D.D. Ganji, M. Rahimi and M. Rahgoshay
The purpose of this paper is to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity by using Homotopy Perturbation Method.
Abstract
Purpose
The purpose of this paper is to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity by using Homotopy Perturbation Method.
Design/methodology/approach
Most engineering problems, especially heat transfer equations are in nonlinear form. Homotopy Perturbation Method (HPM) has been applied to solve a wide series of nonlinear differential equations. In this paper, HPM is used for obtaining the fin efficiency of convective straight fins with temperature‐dependent thermal conductivity. Comparison of the results with those of Homotopy Perturbation Method, exact solution, numerical results and Adomian's decomposition method (ADM) were been done by Cihat Arslanturk.
Findings
Results show that both Homotopy Perturbation Method and ADM applied to the nonlinear equations were capable of solving them with successive rapidly convergent approximations without any restrictive assumptions or transformations causing changes in the physical properties of the problem. Moreover, adding up the number of iterations leads to explicit solution for the problem. The results are just obtained with two iterations. This shows the accuracy and great potential of this method. Finally, it can be seen that, with increase of thermo‐geometric fin parameter (v), the fin efficiency increases too.
Originality/value
The results demonstrate good validity and great potential of the HPM for Heat Transfer equations in engineering problems.
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This paper aims to revisite the traditional Adomian decomposition method frequently used for the solution of highly nonlinear extended surface problems in order to understand the…
Abstract
Purpose
This paper aims to revisite the traditional Adomian decomposition method frequently used for the solution of highly nonlinear extended surface problems in order to understand the heat transfer enhancement phenomenon. It is modified to include a parameter adjusting and controlling the convergence of the resulting Adomian series.
Design/methodology/approach
It is shown that without such a convergence control parameter, some of the published data in the literature concerning the problem are lacking accuracy or the worst is untrustful. With the proposed amendment over the classical Adomian decomposition method, it is easy to gain the range of parameters guaranteeing the convergence of the Adomian series.
Findings
With the presented improvement, the reliable behavior of the fin tip temperature and the fin efficiency of the most interested from practical perspective are easily predicted.
Originality/value
The relevant future studies involving the fin problems covering many physical nonlinear properties must be properly treated as guided in this paper, while the Adomian decomposition method is adopted for the solution procedure.
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D.D. Ganji and Mohammad Hatami
The purpose of this paper is to demonstrate the eligibility of the weighted residual methods (WRMs) applied to Jeffery-Hamel Flow. Selecting the most appropriate method among the…
Abstract
Purpose
The purpose of this paper is to demonstrate the eligibility of the weighted residual methods (WRMs) applied to Jeffery-Hamel Flow. Selecting the most appropriate method among the WRMs and discussing about Jeffery-Hamel flow's treatment in divergent and convergent channels are the other important purposes of the present research.
Design/methodology/approach
Three analytical methods (collocation, Galerkin and least square method) have been applied to solve the governing equations. The reliability of the methods is also approved by a comparison made between the forth order Runge-Kutta numerical method.
Findings
The obtained solutions revealed that WRMs can be simple, powerful and efficient techniques for finding analytical solutions in science and engineering non-linear differential equations.
Originality/value
It could be considered as a first endeavor to use the solution of the Jeffery-Hamel flow using these kind of analytical methods along with the numerical approach.
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– The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems.
Abstract
Purpose
The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems.
Design/methodology/approach
The proposed numerical technique is based on HPM to determine a heat source in the parabolic heat equation using the usual conditions. Then this shows the pertinent features of the technique in inverse problems.
Findings
Using this HPM, a rapid convergent sequence which tends to the exact solution of the problem can be obtained. And the HPM does not require the discretization of the inverse problems. So HPM is a powerful and efficient technique in finding exact and approximate solutions without dispersing the inverse problems.
Originality/value
The essential idea of this method is to introduce a homotopy parameter p which takes values from 0 to 1. When p=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation.
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Hong-Yan Liu, Ji-Huan He and Zheng-Biao Li
Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable…
Abstract
Purpose
Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus.
Design/methodology/approach
This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy perturbation method and the fractional complex transform, are outlined and the main solution processes are given.
Findings
Heat conduction in silk cocoon and ground water flow are modeled by the local fractional calculus, the solutions can explain well experimental observations.
Originality/value
Particular attention is paid throughout the paper to giving an intuitive grasp for fractional calculus. Most cited references are within last five years, catching the most frontier of the research. Some ideas on this review paper are first appeared.
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S. Hoseinzadeh, S.M. Taheri Otaghsara, M.H. Zakeri Khatir and P.S. Heyns
The purpose of this study is to investigate the pulsating flow in a three-dimensional channel. Channel flow is laminar and turbulent. After validation, the effect of different…
Abstract
Purpose
The purpose of this study is to investigate the pulsating flow in a three-dimensional channel. Channel flow is laminar and turbulent. After validation, the effect of different channel cross-sectional geometries (circular, hexagonal and triangular) with the pulsating flow are investigated. For this purpose, the alumina nanofluid was considered as a working fluid with different volume percentages (0 per cent [pure water], 3 per cent and 5 per cent).
Design/methodology/approach
In this study, the pulsatile flow was investigated in a three-dimensional channel. Channel flow is laminar and turbulent.
Findings
The results show that the fluid temperature decreases by increasing the volume percentage of particles of Al2O3; this is because of the fact that the input energy through the wall boundary is a constant value and indicates that with increasing the volume percentage, the fluid can save more energy at a constant temperature. And by adding Al2O3 nanofluid, thermal performance improves in channels, but it should be considered that the use of nanofluid causes a pressure drop in the channel.
Originality/value
Alumina/water nanofluid with the pulsating flow was investigated and compared in three different cross-sectional channel geometries (circular, hexagonal and triangular). The effect of different volume percentages (0 per cent [pure water], 3 per cent and 5 per cent) of Al2O3 nanofluid on temperature, velocity and pressure are studied.
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Vahid Jaferian, Davood Toghraie, Farzad Pourfattah, Omid Ali Akbari and Pouyan Talebizadehsardari
The purpose of this study is three-dimensional flow and heat transfer investigation of water/Al2O3 nanofluid inside a microchannel with different cross-sections in two-phase mode.
Abstract
Purpose
The purpose of this study is three-dimensional flow and heat transfer investigation of water/Al2O3 nanofluid inside a microchannel with different cross-sections in two-phase mode.
Design/methodology/approach
The effect of microchannel walls geometry (trapezoidal, sinusoidal and stepped microchannels) on flow characteristics and also changing circular cross section to trapezoidal cross section in laminar flow at Reynolds numbers of 50, 100, 300 and 600 were investigated. In this study, two-phase water/Al2O3 nanofluid is simulated by the mixture model, and the effect of volume fraction of nanoparticles on performance evaluation criterion (PEC) is studied. The accuracy of obtained results was compared with the experimental and numerical results of other similar papers.
Findings
Results show that in flow at lower Reynolds numbers, sinusoidal walls create a pressure drop in pure water flow which improves heat transfer to obtain PEC < 1. However, in sinusoidal and stepped microchannel with higher Reynolds numbers, PEC > 1. Results showed that the stepped microchannel had higher pressure drop, better thermal performance and higher PEC than other microchannels.
Originality/value
Review of previous studies showed that existing papers have not compared and investigated nanofluid in a two-phase mode in inhomogeneous circular, stepped and sinusoidal cross and trapezoidal cross-sections by considering the effect of changing channel shape, which is the aim of the present paper.