Application of differential transformation method for an annular fin with variable thermal conductivity

Fin Efficiency ◽

Annular Fin ◽

Constant Thermal Conductivity ◽

Dimensional Parameters

The thermal analysis of the annular fin is performed by applying the differential transformation method. The thermal conductivity of the annular fin has been considered as a function of temperature. The effects of non-dimensional parameters, namely thermal conductivity and thermo-geometric fin parameters on the fin efficiency and temperature distribution are determined. Obtained results from the differential transformation method are also compared with the exact analytical results and the results of the finite difference method in the constant thermal conductivity condition. It has been concluded that the differential transformation method provides accurate results in the solution of nonlinear problems.

Differential Transformation Method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity

International Communications in Heat and Mass Transfer ◽

10.1016/j.icheatmasstransfer.2009.03.020 ◽

2009 ◽

Vol 36 (7) ◽

pp. 757-762 ◽

Cited By ~ 130

Author(s):

A.A. Joneidi ◽

D.D. Ganji ◽

M. Babaelahi

Keyword(s):

Thermal Conductivity ◽

Transformation Method ◽

Temperature Dependent ◽

Fin Efficiency ◽

Temperature Dependent Thermal Conductivity

Nonlinear Vibration Analysis of an Electrostatically Actuated Microbeam using Differential Transformation Method

Semiconductor Science and Information Devices ◽

10.30564/ssid.v2i2.1887 ◽

2020 ◽

Vol 2 (2) ◽

Author(s):

Gbeminiyi Musibau Sobamowo ◽

A A. Yinusa ◽

O. A. Adesina ◽

O. M. Oyekeye

Keyword(s):

Nonlinear Vibration ◽

Nonlinear Problems ◽

Transformation Method ◽

Velocity Variation ◽

Electrostatically Actuated ◽

Homotopy Analysis ◽

Comparison Of The Results ◽

High Level

In this paper, nonlinear vibration of electrostatically actuated microbeam is analyzed using differential transformation method. The high level of accuracy of the analytical solutions of the method was established through comparison of the results of the solutions of exact analytical method, variational approach, homotopy analysis method and energy balance methods. Also, with the aid of the present analytical solution, the time response, velocity variation and the phase plots of the system are presented graphically. It is hope that the method will be widely applied to more nonlinear problems of systems in various fields of study.

The Vibration Problem Studying in Micro Actuator System Using the Differential Transformation Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.284-287.1966 ◽

2013 ◽

Vol 284-287 ◽

pp. 1966-1970

Author(s):

Chin Chia Liu ◽

Ming Fei Chen

Keyword(s):

Natural Frequencies ◽

Analytical Data ◽

Nonlinear Problems ◽

Transformation Method ◽

Electrostatically Actuated ◽

Actuator System ◽

Fixed Beam ◽

Good Agreement

The aim of this study is to derive the governing equation of an electrostatically actuated micro system by use of the Hamilton principle, and then the natural frequencies of a micro fixed-fixed beam are derived as the solutions to a boundary value problem with prescribed boundary conditions through the differential transformation method (D.T.M.). The differential transformation employed is a transformed function based on the Taylor series that is effective in solving nonlinear problems with fast convergence. The numerical results of the calculated natural frequencies are compared with the analytical data and were found to be in good agreement. Hence, the differential transformation method is one of the most efficient methods of simulating the electrostatic behavior of a micro-structure system, and it has a great potential for use in the analysis of the micro fixed-fixed beam.

The Efficiency of Convective-radiative Fin with Temperature-dependent Thermal Conductivity by the Differential Transformation Method

Research Journal of Applied Sciences Engineering and Technology ◽

10.19026/rjaset.6.3956 ◽

2013 ◽

Vol 6 (8) ◽

pp. 1354-1359 ◽

Cited By ~ 5

Author(s):

Sadegh Poozesh ◽

Sajjad Nabi ◽

Majid Saber ◽

Saeed Dinarvand ◽

Behzad Fani

Keyword(s):

Thermal Conductivity ◽

Transformation Method ◽

Temperature Dependent ◽

Temperature Dependent Thermal Conductivity

Thermal behaviour of annular hyperbolic fin with temperature dependent thermal conductivity by differential transformation method and Pade approximant

Physica Scripta ◽

10.1088/1402-4896/ac0c94 ◽

2021 ◽

Author(s):

Deepak Umrao Sarwe ◽

V. S Kulkarni

Keyword(s):

Thermal Conductivity ◽

Thermal Behaviour ◽

Transformation Method ◽

Padé Approximant ◽

Temperature Dependent ◽

Temperature Dependent Thermal Conductivity

Pade Approximant ◽

Numerical Multistep Approach for Solving Fractional Partial Differential Equations

International Journal of Computational Methods ◽

10.1142/s0219876217500293 ◽

2017 ◽

Vol 14 (03) ◽

pp. 1750029 ◽

Cited By ~ 31

Author(s):

Mohammed Al-Smadi ◽

Asad Freihat ◽

Hammad Khalil ◽

Shaher Momani ◽

Rahmat Ali Khan

Keyword(s):

Fractional Derivatives ◽

Nonlinear Problems ◽

Approximate Solutions ◽

Transformation Method ◽

Time Frame ◽

Heat Equations ◽

One Dimensional ◽

Analytical Technique ◽

Differential Transformation

In this paper, we proposed a novel analytical technique for one-dimensional fractional heat equations with time fractional derivatives subjected to the appropriate initial condition. This new analytical technique, namely multistep reduced differential transformation method (MRDTM), is a simple amendment of the reduced differential transformation method, in which it is treated as an algorithm in a sequence of small intervals, in order to hold out accurate approximate solutions over a longer time frame compared to the traditional RDTM. The fractional derivatives are described in the Caputo sense, while the behavior of solutions for different values of fractional order [Formula: see text] compared with exact solutions is shown graphically. The analysis is accompanied by four test examples to demonstrate that the proposed approach is reliable, fully compatible with the complexity of these equations, and can be strongly employed for many other nonlinear problems in fractional calculus.