Magnetohydrodynamic flow and heat transfer in a porous medium along a stretching cylinder with radiation: homotopy analysis method

Chauhan, Dileep Singh; Rastogi, Priyanka; Agrawal, Rashmi

doi:10.1007/s13370-012-0102-x

Cited by 23 publications

(24 citation statements)

References 31 publications

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“…We have compared our results with those in [6,8] for special cases of our study and we note that there is good agreement between the different numerical solutions. It is worth mentioning that the recent studies in [9,11] do not provide tables of the relevant boundary derivatives and this can be considered a shortcoming. Figures 2 and 3 show the variation in velocity profiles for varying values of the Reynolds number Re and magnetic parameter , respectively, for both the suction > 0 and injection < 0 cases.…”

Section: Resultsmentioning

confidence: 99%

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Magnetohydrodynamic Stagnation Flow and Heat Transfer toward a Stretching Permeable Cylinder

Mastroberardino

Siddique

2014

Advances in Mechanical Engineering

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We perform an analysis of MHD flow and heat transfer on a stretching, permeable cylinder. We prove existence of solutions for all values of the relevant parameters and provide uniqueness results in the case of a monotonic solution. The nonlinear boundary value problem that is derived from a similarity transformation of the governing system of nonlinear partial differential equations is solved numerically and the results are presented with graphs and tables.

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Section: Resultsmentioning

confidence: 99%

“…Chauhan et al [11] generalized the results of Joneidi et al by considering the cylinder to be embedded in a porous medium along with a partial slip boundary condition. Munawar et al [12] examined unsteady flow and heat transfer due to a stretching cylinder in consideration of two general types of thermal boundary conditions.…”

Section: Introductionmentioning

confidence: 97%

Magnetohydrodynamic Stagnation Flow and Heat Transfer toward a Stretching Permeable Cylinder

Mastroberardino

Siddique

2014

Advances in Mechanical Engineering

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“…This method has found an application for solving many problems formulated with the aid of ordinary and partial differential equations [24][25][26][27], including the heat conduction problems [28][29][30][31], fractional differential equations [32,33] (for some other applications of the fractional calculus see for example [34][35][36]), integral equations [37][38][39], integro-differential equations [40,41] and others. A particular case of the homotopy analysis method is the homotopy perturbation method [16,17,42].…”

Section: Introductionmentioning

confidence: 99%

An analytical method for solving the two-phase inverse Stefan problem

Hetmaniok¹,

Słota²,

Wituła³

et al. 2015

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. In the paper we present an application of the homotopy analysis method for solving the two-phase inverse Stefan problem. In the proposed approach a series is created, having elements which satisfy some differential equation following from the investigated problem. We reveal, in the paper, that if this series is convergent then its sum determines the solution of the original equation. A sufficient condition for this convergence is formulated. Moreover, the estimation of the error of the approximate solution, obtained by taking the partial sum of the considered series, is given. Additionally, we present an example illustrating an application of the described method.

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“…It enables to solve the operator equations of different kind. In particular, the method has found a number of applications in heat conduction problems [1,16,18,26,56]. It is also used, among others, for solving the nonlocal initial boundary value problem [35], nonlinear reaction-diffusion-convection problems [41] and fractional differential equations [4,54,58].…”

Section: Introductionmentioning

confidence: 99%

Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

et al. 2013

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The paper presents an application of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind. In this method a series is created, sum of which (if the series is convergent) gives the solution of discussed equation. Conditions ensuring convergence of this series are presented in the paper. Error of approximate solution, obtained by considering only partial sum of the series, is also estimated. Examples illustrating usage of the investigated method are presented as well, including the example having practical application for calculating the charge in supply circuit of flash lamps used in cameras.

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Magnetohydrodynamic flow and heat transfer in a porous medium along a stretching cylinder with radiation: homotopy analysis method

Cited by 23 publications

References 31 publications

Magnetohydrodynamic Stagnation Flow and Heat Transfer toward a Stretching Permeable Cylinder

Magnetohydrodynamic Stagnation Flow and Heat Transfer toward a Stretching Permeable Cylinder

An analytical method for solving the two-phase inverse Stefan problem

Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

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