Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity

Peng, Huan; Chen, Chieh Li

doi:10.1016/j.ijheatmasstransfer.2011.02.019

Cited by 50 publications

(17 citation statements)

References 16 publications

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“…As was noted, multi-step DTM usually is used for solving problems in which Taylor series is diverged in the solution domain. This technique was already used to solve engineering and computational problems [49][50][51][52][53][54][55][56][57].…”

Section: Applying Multi-mentioning

confidence: 99%

Solution of the Boundary Layer Equation of the Power-Law Pseudoplastic Fluid Using Differential Transform Method

Mosayebidorcheh

2013

Mathematical Problems in Engineering

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The boundary layer equation of the pseudoplastic fluid over a flat plate is considered. This equation is a boundary value problem (BVP) with the high nonlinearity and a boundary condition at infinity. To solve such problems, powerful numerical techniques are usually used. Here, through using differential transform method (DTM), the BVP is replaced by two initial value problems (IVP) and then multi-step differential transform method (MDTM) is applied to solve them. The differential equation and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated in every sub domain. In this solution, there is no need for restrictive assumptions or linearization. Finally, DTM results are compared with the numerical solution of the problem, and a good accuracy of the proposed method is observed.

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Section: Applying Multi-mentioning

confidence: 99%

Solution of the Boundary Layer Equation of the Power-Law Pseudoplastic Fluid Using Differential Transform Method

Mosayebidorcheh

2013

Mathematical Problems in Engineering

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“…In recent studies, DTM is hybridized with the finite difference method and is used for solving ODEs. Approximate solutions for different problems are reported in [12]- [14]. Other approximate techniques, including hybrids of homotopy perturbation method, Variational iterative method, DTM, and Padé approximation technique, are developed to overcome the weaknesses of its earlier versions [15].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Temperature Profiles in Longitudinal Fin Designs by a Novel Neuroevolutionary Approach

et al. 2020

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Real application problems in physics, engineering, economics, and other disciplines are often modeled as differential equations. Classical numerical techniques are computationally expensive when we require solutions to our mathematical problems with no prior information. Hence, researchers are more interested in developing numerical methods that can obtain better solutions with fewer efforts and computational time. Heuristic algorithms are considered suitable candidates for such type of problems. In this research, we have developed a new neuroevolutionary algorithm that combines the power of feed-forward artificial neural networks (ANNs) and a modern metaheuristic, the Symbiotic Organism Search (SOS) algorithm. With our new approach, we have analyzed the simultaneous surface convection and radiation during heat transfer in different models of fins/ heat exchangers. Longitudinal fins are considered with concave parabolic, rectangular and trapezoidal shapes. We have analyzed our problem in two scenarios and six sub-cases. Our solutions are of high quality, with minimum residual errors in all cases. We have established the quality of our results by calculating values of different performance indicators like Root-mean-square error (RMSE), Absolute error (AE), Generational distance (GD), Mean absolute deviation (MAD), Nash-Sutcliffe efficiency (NSE), Error in Nash-Sutcliffe efficiency (ENSE). Statistical and graphical analysis of our results suggests that our approach is suitable for handling real application problems. We have compared our results with state-of-the-art results, and the outcome of our analysis points to the superiority of our approach. INDEX TERMS Approximate solutions, Artificial neural networks, Heat transfer analyses, Longitudinal fins, Metaheuristics, Symbiotic organism search optimizer.

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“…Numerical analysis and modeling of transient heat conduction problems with inhomogeneous heat sources have very important applications in engineering fields, such as ignition of reactive solids and microwave heating. Various numerical simulation tools had been applied in research studies of transient heat conduction problems, and the most common of these are the finite element method (FEM), finite difference method (FDM), and boundary element method (BEM) . Compared with these mesh‐dependent algorithms, more and more researchers pay attentions to meshless methods because of being free from mesh generation .…”

Section: Introductionmentioning

confidence: 99%

A combined scheme of generalized finite difference method and Krylov deferred correction technique for highly accurate solution of transient heat conduction problems

Zhang

et al. 2018

Numerical Meth Engineering

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This paper presents a numerical framework for the highly accurate solutions of transient heat conduction problems. The numerical framework discretizes the temporal direction of the problems by introducing the Krylov deferred correction (KDC) approach, which is arbitrarily high order of accuracy while remaining the computational complexity same as in the time-marching of first-order methods. The discretization by employing the KDC method yields a boundary value problem of the inhomogeneous modified Helmholtz equation at each time step. The meshless generalized finite difference method (GFDM) or meshless finite difference method (MFDM), a meshless method, is then applied to the solution of resulting boundary value problems at each time step. Six numerical experiments in one-, two-, and three-dimensional cases show that the proposed hybrid KDC-GFDM scheme allows big time step size for a long-time dynamic simulation and has a great potential for the problems with complex boundaries.In addition, some comparisons are also presented between the present method, the COMSOL software, and the GFDM with implicit Euler method. KEYWORDS generalized finite difference method, Krylov deferred correction method, long-time simulation, meshless method, transient heat conduction 1 INTRODUCTION Numerical analysis and modeling of transient heat conduction problems with inhomogeneous heat sources have very important applications in engineering fields, such as ignition of reactive solids and microwave heating. Various Int J Numer Methods Eng. 2019;117:63-83.wileyonlinelibrary.com/journal/nme

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Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity

Cited by 50 publications

References 16 publications

Solution of the Boundary Layer Equation of the Power-Law Pseudoplastic Fluid Using Differential Transform Method

Solution of the Boundary Layer Equation of the Power-Law Pseudoplastic Fluid Using Differential Transform Method

Analysis of Temperature Profiles in Longitudinal Fin Designs by a Novel Neuroevolutionary Approach

A combined scheme of generalized finite difference method and Krylov deferred correction technique for highly accurate solution of transient heat conduction problems

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