Effective Computation of Solutions for Nonlinear Heat Transfer Problems in Fins

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Heat Transfer ◽  
Approximate Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
The Other ◽  
Engineering Applications ◽  
Nonlinear Heat Transfer ◽  
Base Functions ◽  
Transfer Problems

Fins are essentially used in diverse engineering applications to increase the heat transfer between the hot and cold media. In this paper, a technique for computing the analytic approximate solution of the nonlinear differential equations resulting from heat transfer problems, in particular through fins, is developed. The simplicity of the approach presented here is due to its base functions, which makes this method straightforward to apply and formulate without any need for discretization. Analysis of the error and comparisons with the other methods are presented. A few physically interesting fin problems of heat transfer are treated to illustrate that the proposed algorithm generates highly accurate solutions.

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

scholarly journals Double trials method for nonlinear problems arising in heat transfer

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 153-155 ◽  
Author(s):  
Chun-Hui He ◽  
Ji-Huan He
Keyword(s):  
Heat Transfer ◽  
Approximate Solution ◽  
Differential Equations ◽  
Unknown Parameter ◽  
Nonlinear Differential Equations ◽  
Nonlinear Problems ◽  
Solution Procedure ◽  
Second Century ◽  
Algebraic Equations ◽  
False Position

According to an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD, two trial roots are assumed to solve algebraic equations. The solution procedure can be extended to solve nonlinear differential equations by constructing an approximate solution with an unknown parameter, and the unknown parameter can be easily determined using the Ying Buzu Shu. An example in heat transfer is given to elucidate the solution procedure.

THE MODAL IDENTIFICATION METHOD IN NONLINEAR HEAT TRANSFER PROBLEMS

Equipment ◽  
2006 ◽  
Author(s):  
O. Balima ◽  
D. Petit ◽  
J. B. Saulnier ◽  
M. Girault ◽  
Y. Favennec
Keyword(s):  
Heat Transfer ◽  
Modal Identification ◽  
Identification Method ◽  
Nonlinear Heat Transfer ◽  
Transfer Problems

scholarly journals Construction of Analytic Solution to Axisymmetric Flow and Heat Transfer on a Moving Cylinder

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1335
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stokes Equations ◽  
Nonlinear Differential Equations ◽  
Axisymmetric Flow ◽  
Control Parameters ◽  
Auxiliary Functions ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Convergence Control

Based on a new kind of analytical approach, namely the Optimal Auxiliary Functions Method (OAFM), a new analytical procedure is proposed to solve the problem of the annular axisymmetric stagnation flow and heat transfer on a moving cylinder with finite radius. As a novelty, explicit analytical solutions were obtained for the considered complex problem. First, the Navier–Stokes equations were simplified by means of similarity transformations that depended on different parameters and some combinations of these parameters, and the problem under study was reduced to six nonlinear ordinary differential equations with six unknowns. The OAFM proves to be a powerful tool for finding an accurate analytical solution for nonlinear problems, ensuring a fast convergence after the first iteration, even if the small or large parameters are absent, since the determination of the convergence-control parameters is independent of the magnitude of the coefficients that appear in the nonlinear differential equations. Concerning the main novelties of the proposed approach, it is worth mentioning the presence of some auxiliary functions, the involvement of the convergence-control parameters, the construction of the first iteration and much freedom to select the procedure for determining the optimal values of the convergence-control parameters.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

2021 ◽  
Vol 8 (4) ◽  
pp. 807-820
Author(s):  
M. Zaydan ◽  
◽  
A. Wakif ◽  
E. Essaghir ◽  
R. Sehaqui ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Nonlinear Differential Equations ◽  
Convection Heat Transfer ◽  
Local Heat Transfer ◽  
Physical Parameters ◽  
Convection Heat ◽  
Linear Temperature ◽  
Mixed Convection Heat Transfer

The phenomenon of mixed convection heat transfer in a homogeneous mixture is deliberated thoroughly in this study for cooper-water nanofluids flowing inside a lid-driven square cavity. By adopting the Oberbeck-Boussinesq approximation and using the single-phase nanofluid model, the governing partial differential equations modeling the present flow are stated mathematically based on the Navier--Stokes and thermal balance formulations, where the important features of the scrutinized medium are presumed to remain constant at the cold temperature. Note here that the density quantity in the buoyancy body force is a linear temperature-dependent function. The characteristic quantities are computed realistically via the commonly used phenomenological laws and the more accurate experimental correlations. A feasible non-dimensionalization procedure has been employed to derive the dimensionless conservation equations. The resulting nonlinear differential equations are solved numerically for realistic boundary conditions by employing the fourth-order compact finite-difference method (FOCFDM). After performing extensive validations with the previously published findings, the dynamical and thermal features of the studied convective nanofluid flow are revealed to be in good agreement for sundry values of the involved physical parameters. Besides, the present numerical outcomes are discussed graphically and tabularly with the help of streamlines, isotherms, velocity fields, temperature distributions, and local heat transfer rate profiles.

scholarly journals Approximate Solution of Bratu Differential Equations Using Trigonometric Basic Functions

2021 ◽  
Vol 45 (02) ◽  
pp. 203-214
Author(s):  
BAHRAM AGHELI
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Absolute Error ◽  
Approximate Methods ◽  
Transform Method ◽  
Solution Function ◽  
Base Functions ◽  
Approximate Function ◽  
Basic Functions ◽  
Trigonometric Transform

In this paper, I have proposed a method for finding an approximate function for Bratu differential equations (BDEs), in which trigonometric basic functions are used. First, by defining trigonometric basic functions, I define the values of the transformation function in relation to trigonometric basis functions (TBFs). Following that, the approximate function is defined as a linear combination of trigonometric base functions and values of transform function which is named trigonometric transform method (TTM), and the convergence of the method is also presented. To get an approximate solution function with discrete derivatives of the solution function, we have determined the approximate solution function which satisfies in the Bratu differential equations (BDEs). In the end, the algorithm of the method is elaborated with several examples. In one example, I have presented an absolute error comparison of some approximate methods.

Computational Study of Streamfunction-Vorticity Formulation of Incompressible Flow and Heat Transfer Problems

2011 ◽  
Vol 52-54 ◽  
pp. 511-516 ◽  
Author(s):  
Arup Kumar Borah
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Boundary Conditions ◽  
Incompressible Flow ◽  
Computational Study ◽  
The Other ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Continuity Constraint ◽  
Transfer Problems

In this paper we have studied the streamfunction-vorticity formulation can be advantageously used to analyse steady as well as unsteady incompressible flow and heat transfer problems, since it allows the elimination of pressure from the governing equations and automatically satisfies the continuity constraint. On the other hand, the specification of boundary conditions for the streamfunction-vorticity is not easy and a poor evaluation of these conditions may lead to serious difficulties in obtaining a converged solution. The main issue addressed in this paper is the specification in the boundary conditions in the context of finite element of discretization, but approach utilized can be easily extended to finite volume computations.

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