Comparative Evaluation of the Optimal Auxiliary Function Method and Numerical Method to Explore the Heat Transfer between Two Parallel Porous Plates of Steady Nanofluids with Brownian and Thermophoretic Influences

Ullah, Hakeem; Khan, Rafaqat Ali; Fiza, Mehreen; Islam, Saeed; AL–Mekhlafi, S.M.

doi:10.1155/2022/7975101

Cited by 5 publications

(3 citation statements)

References 49 publications

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“…The FEM is a powerful method to evaluate the nonlinear differential equations and can be used to engineering problems such as fluid mechanics, biomathematics, physics, and channel process [49][50][51].…”

Section: Finite Element Methodsmentioning

confidence: 99%

Effect of Joule Heating and Thermal Radiation of MHD Boundary Layer Oldroyd‐B Nanofluid Flow with Heat Transfer over a Porous Stretching Sheet by Finite Element Method

Ullah

Fiza

Khan

et al. 2022

Journal of Nanomaterials

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In this study, an incompressible two-dimensional Oldroyd-B nanofluid steady flow past a stretching sheet considering the outcomes of magneto-hydrodynamics (MHD) and porous medium with magnetic, electrical, and thermal radiation effects is investigated. Using a similarity transformation, the governing equations in the form of partial differential equations (PDEs) are converted into a nonlinear ordinary differential equations (ODEs) system. The acquired system is numerically solved by the finite element method (FEM). The effects of physical parameters like Deborah numbers “ β 1 ” and “ β 2 ”, Brownian motion “ N b ”, thermophoresis parameter “ N t ”, Prandtl parameter “ Pr ”, Lewis number “ L e ”, thermal conductivity “ k ”, dynamic viscosity “μ”, magnetic and electric effects as “ M ” and “ E 1 ”, and thermal radiation effect “ Rd ” on the flow are studied in detail. For higher N b values, regional Nusselt numbers are increasing in magnitude. The local Sherwood number’s size rises for high N b numbers.

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Section: Finite Element Methodsmentioning

confidence: 99%

Effect of Joule Heating and Thermal Radiation of MHD Boundary Layer Oldroyd‐B Nanofluid Flow with Heat Transfer over a Porous Stretching Sheet by Finite Element Method

Ullah

Fiza

Khan

et al. 2022

Journal of Nanomaterials

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“…Analytically addressing the solutions of these scientific models is often challenging, necessitating the use of specialized numerical techniques. Traditional numerical approaches such as the variation iteration method [23], the Adam-Bashforth method [24], the Runge-kutta approach [25], and the finite element method [26] have been applied for this purpose.…”

Section: Introductionmentioning

confidence: 99%

A stagnation point flow of cross nanofluid flow: Levenberg Marquardt backpropagation computational approach

Shoaib,

Nisar,

Raja

et al. 2023

Z Angew Math Mech

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In the present article, the intelligence based numerical investigation by Levenberg–Marquardt algorithm with Back‐propagated Artificial Neural Networks (LMA–BANN) is exploited to analyze the nonlinear radiative stagnation point flow of cross nanofluid system (NRS‐CNFS) past a stretching surface. The designed NRS‐CNFS, initially represented by system of partial differential equations (PDEs), is converted into system of non‐linear ODEs through the applicability of mathematical conversion analysis. The desired reference solution in the form of a dataset for LMA–BANN is achieved from the Adam method for NRS‐CNFS's different scenarios by varying the magnetic parameter (Ha), Prandlt number (Pr), thermal radiation parameter(R), Eckert number (Ec), thermophoresis diffusion coefficients (Nt), and non‐dimensional activation energy (E). The obtained results are construed for the NRS‐CNFS through the performances of the testing, validation, and training. In addition, the comparison is provided using the LMA ‐BANN analysis, which is validated in terms of regression, fitness estimations, and histograms along with MSE performances. Hence, the article provides an impeccable innovative approach to problem‐solving by implementing a soft computation paradigm. It promotes the use of an effective and dependable alternative framework that is based on soft computing environments and emphasizes descriptive analysis to successfully handle the problems brought on by varied physical features.

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“…Ullah et al [31] have just recently utilized this strategy in order to evaluate fractional KdV equations. In reference [32], the proposed method has been employed for the steady nanofluids. The method has recently been applied in biological modeling [33].…”

Section: Introductionmentioning

confidence: 99%

Approximations of Time-Dependent Nonlinear Partial Differential Equations using Galerkin Optimal Auxiliary Function Method

Trisha,

Islam

2023

GANIT: J. Bangladesh Math. Soc.

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The purpose of this research work is to employ the Optimal Auxiliary Function Method (OAFM) for obtaining numerical approximations of time-dependent nonlinear partial differential equations (PDEs) that arise in many disciplines of science and engineering. The initial and first approximations of parabolic nonlinear PDEs associated with initial conditions have been generated by utilizing this method. Then the Galerkin method is applied to estimate the coefficients that remain unknown. Finally, the values of the coefficients generated by the Galerkin method have been inserted into the first approximation. In each example, all numerical computations and corresponding absolute errors are provided in schematic representations. The rate of convergence attained by the proposed method is depicted in tabular form. GANIT J. Bangladesh Math. Soc. 43.1 (2023) 001- 016

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Comparative Evaluation of the Optimal Auxiliary Function Method and Numerical Method to Explore the Heat Transfer between Two Parallel Porous Plates of Steady Nanofluids with Brownian and Thermophoretic Influences

Cited by 5 publications

References 49 publications

Effect of Joule Heating and Thermal Radiation of MHD Boundary Layer Oldroyd‐B Nanofluid Flow with Heat Transfer over a Porous Stretching Sheet by Finite Element Method

Effect of Joule Heating and Thermal Radiation of MHD Boundary Layer Oldroyd‐B Nanofluid Flow with Heat Transfer over a Porous Stretching Sheet by Finite Element Method

A stagnation point flow of cross nanofluid flow: Levenberg Marquardt backpropagation computational approach

Approximations of Time-Dependent Nonlinear Partial Differential Equations using Galerkin Optimal Auxiliary Function Method

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