Application of He’s Method in Solving a System of Nonlinear Coupled Equations Arising in Non-Newtonian Fluid Mechanics

Farooq, Asim; Siddiqui, A. M.; Rana, MA; Haroon, T.

doi:10.14419/ijamr.v1i2.42

Cited by 3 publications

(4 citation statements)

References 11 publications

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“…It is observed that the velocity and temperature distributions decrease with the increase of the non-Newtonian viscous parameter δ, and the highest velocity is manifested in the neighborhood of η = -0.5 in the case at which the non-Newtonian viscous parameter δ is zero In what follows, we investigate the effects of volume fraction φ and the nature of the nanoparticles on the friction and heat transfer coefficients as shown in Figures (10)(11).…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore, a comparison was made between the numerical and analytical results that were obtained. The work of A.A. Farooq [10] included a thorough comparison between the Runge-Kutta fourth order and the HPM methods; and the study reveals a range of applicability for HPM. Y. Rahmani [11], for his part, considered the presence of nanoparticles (Ag, Cu, 2 3 , and…”

Section: Introductionmentioning

confidence: 99%

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A New Analytical Investigation of Natural Convection of Non-Newtonian Nanofluids Flow Between Two Vertical Flat Plates by the Generalized Decomposition Method (Gdm)

Tabet¹

2018

Journal of Thermal Engineering

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In this work, natural convection in a non-Newtonian fluid/nanofluid between two vertical plates is investigated. The study was carried out on three types of nanofluids, namely Silver/Water, Oxide Copper-Water and Titanium oxide/Water. The mathematical formulation gives a set of strongly coupled nonlinear ordinary differential equations of the second order. These equations, characterizing velocity and temperature distributions, were solved numerically by the Runge-Kutta fourth order method, and analytically by a new Adomian of decomposition approach named the Adomian generalized method (GDM). The results show clearly the effectiveness, accuracy and applicability of the used technique (GDM). Using nanoparticles (Ag, CuO and 2) in water as a base fluid substantially increases the coefficient of friction and characteristics of heat transfer. Compared to other works, the generalized Adomian decomposition technique (GDM) offers the advantages of precision and velocity of convergence.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Analytical Investigation of Natural Convection of Non-Newtonian Nanofluids Flow Between Two Vertical Flat Plates by the Generalized Decomposition Method (Gdm)

Tabet¹

2018

Journal of Thermal Engineering

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“…The natural convection of non-Newtonian fluids has been studied by many authors. [1][2][3][4][5][6][7][8][9][10][11] The natural convection problem between vertical flat plates for a certain class of non-Newtonian fluids has been carried out by Bruce and Na. 1 Rajagopal and Na 2 introduced a numerical solution for natural convection flow of Rivlin-Ericksen fluid and heat transfer between parallel plates.…”

Section: Introductionmentioning

confidence: 99%

“…The method is a useful tool for non-linear problems in science and engineering. Farooq et al 5 presented He's HPM to solve a non-linear coupled system of ordinary differential equations that arises in the fully developed natural convection flow of a third-grade fluid between two vertical parallel walls. The same problem is also solved by a numerical method (Runge-Kutta method of order 4) using the software MAPLE.…”

Section: Introductionmentioning

confidence: 99%

Natural convection flow of Rivlin–Ericksen fluid and heat transfer through non-Darcy medium with radiation

Ewis

2019

Advances in Mechanical Engineering

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The natural convection of non-Newtonian fluids between parallel plates has many engineering applications such as heat exchangers, cooling of electronic equipments, nuclear reactors, solar devices, polymer processing industries, food industries, and petroleum reservoirs. Numerical solution is introduced to solve the governing equations of natural convection of non-Newtonian (Rivlin–Ericksen) fluid flow and heat transfer under the influences of non-Darcy resistance force, constant pressure gradient, dissipation, and radiation. The novelty of this article is to solve this problem between parallel plates channel instead of one plate. The fluid flows between two heated parallel plates that are kept at constant temperatures. Second-order accurate finite difference schemes transform the coupled non-linear differential (momentum and energy) equations to linearized system of algebraic equations. Some comparisons are made to study the convergence and stability of the present results. Effects of parameters of fluid and heat on the velocity field, temperature, skin friction factor, and Nusselt number are illustrated and discussed. The present results and their comparisons with available results are listed and shown in tables and figures. The present results show that the numerical solution is of good agreement with previous analytical and numerical solutions.

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Simultaneous Impacts of Fe3O4{\text{Fe}_{3}}{\text{O}_{4}} Particles and Thermal Radiation on Natural Convection of Non-Newtonian Flow Between Two Vertical Flat Plates Using ADM

Gabli

Kezzar

Zighed

et al. 2020

Journal of Non-Equilibrium Thermodynamics

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The main aim of this research work is to show the simultaneous effects of ferro-particles ({\text{Fe}_{3}}{\text{O}_{4}}) and thermal radiation on the natural convection of non-Newtonian nanofluid flow between two vertical flat plates. The studied nanofluid is created by dispersing ferro-particles ({\text{Fe}_{3}}{\text{O}_{4}}) in sodium alginate (SA), which is considered as a non-Newtonian base fluid. Resolution of the resulting set of coupled non-linear second order differential equations characterizing dynamic and thermal distributions (velocity/temperature) is ensured via the Adomian decomposition method (ADM). Thereafter the obtained ADM results are compared to the Runge–Kutta–Feldberg based shooting data. In this investigation, a parametric study was conducted showing the influence of varying physical parameters, such as volumic fraction of {\text{Fe}_{3}}{\text{O}_{4}} nanoparticles, Eckert number ({E_{c}}) and thermal radiation parameter (N), on the velocity distribution, the skin friction coefficient, the heat transfer rate and the temperature distribution. Results obtained also show the advantages of ferro-particles over other types of standard nanoparticles. On the other hand, this investigation demonstrates the accuracy of the adopted analytical ADM technique.

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Application of He’s Method in Solving a System of Nonlinear Coupled Equations Arising in Non-Newtonian Fluid Mechanics

Cited by 3 publications

References 11 publications

A New Analytical Investigation of Natural Convection of Non-Newtonian Nanofluids Flow Between Two Vertical Flat Plates by the Generalized Decomposition Method (Gdm)

A New Analytical Investigation of Natural Convection of Non-Newtonian Nanofluids Flow Between Two Vertical Flat Plates by the Generalized Decomposition Method (Gdm)

Natural convection flow of Rivlin–Ericksen fluid and heat transfer through non-Darcy medium with radiation

Simultaneous Impacts of Fe3O4{\text{Fe}_{3}}{\text{O}_{4}} Particles and Thermal Radiation on Natural Convection of Non-Newtonian Flow Between Two Vertical Flat Plates Using ADM

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