On linearization method to MHD boundary layer convective heat transfer with low pressure gradient

Ahmed, M. A.; Mohammed, Mohammed E.; Khidir, Ahmed A.

doi:10.1016/j.jppr.2015.04.001

Cited by 26 publications

(15 citation statements)

References 18 publications

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“…He then solved the governing PDEs by using homotopy perturbation and homotopy analysis methods to convert them to ODEs. e thirdorder nonlinear ordinary differential equations ( 7) and the second-order nonlinear ordinary differential equations ( 8) are expressed as differential equations and solved using the successive linearization technique (SLM) [26,31] in this article.…”

Section: Solution Methodologymentioning

confidence: 99%

Chemical Reaction and Generalized Heat Flux Model for Powell–Eyring Model with Radiation Effects

Salah

2022

International Journal of Mathematics and Mathematical Sciences

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In the current research, the numerical solutions for heat transfer in an Eyring–Powell fluid that conducts electricity past an exponentially growing sheet with chemical reactions are examined. As the sheet is stretched in the x direction, the flow occupies the region y > 0 . MHD, radiation, joule heating effects, and thermal relaxation time are all used to represent the flow scenario. The emergent problem is represented using PDEs, which are then converted to ODEs using appropriate similarity transformations. The converted problem is solved numerically using the SLM method. The main goal of this paper is to compare the results of solving the velocity and temperature equations in the presence of K changes through SLM, introducing it as a precise and appropriate method for solving nonlinear differential equations. Tables with the numerical results are created for comparison. This contrast is important because it shows how precisely the successive linearization method can resolve a set of nonlinear differential equations. Following that, the generated solution is studied and explained in relation to a variety of engineering parameters. Additionally, the thermal relaxation period is inversely proportional to the thickness of the thermal boundary layer and the temperature, but the Eckert number E c is the opposite. As E c grows, the temperature within the channel increases.

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Section: Solution Methodologymentioning

confidence: 99%

Chemical Reaction and Generalized Heat Flux Model for Powell–Eyring Model with Radiation Effects

Salah

2022

International Journal of Mathematics and Mathematical Sciences

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“…Recently some studies have presented a new method called Successive Linearization Method (SLM). This method has been applied successfully in many nonlinear problems in sciences and engineering, such as the MHD flows of non-Newtonian fluids and heat transfer over a stretching sheet (Shateyi and Motsa, 2010), viscoelastic squeezing flow between two parallel plates, (Makukula et al, 2010a), two dimensional laminar flow between two moving porous walls (Makukula et al, 2010b) and convective heat transfer for MHD boundary layer with pressure gradient (Ahmed et al, 2015). Therefore, the effectiveness, validity, accuracy and flexibility of the SLM are verified among of all these successful applications.…”

Section: Introductionmentioning

confidence: 91%

“…10 with the boundary condition Eq. 11 were solved using a successive linearization method (SLM) (Makukula et al, 2010a;2010b;Ahmed et al, 2015) for SLM solution we choose the unknown function ( ) in the form…”

Section: Solution Of the Lifting Problemmentioning

confidence: 99%

A note on thin-film flow of Eyring-Powell fluid on the vertically moving belt using successive linearization method

Salah¹

2019

Int. j. adv. appl. sci.

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The main goal of this work is to obtain the numerical solution for thin film flow of MHD an incompressible Eyring-Powell fluid on a vertically moving belt. The nonlinear equation governing the flow problem is modeled and then solved numerically by means of a successive linearization method (SLM). The numerical results are derived in tables for comparisons. The important result of this comparison is the high precision of the SLM in solving nonlinear differential equations. The solutions take into account the behavior of Newtonian and non-Newtonian fluids. Graphical outcomes of various non-Newtonian parameters such as Hartman number and Stokes number on the flow field are discussed and analyzed. Besides this, the present results have been tested and compared with the available published results in a limiting manner and an excellent agreement is found.

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“…Here successive linearization method (SLM) (Makukula et al, 2020b;Salah et al, 2019;Ahmed et al, 2015) is implemented to obtain the numerical solutions for nonlinear systems in Eqs. 8 and 10 corresponding to the boundary condition in Eqs.…”

Section: Procedures Of Computationalmentioning

confidence: 99%

“…Recently some studies have shown a new method called the successive linearization method (SLM). This method has been successfully applied to many non-linear problems in science and engineering, such as MHD flows of non-Newtonian fluids and transfer over a stretching sheet (Shateyi and Motsa, 2010), and the viscous pressure-flow between two parallel plates (Makukula et al, 2010a), a two-dimensional plate flowing between two porous walls (Makukula et al, 2010b), on the thin-film flow of Eyring-Powell fluid on the vertically moving belt (Salah et al, 2019) and convective thermal transfer heat to the MHD boundary layer with a pressure gradient (Ahmed et al, 2015). Therefore, this method has shown very high efficiency, accuracy, and flexibility of SLM in solving nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for heat transfer of Oldroyd–B fluid over a stretching sheet using successive linearization method

Salah¹

2020

Int. j. adv. appl. sci.

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The objective of this study is to find the numerical solution for the MHD flow of heat transfer to the incompressible Oldroyd-B liquid on a stretching sheet channel. The partial differential equations governing this system are converted into ordinary differential equations using similarity conversion. The resulting nonlinear equations governing the flow problem are numerically solved by the successive line method (SLM). Numerical results are derived and presented in tables for some comparisons. These comparisons are important in demonstrating the high accuracy of SLM in solving the system of nonlinear differential equations. These solutions take into account the behavior of Newtonian and non-Newtonian fluids. It is reported that Deborah number in terms of relaxation time resists and slows down the motion of fluid particles at various time instants. Temperature profile increase by increasing Deborah number in terms of relaxation time. The graphical results of various non-Newtonian parameters such as coefficient of mixed convection, Hartman, Deborah, and Prandtl number on the flow, field, and analysis are also discussed. In addition, the current results were tested and compared to the published results available in a limited manner, and an excellent agreement was reached.

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On linearization method to MHD boundary layer convective heat transfer with low pressure gradient

Cited by 26 publications

References 18 publications

Chemical Reaction and Generalized Heat Flux Model for Powell–Eyring Model with Radiation Effects

Chemical Reaction and Generalized Heat Flux Model for Powell–Eyring Model with Radiation Effects

A note on thin-film flow of Eyring-Powell fluid on the vertically moving belt using successive linearization method

Numerical solution for heat transfer of Oldroyd–B fluid over a stretching sheet using successive linearization method

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