [ABSTRACT FROM AUTHOR]

In this paper, the steady fully developed non-Darcy mixed convection flow of a nanofluid in a vertical channel filled with a porous medium with different viscous dissipation models is analyzed. The Brinkman-Forchheimer extended Darcy model is used to describe the fluid flow pattern in the channel. The transport equations for a nanofluid are solved analytically using the seminumerical-analytical method known as differential transformation method, and numerically with the Runge-Kutta shooting method. Finally, the influence of pertinent parameters, such as solid volume fraction, different nanoparticles, mixed convection parameter, Brinkman number, Darcy number, and inertial parameter on the velocity and temperature fields are shown graphically. The results show that velocity and temperature are enhanced when the mixed convection parameter, Brinkman number, and Darcy number increases whereas solid volume fraction and inertial parameter decreases the velocity and temperature fields. The obtained results show that the nanofluid enhances the heat transfer process significantly. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a novel computational approach to generate the suboptimal solutions for a class of nonlinear optimal control problems (OCP's) with a quadratic performance index. Our method is based on the one-dimensional differential transform method (DTM) and new polynomials that are called DT's polynomials. This method simplifies the difficulties and massive computational work for calculating the differential transform of nonlinear function. The convergence of proposed method are discussed in detail. This method consists of a new modified version of the DTM together with a shooting method such as procedure, for solving the extreme conditions obtained from the Pontryagin's maximum principle. The results reveal that the proposed methods are very effective and simple. Comparisons are made between new DTM generated results, results from literature, and MATLAB bvp4c generated results, and good agreement is observed. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, coupled nonlinear equations governing the flow for magnetoconvection in a vertical channel for open and short circuits are solved. The calculations are carried out by using differential transformation method (DTM) which is a semi-numerical-analytical solution technique. By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related initial conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced, and then applied for the aforementioned problems. The current results are then compared with those derived from the finite difference method (FDM) and perturbation method (PM) in order to verify the accuracy of the proposed method. The findings reveal that the DTM can achieve more suitable results in predicting the solution of such problems. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21035 [ABSTRACT FROM AUTHOR]

This study investigates the boundary-layer flow and heat transfer characteristics in a second-grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM-Padé. The DTM-Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary-layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM-Padé with numerical solution (fourth-order Runge-Kutta with shooting method) illustrates that the DTM-Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030 [ABSTRACT FROM AUTHOR]

The free vibration analysis of semi-rigid-connected Reddy-Bickford beams on elastic soil with/without axial force effect using the differential transform method (DTM) and the differential quadrature element method (DQEM) has not been investigated by any of the studies in the open literature so far. In this study, DTM and the recently proposed DQEM are employed in order to solve the governing differential equations of a Reddy-Bickford beam with two regions on elastic soil. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. An efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The equilibrium equations are deduced, together with the boundary conditions, and then a recently proposed DQEM is employed, in order to solve the resulting boundary value problem. The calculated natural frequencies of semi-rigid-connected Reddy-Bickford beam with two regions on elastic soil using DTM and DQEM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]