Boundary layer convective heat transfer with pressure gradient using Homotopy Perturbation Method (HPM) over a flat plate

Fathizadeh, Mahdi; Rashidi, Fariborz

doi:10.1016/j.chaos.2009.03.135

Cited by 24 publications

(26 citation statements)

References 16 publications

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“…Numerical comparison between present HPM with other different approximate solution is tabulated in Table 1 and 2. It is interesting to note that present HPM is very close to the numerical results in comparison with [20], [21]. The approximations of the f ˝ (0) obtained by HPM and their relative error with respect to the Howarth [15] results are listed in Table [20] 0.348505 4.9 % HPM [21] 0.348 4.8 % HPM [18] 0.3095 6.8 % HAM [19] 0.3296 0.7 % …”

Section: Resultsmentioning

confidence: 87%

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Analytical Solution of Laminar Boundary Layer Equations Over A Flat Plate by Homotopy Perturbation Method

Majidian

Khaki²,

Khazayinejad³

2012

International Journal of Applied Mathematical Research

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In this paper, the problem of an incompressible viscous flow over a flat plate is presented. The Homotopy perturbation method (HPM) is employed to solve the well-known Blasius nonlinear differential equation. It has been tried to use a special technique by which one be able to obtain solutions that are very close to the exact solution of the equation. The obtained results have been compared with the exact solution of Blasius equation and another results obtained in previous works so that the high accuracy of results are clear. Also it is found that this method is powerful mathematical tool and can be applied to a large class of linear and nonlinear problems in different fields of science and engineering especially some fluid mechanics equations.

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Section: Resultsmentioning

confidence: 87%

“…We can see a very good agreement between the present HPM and the numerical results. So, the solutions are obtained present HPM are more accurate than [20], [21]. Numerical comparison between present HPM with other different approximate solution is tabulated in Table 1 and 2.…”

Section: Resultsmentioning

confidence: 99%

Analytical Solution of Laminar Boundary Layer Equations Over A Flat Plate by Homotopy Perturbation Method

Majidian

Khaki²,

Khazayinejad³

2012

International Journal of Applied Mathematical Research

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“…In our study we assume the stream of cold fluid at temperature ∞ moving on the top surface of the plate with uniform velocity ∞ . The equations showing the flow can be written as Fathizadeh and Rashidi (2009).…”

Section: Mathematical Analysismentioning

confidence: 99%

“…Makinde and Olanrewaju (2010) extended the work of Aziz (2009) to the presence of buoyancy force. Fathizadeh and Rashidi (2009) study convective heat transfer equations of boundary layer in presence of pressure gradient over a flat plate.…”

Section: Introductionmentioning

confidence: 99%

Presence of Pressure Gradient on Laminar Boundary Layer over a Permeable Surface with Convective Boundary Condition

Shagaiya¹,

Daniel²

2015

AJHMT

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This paper concerns with pressure gradient on laminar thermal boundary layer over a permeable surface in a uniform stream of fluid with convective boundary condition. The analytical series solution is used to study the effects of Prandtl number ( ), Suction or Injection parameter ( ), and pressure gradient ( ) on both velocity and temperature profiles in the boundary layer. The governing equations which are non-linear partial differential equations are reduced to ordinary differential equations by using similarity transformations. Homotopy Analysis Method (HAM) is used to obtain the solutions for velocity and temperature. The effects of various parameters of interest on the velocity and temperature distribution are discussed. We compared our numerical values obtained with previous published work in the literature and found to be in good agreement.

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“…During the recent years, some of the nonlinear engineering problems have been solved using some of these methods, such as HAM Dinarvand *Corresponding author. E-mail:sobhanmosayebi@yahoo.com, Tel: (+98) Liao, 2009;Ziabakhsh and Domairry, 2009;Abbasbandy and Hayat, 2009), HPM (Raftari and Yildirim, 2010;Esmaeilpour and Ganji, 2007;Fathizadeh and Rashidi, 2009;Bararnia et al, 2012), VIM (Mohyud-Din et al, 2010;Rashidi and Shahmohamadi, 2009;Wazwaz, 2007) and DM (Wazwaz 2006;Alizadeh et al, 2009;Kechil and Hashim, 2007). In most of the researches, some modifications introduced to overcome the nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the steady state condensation film on the inclined rotating disk by a new hybrid method

Mosayebidorcheh¹,

Mosayebidorcheh²,

Rashidi³

2014

Sci. Res. Essays

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In this paper, a similarity transformation is used to reduce the three-dimensional steady state condensation film on an inclined rotating disk by a set of nonlinear boundary value problems. This problem is solved using a new hybrid technique based on differential transform method (DTM) and Iterative Newton's Method (INM). The differential equations and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated. After finding Jacobian matrix, the unknown parameters computed using Multi-Variable Iterative Newton's Method. These techniques are used to obtain an approximate solution of the problem. In this solution, there is no need to restrictive assumptions or linearization. The results compared with the numerical solution of the problem, and a good accuracy of the proposed hybrid method observed. Finally, the velocity and temperature profiles demonstrated for different values of problem parameters.

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Boundary layer convective heat transfer with pressure gradient using Homotopy Perturbation Method (HPM) over a flat plate

Cited by 24 publications

References 16 publications

Analytical Solution of Laminar Boundary Layer Equations Over A Flat Plate by Homotopy Perturbation Method

Analytical Solution of Laminar Boundary Layer Equations Over A Flat Plate by Homotopy Perturbation Method

Presence of Pressure Gradient on Laminar Boundary Layer over a Permeable Surface with Convective Boundary Condition

Analytical solution of the steady state condensation film on the inclined rotating disk by a new hybrid method

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