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

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
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.

scholarly journals Modified variational iteration method for straight fins with temperature dependent thermal conductivity

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 229-236 ◽  
Author(s):  
Mustafa Inc ◽  
Hasib Khan ◽  
Dumitru Baleanu ◽  
Aziz Khan
Keyword(s):  
Thermal Conductivity ◽  
Iteration Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Temperature Dependent ◽  
Convergence Region ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Temperature Dependent Thermal Conductivity ◽  
Modified Variational Iteration Method

The modified variational iteration method (MVIM) has been used to calculate the efficiency of straight fins with temperature dependent thermal conductivity. The obtained results are compared with homotopy analysis method (HAM), homotopy perturbation method (HPM), and Adomian decomposition method (ADM). It is used w ? 0 auxiliary parameter to keep under control convergence region of solution series in MVIM. As a result, although MVIM and HAM give results close to each other; HPM and ADM give divergent results from analytical solution.

Convective Fins Problem with Variable Thermal Conductivity: An Approach Based on Embedding Green’s Functions into Fixed Point Iterative Schemes

2016 ◽  
Vol 71 (12) ◽  
pp. 1105-1110
Author(s):  
H.Q. Kafri ◽  
S.A. Khuri ◽  
Ali Sayfy
Keyword(s):  
Thermal Conductivity ◽  
Fixed Point ◽  
Current Method ◽  
Numerical Approach ◽  
Variable Thermal Conductivity ◽  
Iteration Scheme ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Range Of Values ◽  
Temperature Dependent Thermal Conductivity

AbstractThis article introduces a new numerical approach to solve the equation that models a rectangular purely convecting fin with temperature-dependent thermal conductivity. The algorithm embeds an integral operator, defined in terms of Green’s function, into Krasnoselskii–Mann’s fixed point iteration scheme. The validity of the method is demonstrated by a number of examples that consist of a range of values of the parameters that appear in the model. In addition, the evaluation of the fin efficiency is presented. The residual error computations show that the current method provides highly accurate approximations.

Exact solution of a nonlinear fin problem of temperature-dependent thermal conductivity and heat transfer coefficient

2020 ◽  
Vol 98 (7) ◽  
pp. 700-712 ◽  
Author(s):  
Sheng-Wei Sun ◽  
Xian-Fang Li
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Temperature Distribution ◽  
Transfer Coefficient ◽  
Power Law ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Special Cases ◽  
Temperature Dependent Thermal Conductivity

This paper studies a class of nonlinear problems of convective longitudinal fins with temperature-dependent thermal conductivity and heat transfer coefficient. For thermal conductivity and heat transfer coefficient dominated by power-law nonlinearity, the exact temperature distribution is obtained analytically in an implicit form. In particular, the explicit expressions of the fin temperature distribution are derived explicitly for some special cases. An analytical expression for fin efficiency is given as a function of a thermogeometric parameter. The influences of the nonlinearity and the thermogeometric parameter on the temperature and thermal performance are analyzed. The temperature distribution and the fin efficiency exhibit completely different behaviors when the power-law exponent of the heat transfer coefficient is more or less than negative unity.

scholarly journals Analytical Solution of Nonlinear Boundary Value Problem for Fin Efficiency of Convective Straight Fins with Temperature-Dependent Thermal Conductivity

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
K. Saravanakumar ◽  
V. Ananthaswamy ◽  
M. Subha ◽  
L. Rajendran
Keyword(s):  
Thermal Conductivity ◽  
Analytical Solution ◽  
Nonlinear Equation ◽  
Nonlinear Boundary ◽  
Dimensionless Temperature ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Homotopy Analysis ◽  
Thermal Conductivity Problem ◽  
Temperature Dependent Thermal Conductivity

We have employed homotopy analysis method (HAM) to evaluate the approximate analytical solution of the nonlinear equation arising in the convective straight fins with temperature-dependent thermal conductivity problem. Solutions are presented for the dimensionless temperature distribution and fin efficiency of the nonlinear equation. The analytical results are compared with previous work and satisfactory agreement is noted.

scholarly journals A Study on Convective-Radial Fins with Temperature-dependent Thermal Conductivity and Internal Heat Generation

2019 ◽  
Vol 8 (1) ◽  
pp. 145-156
Author(s):  
Trushit Patel ◽  
Ramakanta Meher
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Fractional Order ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Temperature Dependent Thermal Conductivity

Abstract In this paper, the temperature distribution in a convective radial fins is analyzed through a fractional order energy balance equation with the consideration of internal heat generation and temperature dependent thermal conductivity. Adomian decomposition Sumudu transform method is used to study the influence of temperature distribution and the efficiency of radial fins for different values of thermal conductivity and to determine the role of thermal conductivity, thermo-geometric fin parameter as well as fractional order values in finding the temperature distribution and the fin efficiency of the convective radial fins. Finally, the efficiency of this proposed method has been studied by comparing the obtained results with the classical order results obtained by using numerical method and Variational Iteration Method (Coskun and Atay, 2007).

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