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

In the current work, thermal behaviour analysis of a natural convection porous fin with internal heat generation and temperature-dependent thermal conductivity is studied. The developed symbolic heat transfer models are for the purpose of the investigation of the effects of various parameters on the thermal behaviour of the porous fin. It is shown that its governing nonlinear differential with proper boundary conditions is exactly solvable. To this aim, we reduce the order of differential equations first and then convert into a total differential equation by multiplying a convenient integrating factor. A full discussion and exact analytical solution in the implicit form is given for further physical interpretation and it is proved that a solution to the problem may not exist or the solution is mathematically unique depending on the values of the parameters of the model.

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Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

Chinese Journal of Engineering ◽

10.1155/2013/470696 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 8

Author(s):

Mohsen Torabi ◽

Hessameddin Yaghoobi ◽

Andrea Colantoni ◽

Paolo Biondi ◽

Karem Boubaker

Keyword(s):

Thermal Conductivity ◽

Adomian Decomposition Method ◽

Solution Technique ◽

Inverse Transformation ◽

Algebraic Equations ◽

Temperature Dependent ◽

Fin Efficiency ◽

Differential Transformation ◽

Adomian Decomposition ◽

Temperature Dependent Thermal Conductivity

Radiative radial fin with temperature-dependent thermal conductivity is analyzed. The calculations are carried out by using differential transformation method (DTM), which is a seminumerical-analytical solution technique that can be applied to various types of differential equations, as well as the Boubaker polynomials expansion scheme (BPES). By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced and then applied to the aforementioned equations. Solutions are subsequently obtained by a process of inverse transformation. The current results are then compared with previously obtained results using variational iteration method (VIM), Adomian decomposition method (ADM), homotopy analysis method (HAM), and numerical solution (NS) in order to verify the accuracy of the proposed method. The findings reveal that both BPES and DTM can achieve suitable results in predicting the solution of such problems. After these verifications, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as radiation-conduction fin parameter, radiation sink temperature, heat generation, and thermal conductivity parameters.

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Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity

Mathematical Problems in Engineering ◽

10.1155/2010/568263 ◽

2010 ◽

Vol 2010 ◽

pp. 1-15 ◽

Cited By ~ 24

Author(s):

A. Moradi ◽

H. Ahmadikia

Keyword(s):

Heat Transfer ◽

Thermal Conductivity ◽

Numerical Data ◽

Transformation Method ◽

Base Temperature ◽

Temperature Dependent ◽

Fin Efficiency ◽

Runge Kutta Method ◽

Range Of Values ◽

Temperature Dependent Thermal Conductivity

Three different profiles of the straight fin that has a temperature-dependent thermal conductivity are investigated by differential transformation method (DTM) and compared with numerical solution. Fin profiles are rectangular, convex, and exponential. For validation of the DTM, the heat equation is solved numerically by the fourth-order Runge-Kutta method. The temperature distribution, fin efficiency, and fin heat transfer rate are presented for three fin profiles and a range of values of heat transfer parameters. DTM results indicate that series converge rapidly with high accuracy. The efficiency and base temperature of the exponential profile are higher than the rectangular and the convex profiles. The results indicate that the numerical data and analytical method are in agreement with each other.

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

Thermal Science ◽

10.2298/tsci210608315a ◽

2021 ◽

pp. 315-315

Author(s):

Gökhan Aksoy

Keyword(s):

Thermal Conductivity ◽

Nonlinear Problems ◽

Transformation Method ◽

Variable Thermal Conductivity ◽

Differential Transformation Method ◽

Fin Efficiency ◽

Differential Transformation ◽

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.

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