scholarly journals A STUDY ON TEMPERATURE-DISTRIBUTION AND FIN EFFICIENCY OF CONVECTIVE STRAIGHT FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY OF FRACTIONAL ORDER ENERGY BALANCE EQUATION BY USING ADOMIAN DECOMPOSITION SUMUDU TRANSFORM METHOD

2016 ◽  
Vol 110 (2) ◽  
Author(s):  
T. Patel ◽  
R. Meher
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Energy Balance Equation ◽  
Temperature Dependent ◽  
Transform Method ◽  
Fin Efficiency ◽  
Order Energy ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Temperature Dependent Thermal Conductivity

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).

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 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.

Estimation of parameters in a fin with temperature-dependent thermal conductivity and radiation

2016 ◽  
Vol 230 (6) ◽  
pp. 474-485 ◽  
Author(s):  
Ranjan Das
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Numerical Study ◽  
Estimation Of Parameters ◽  
Temperature Dependent ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Homotopy Analysis ◽  
Conductivity Parameter ◽  
Temperature Dependent Thermal Conductivity

In this paper an inverse numerical study of a conductive, convective and radiative rectangular fin is carried out with temperature-dependent thermal conductivity. At first, an implicit Runge-Kutta method-based solution is obtained for calculating the temperature distribution, and then an inverse problem is solved for estimation of unknown thermo-physical properties. The convection–conduction parameter, variable conductivity parameter and radiative parameter have been simultaneously predicted for satisfying a prescribed temperature distribution. This is achieved by minimizing a least squares-based objective function using a hybrid differential evolution-nonlinear programming optimization algorithm. The results obtained from the forward method are compared with Adomian decomposition and homotopy analysis methods which are found to be satisfactory. It is observed that many feasible combinations of parameters exist which satisfy the same temperature distribution, thus providing an opportunity for selecting any combination from the available alternatives. The effect of convection–conduction parameter on the temperature distribution is observed to be more than other parameters. A case study of different fin materials is also carried out for demonstrating the application of the present methodology.

scholarly journals Solutions of fractional order differential equations modeling temperature distribution in convective straight fins design

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ashfaq Ahmad ◽  
Muhammad Sulaiman ◽  
Poom Kumam
Keyword(s):  
Temperature Distribution ◽  
Performance Metrics ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Cuckoo Search ◽  
Energy Balance Equation ◽  
Temperature Dependent ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, the problem of temperature distribution for convective straight fins with constant and temperature-dependent thermal conductivity is solved by using artificial neural networks trained by the biogeography-based heterogeneous cuckoo search (BHCS) algorithm. We have solved the integer and noninteger order energy balance equation in order to analyse the temperature distribution in convective straight fins. We have compared our results with homotopy perturbation method (HPM), variational iteration method (VIM), and homotopy perturbation Sumudu transform method (HPSTM). The results show that the ANN–BHCS algorithm gives better results than other analytical techniques. We have further checked the efficiency of the ANN–BHCS algorithm by using the performance metrics MAD, TIC, and ENSE. We have calculated the values of MAD, TIC, and ENSE for case 1 of the problem, and histograms of these metrics show the efficiency of our algorithm.

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.

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