Non-Linear Model for a Spiral Porous Fin Subjected to Darcy Flow

2019 ◽  
Vol 26 ◽  
pp. 84-92
Author(s):  
N. Daradji ◽  
Mohamed Nadjib Bouaziz
Keyword(s):  
Linear Problem ◽  
Hostile Environment ◽  
Characteristic Parameters ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Thermal Transfer ◽  
Porous Fin ◽  
Non Linear ◽  
Temperature Dependent Thermal Conductivity ◽  
Distribution Equation

In this study, the temperature distribution equation for a spiral porous fin is presented. Based on Darcy’s model, a mathematical equation of the energy is derived and a suitable dimensionless form is outlined to highlight some characteristic parameters, namely, the spiral fin pitch, the porosity, and the modified Rayleigh number. The behavior of the solution is analyzed for two cases of interest, taking into account the temperature-dependent thermal conductivity of the fin encountered in a hostile environment. A Numerical method is applied to solve this non-linear problem. It is found that the thermal transfer is not affected by the change of the spiral fin pitch, whereas increasing the porosity or the parameter β* makes higher fin temperature and improve the fin efficiency.

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.

The exact closed solution in the analysis of a natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation

2019 ◽  
Vol 97 (5) ◽  
pp. 566-575
Author(s):  
S. Abbasbandy ◽  
E. Shivanian
Keyword(s):  
Thermal Conductivity ◽  
Natural Convection ◽  
Thermal Behaviour ◽  
Heat Generation ◽  
Exact Analytical Solution ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Porous Fin ◽  
Temperature Dependent Thermal Conductivity

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.

scholarly journals Non-linear Temperature Profiles

10.14311/294 ◽  
2001 ◽  
Vol 41 (6) ◽  
Author(s):  
T. Ficker ◽  
J. Myslín ◽  
Z. Podešvová
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Resistance ◽  
Temperature Profiles ◽  
Temperature Dependent ◽  
Linear Temperature ◽  
Non Linear ◽  
Wall Materials ◽  
Temperature Dependent Thermal Conductivity

Non-linear temperature profiles caused by temperature-dependent thermal conductivity l(T) of wall materials are discussed. Instead of conventional thermal resistance, modified effective resistance has been introduced.

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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