Application of homotopy perturbation method for MHD boundary layer flow of an upper-convected Maxwell fluid in a porous medium

Jhankal, Anuj Kumar

doi:10.3329/cerb.v18i1.26216

Cited by 5 publications

(3 citation statements)

References 27 publications

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“…The problem's exact solution is 𝑢(𝑥) = 1 1+𝑥 . Here we consider only two cases: case-IA (equation ( 21)) with one unknown parameter 𝜆 1 for which the initial guess (from (20) and ( 34)) is…”

Section: Figurementioning

confidence: 99%

“…But HPM is easier to use than HAM due to the absence of the auxiliary parameter and is widely used in science, and engineering. 20,21,15,12 Liang and Jeffrey 3 noted that HPM's series solution may be divergent except at the initial assumption. Liao 6 mentioned that the convergence of Liao's series solution depends on four factors: the initial guess (𝑢 0 (𝑥)), the linear operator (𝐿(𝑢)), the artificial function (𝐻(𝑥)), and the artificial parameter (𝑐 0 ).…”

Section: Introductionmentioning

confidence: 99%

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A General Mathematical Approach On the Selection of Auxiliary Linear Operator and Initial Guess for Homotopy Methods

Maiti

ROY

2023

Preprint

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In this study we propose a general mathematical algorithm for the selection of aux- iliary linear operator () and initial guess 0(), which are the principal parts of Homotopy methods: Homotopy Perturbation Method (HPM) and Homotopy Anal- ysis Method (HAM). We assume the coefficients of derivatives involved in () as a functions of auxiliary roots of () = 0. Based on the residual error minimization we compute unknown roots and thereby obtain the best fitted optimal linear operator. Additionally, from the efficiency standpoint, we suggest discretize the exact square residual using the Simson’s 31 algorithm. We applied our algorithms to six nonlin- ear problems: (i) two nonlinear initial value problem (IVP) (ii) two highly nonlinear BVPs with quadratic and cubic nonlinearity, (iii) Bessel equation of zero-order and (iv) A singular and highly nonlinear BVP (for fluid electrohydrodynamics). We then compare our technique’s accuracy and efficiency to other existing analytical and nu- merical methods. It demonstrates that our best fitted optimal linear operator is much more efficient, important (than the artificial controlling parameters or functions of optimal HAM) and self-sufficient for the convergence of series solutions over the whole domain, specially for IVP. Also, an effort is made to search the best () for different choices of real roots and by means of fastest converges of the solution. Our approach is more effective, straightforward and easy to use when applied to many nonlinear problems arises in science and engineering, and using our propose ap- proach homotopy methods (HAM and HPM) will be more powerful.

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Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A General Mathematical Approach On the Selection of Auxiliary Linear Operator and Initial Guess for Homotopy Methods

Maiti

ROY

2023

Preprint

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“…Ilyas Khan et al, [40] discussed some interesting results on the required time for the steady state of MHD Maxwell fluid in a porous half space. Anuj Kumar [41] presented an analytical solution and velocity profiles for electrically conducting UCM fluid in a porous medium.…”

Section: Introductionmentioning

confidence: 99%

Analysis of MHD and Heat Transfer Characteristics of Thermally Radiative Upper-Convected Maxwell Fluid Flow between Moving Plates: Semi-Analytical and Numerical Solution

Sampath Kumar V S,

Devaki B,

Nityanand P Pai

2024

CFDL

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The current paper studies the MHD and heat transfer characteristics of radiative upper-convected Maxwell fluid flow between two plates approaching or receding from each other with injection at the fixed lower porous plate. The governing momentum and energy equations are reduced into non-linear ordinary differential equations employing similarity transformations. With the help of the Homotopy Perturbation Method (HPM), an approximate analytic solution is obtained. This work aims to determine the effects of Reynolds number (R), Deborah number (De), Radiation parameter (Rd), Magnetic parameter (M), and Prandtl number (Pr) on the velocity and temperature profiles. It is observed that the Deborah number has a direct impact on the velocity profile when there is a squeezed flow. It is also observed that the magnetic parameter shows an indirect impact on the temporal distribution for both the upper plate moving away and towards the lower. The variations in the significant physical parameters on the coefficient of skin friction and heat transfer rates are also calculated. The results are then compared with the classical finite difference method and are in excellent agreement. It is found that larger the magnetic parameter, the dominance of viscous forces retards the velocity in the core region, and the increase in radiation parameter suppresses the heat transfer rates. This study is helpful in industrial applications, specifically in polymer processing.

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Pseudoplastic Magnetorheological Fluid Flow on a Moving Horizontal Flat Plate

Silva-Zea

Erazo-Bone

Chuchuca-Aguilar

et al. 2020

Communications in Computer and Information Science

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Application of homotopy perturbation method for MHD boundary layer flow of an upper-convected Maxwell fluid in a porous medium

Cited by 5 publications

References 27 publications

A General Mathematical Approach On the Selection of Auxiliary Linear Operator and Initial Guess for Homotopy Methods

A General Mathematical Approach On the Selection of Auxiliary Linear Operator and Initial Guess for Homotopy Methods

Analysis of MHD and Heat Transfer Characteristics of Thermally Radiative Upper-Convected Maxwell Fluid Flow between Moving Plates: Semi-Analytical and Numerical Solution

Pseudoplastic Magnetorheological Fluid Flow on a Moving Horizontal Flat Plate

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