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.

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

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
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.

Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1073-1083
Author(s):  
Muhammad Sohail ◽  
Umar Nazir ◽  
Yu-Ming Chu ◽  
Hussam Alrabaiah ◽  
Wael Al-Kouz ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Variable Temperature ◽  
Variable Thermal Conductivity ◽  
Skin Friction Coefficient ◽  
Temperature Dependent ◽  
Similarity Transformations ◽  
Rate Dependent ◽  
And Diffusion ◽  
Temperature Dependent Thermal Conductivity

Abstract This article addresses the effects of thermal radiation, stratification, and Joule heating for the flow of magnetohydrodynamics Sutterby nanofluid past over a stretching cylinder. The transport phenomenon of heat and mass are modeled under temperature-dependent thermal conductivity and diffusion coefficients, respectively. Moreover, traditional Fourier and Fick’s laws have been implemented in thermal and mass transport expressions. The governing model that consists of a set of coupled partial differential equations is converted into system of nonlinear coupled ordinary differential equations via suitable similarity transformations. The resulting set of expressions is analytically treated through an optimal homotopy scheme. The effects of different dimensionless flow parameters on the velocity, temperature, and concentration fields are illustrated through graphs. The patterns of skin friction coefficient, local Nusselt, and Sherwood numbers are examined via bar charts. The major outcome of the proposed study is that variable thermal conductivity decays the temperature and radiation raises the temperature of the system. Stratification parameters show the reverse behavior for temperature and concentration boundary layers. Shear rate-dependent rheology in view of Sutterby liquid has the ability to reduce the flow of fluid. Therefore, the ability of flow in rheology of Sutterby liquid becomes reduced. Consequently, layer of momentum boundary has increased with respect to parameter of Sutterby liquid.

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 Determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 111-115 ◽  
Author(s):  
Domiri Ganji ◽  
Ziabkhsh Ganji ◽  
Domiri Ganji
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Variable Thermal Conductivity ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Annular Fin ◽  
Temperature Dependent Thermal Conductivity

In this paper, homotopy perturbation method has been used to evaluate the temperature distribution of annular fin with temperature-dependent thermal conductivity and to determine the temperature distribution within the fin. This method is useful and practical for solving the nonlinear heat transfer equation, which is associated with variable thermal conductivity condition. The homotopy perturbation method provides an approximate analytical solution in the form of an infinite power series. The annular fin heat transfer rate with temperature-dependent thermal conductivity has been obtained as a function of thermo-geometric fin parameter and the thermal conductivity parameter describing the variation of the thermal conductivity

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.

Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Mahdi Anbarloei ◽  
Elyas Shivanian
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Temperature Dependent Thermal Conductivity

In the current paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. It is shown that its governing nonlinear differential equation is exactly solvable. A full discussion and exact analytical solution in the implicit form are given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, and the solutions are dual depending on the values of the parameters of the model. Furthermore, we give exact analytical expressions of fin efficiency as a function of thermogeometric fin parameter.

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.

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