scholarly journals Analysis of Transient Thermal Distribution in a Convective–Radiative Moving Rod Using Two-Dimensional Differential Transform Method with Multivariate Pade Approximant

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1793
Author(s):  
Ganeshappa Sowmya ◽  
Ioannis E. Sarris ◽  
Chandra Sen Vishalakshi ◽  
Ravikumar Shashikala Varun Kumar ◽  
Ballajja Chandrappa Prasannakumara
Keyword(s):  
Heat Generation ◽  
Padé Approximant ◽  
Differential Transform Method ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
Transform Method ◽  
Pade Approximant ◽  
Differential Transform ◽  
Transient Thermal

The transient temperature distribution through a convective-radiative moving rod with temperature-dependent internal heat generation and non-linearly varying temperature-dependent thermal conductivity is elaborated in this investigation. Symmetries are intrinsic and fundamental features of the differential equations of mathematical physics. The governing energy equation subjected to corresponding initial and boundary conditions is non-dimensionalized into a non-linear partial differential equation (PDE) with the assistance of relevant non-dimensional terms. Then the resultant non-dimensionalized PDE is solved analytically using the two-dimensional differential transform method (2D DTM) and multivariate Pade approximant. The consequential impact of non-dimensional parameters such as heat generation, radiative, temperature ratio, and conductive parameters on dimensionless transient temperature profiles has been scrutinized through graphical elucidation. Furthermore, these graphs indicate the deviations in transient thermal profile for both finite difference method (FDM) and 2D DTM-multivariate Pade approximant by considering the forced convective and nucleate boiling heat transfer mode. The results reveal that the transient temperature profile of the moving rod upsurges with the change in time, and it improves for heat generation parameter. It enriches for the rise in the magnitude of Peclet number but drops significantly for greater values of the convective-radiative and convective-conductive parameters.

Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties

2016 ◽  
Vol 71 (2) ◽  
pp. 185-193
Author(s):  
Ryoichi Chiba
Keyword(s):  
Natural Convection ◽  
Special Functions ◽  
Vertical Tube ◽  
Differential Transform Method ◽  
Transient Temperature ◽  
Temperature Dependent ◽  
Transform Method ◽  
Recursive Procedure ◽  
Transient Natural Convection ◽  
Differential Transform

AbstractThe transient natural convection of a viscous fluid in a heated vertical tube is studied using the two-dimensional differential transform method (DTM). A time-dependent Dirichlet boundary condition is imposed for tube wall temperature. The partial differential equations for the velocity and temperature fields within the tube are solved by the DTM while considering temperature-dependent viscosity and thermal conductivity of the fluid. As a result, tractable solutions in double-series form are derived for the temperature and flow velocity. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical results illustrate the effects of temperature-dependent properties on transient temperature and flow behaviour, including the Nusselt number and volumetric flow rate. The DTM gives accurate series solutions without any special functions for nonlinear transient heat transfer problems which are advantageous in finding the derivative or integral.

scholarly journals Using Differential Transform Method and Padé Approximant for Solving MHD Flow in a Laminar Liquid Film from a Horizontal Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Mohammad Mehdi Rashidi ◽  
Mohammad Keimanesh
Keyword(s):  
Liquid Film ◽  
Mhd Flow ◽  
Padé Approximant ◽  
Differential Transform Method ◽  
Stretching Surface ◽  
Transform Method ◽  
Boundary Layer Equations ◽  
Pade Approximant ◽  
Differential Transform ◽  
Padé Method

The purpose of this study is to approximate the stream function and temperature distribution of the MHD flow in a laminar liquid film from a horizontal stretching surface. In this paper DTM-Padé method was used which is a combination of differential transform method (DTM) and Padé approximant. The DTM solutions are only valid for small values of independent variables. Comparison between the solutions obtained by the DTM and the DTM-Padé with numerical solution (fourth-order Runge–Kutta) revealed that the DTM-Padé method is an excellent method for solving MHD boundary-layer equations.

scholarly journals Temperature-Dependent Electrical Conductivity and Thermal Radiation Effects on MHD Peristaltic Motion of Williamson Nanofluids in a Tapered Asymmetric Channel

2019 ◽  
Vol 36 (1) ◽  
pp. 103-118
Author(s):  
W. M. Hasona
Keyword(s):  
Electrical Conductivity ◽  
Thermal Radiation ◽  
Radiation Effects ◽  
Differential Transform Method ◽  
Physical Parameters ◽  
Asymmetric Channel ◽  
Temperature Dependent ◽  
Transform Method ◽  
Differential Transform ◽  
Temperature Dependent Electrical Conductivity

ABSTRACTThis paper is intended for dealing with the peristaltic flow of an electrically conducting Williamson nanofluid in a tapered asymmetric channel through a porous medium with heat and mass transfer. In the current paper, temperature-dependent electrical conductivity formulation was introduced for the first time in peristaltic literature. The flow is pervaded by an oblique uniform magnetic field. The present investigation includes the influences of thermal radiation, Joule heat, viscous dissipation, Hall Current, 1st order chemical reaction, and Dofour and Soret numbers. Current problem is reformulated under the molds of low Reynolds number and long wavelength approximation. Afterwards, semi analytical solutions have been evaluated for the distributions of velocity, temperature, nanoparticle concentrations as well as longitudinal pressure gradient. Solutions can be obtained by using multi-step differential transform method (MS-DTM), a reliable and powerful technique that improve accuracy and overcome drawbacks raised in using the standard differential transform method (DTM). Detailed comparisons have been made at different values of 𝑥 through graphs by Ms-DTM. The graphically results were prepared to visualize the effects of various physical parameters of interest. The semi-analytical results had shown that, as the thermal radiation increases, the nanoparticles diameter and concentration of fluid increase (thermal radiation is a decreasing function in temperature when the temperature decreases the diameter of the nanoparticles increases i.e. the volume of nanoparticle and its concentration increases and become more effective near to tumor tissues). Consequently, it can be used as agents for radiation therapy, generate localized raises in radiation doses and selectively target tumor cells for localized damage (Radiotherapy of oncology).

scholarly journals Approximate Analytic Solutions of Two-Dimensional Nonlinear Klein–Gordon Equation by Using the Reduced Differential Transform Method

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Wayinhareg Gashaw Belayeh ◽  
Yesuf Obsie Mussa ◽  
Ademe Kebede Gizaw
Keyword(s):  
Numerical Solutions ◽  
Initial Conditions ◽  
Type Systems ◽  
Analytical Approximation ◽  
Differential Transform Method ◽  
Two Dimensional ◽  
Transform Method ◽  
Differential Transform ◽  
Klein Gordon ◽  
Reduced Differential Transform Method

In this paper, the reduced differential transform method (RDTM) is successfully implemented for solving two-dimensional nonlinear Klein–Gordon equations (NLKGEs) with quadratic and cubic nonlinearities subject to appropriate initial conditions. The proposed technique has the advantage of producing an analytical approximation in a convergent power series form with a reduced number of calculable terms. Two test examples from mathematical physics are discussed to illustrate the validity and efficiency of the method. In addition, numerical solutions of the test examples are presented graphically to show the reliability and accuracy of the method. Also, the results indicate that the introduced method is promising for solving other type systems of NLPDEs.

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