MHD mixed convective nanofluid flow about a vertical slender cylinder using overlapping multi-domain spectral collocation approach

Mkhatshwa, Musawenkhosi Patson; Motsa, S. S.; Ayano, Mekonnen Shiferaw; Sibanda, Precious

doi:10.1016/j.csite.2020.100598

Cited by 39 publications

(20 citation statements)

References 21 publications

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“…Rafique et al [7] have obtained the numerical solution of casson nanofluid streams over a nonlinear sloping surface through Soret and Dufour effects by the Keller-Box method. Mkhatshwa et al [8] investigated the MHD mixed convective nanofluid flow about a vertical thin cylinder using the interfering multidomain spectral collocation approach. Huang [9] analyzed the effect of non-Darcy and MHD on free convection of non-Newtonian fluids over a vertical plate which can be infiltrated in a pored medium with Soret/Dufour effects and thermal radiation.…”

Section: Introductionmentioning

confidence: 99%

MHD Mixed Convection Nanofluid Flow over Convectively Heated Nonlinear due to an Extending Surface with Soret Effect

et al. 2021

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The aim of this paper is to investigate the flow of MHD mixed convection nanofluid flow under nonlinear heated due to an extending surface. The transfer of heat in nanofluid subject to a magnetic field and boundary conditions of convective is studied to obtain the physical meaning of the convection phenomenon. The governing partial differential equations (PDEs) of the boundary layer are reduced to ordinary differential equations (ODEs) considering a technique of the transformation of similarity. The transformed equations are solved numerically considering the technique of an efficient numerical shooting applying the Runge–Kutta technique scheme from the fourth-fifth order. The results corresponding to the dimensionless speed, temperature, concentration profiles, and the Nusselt number reduced, and the Sherwood numbers are presented by figures to display the physical meaning of the phenomena. A comparison has been made between the obtained results with the previous results obtained by others and agrees with them if the new parameters vanish. The results obtained indicate the impacts of the nondimensional governing parameters, namely, magnetic field parameter M, Soret number Sr, heat source λ, thermal buoyancy parameter λ T , and solutal buoyancy parameter λ C on the flow, temperature, and concentration profiles being discussed and presented graphically.

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Section: Introductionmentioning

confidence: 99%

MHD Mixed Convection Nanofluid Flow over Convectively Heated Nonlinear due to an Extending Surface with Soret Effect

et al. 2021

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“…In the non-overlapping multi-domain BSQLM, the multi-domain technique was only applied in time. Recently, Mkhatshwa et al [8,9] found that the accuracy of the BSQLM can be improved by applying the overlapping multi-domain technique in the space interval and the non-overlapping multi-domain technique in the time interval. Teleei and Dehghan [10] introduced a numerical scheme for the solution of sine-Gordon equation when only space discretization is performed by an overlapping multi-domain pseudo-spectral technique.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of time-dependent Emden-Fowler equations using bivariate spectral collocation method on overlapping grids

Mkhatshwa

Motsa

Sibanda

2020

Nonlinear Engineering

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AbstractIn this work, we present a new modification to the bivariate spectral collocation method in solving Emden-Fowler equations. The novelty of the modified approach is the use of overlapping grids when applying the Chebyshev spectral collocation method. In the case of nonlinear partial differential equations, the quasilinearisation method is used to linearize the equation. The multi-domain technique is applied in both space and time intervals, which are both decomposed into overlapping subintervals. The spectral collocation method is then employed in the discretization of the iterative scheme to give a matrix system to be solved simultaneously across the overlapping subintervals. Several test examples are considered to demonstrate the general performance of the numerical technique in terms of efficiency and accuracy. The numerical solutions are matched against exact solutions to confirm the accuracy and convergence of the method. The error bound theorems and proofs have been considered to emphasize on the benefits of the method. The use of an overlapping grid gives a matrix system with less dense matrices that can be inverted in a computationally efficient manner. Thus, implementing the spectral collocation method on overlapping grids improves the computational time and accuracy. Furthermore, few grid points in each subinterval are required to achieve stable and accurate results. The approximate solutions are established to be in excellent agreement with the exact analytical solutions.

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“…[46][47][48][49] In all these studies, the overlapping multidomain approach was applied only in the spatial domain, and it was found that the accuracy of pseudospectral methods improved through the use of overlapping grid procedure. Mkhatshwa et al 48 and Mkhatshwa et al 49 considered nonlinear PDEs modeling problems that arise in fluid mechanics. The BSQLM on overlapping grids was introduced by Mkhatshwa et al 38 and implemented to solve time-dependent Emden-Fowler equations.…”

Section: Introductionmentioning

confidence: 99%

“…The single‐domain BSQLM method uses quasilinearization technique, 45 the Chebyshev spectral collocation method, as well as the bivariate Lagrange interpolation polynomial with Chebyshev‐Gauss‐Lobatto grid points. The overlapping multidomain technique with pseudospectral methods has been considered by several researchers 46‐49 . In all these studies, the overlapping multidomain approach was applied only in the spatial domain, and it was found that the accuracy of pseudospectral methods improved through the use of overlapping grid procedure.…”

Section: Introductionmentioning

confidence: 99%

MHD mixed convective radiative flow of Eyring‐Powell fluid over an oscillatory stretching sheet using bivariate spectral method on overlapping grids

2020

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The bivariate spectral quasilinearization method (BSQLM) on overlapping grids is presented and applied in the analysis of unsteady magnetohydrodynamic mixed convection flow of Eyring-Powell fluid over an oscillatory stretching sheet embedded in a non-Darcy porous medium with nonlinear radiative heat flux and variable thermophysical properties. The fluid properties, namely the fluid viscosity, thermal conductivity, and mass diffusivity, are assumed to vary with temperature. It is assumed that the first-order chemical reaction with heat generation/absorption takes place in the flow. The flow domain is subject to uniform transverse magnetic field perpendicular to the stretching surface. The transformed flow equations are solved numerically using BSQLM on overlapping grids. The convergence properties and accuracy of the method are assessed. The proposed method is computationally efficient, and it gives stable and highly accurate results after few iterations and using few grid points in each subinterval. The improved accuracy rests upon the use of the overlapping grid, which produces sparse coefficient matrices that are easy to invert and have small condition numbers. The effects of physical parameters on the flow fields, local skin friction, the

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MHD mixed convective nanofluid flow about a vertical slender cylinder using overlapping multi-domain spectral collocation approach

Cited by 39 publications

References 21 publications

MHD Mixed Convection Nanofluid Flow over Convectively Heated Nonlinear due to an Extending Surface with Soret Effect

MHD Mixed Convection Nanofluid Flow over Convectively Heated Nonlinear due to an Extending Surface with Soret Effect

Numerical solution of time-dependent Emden-Fowler equations using bivariate spectral collocation method on overlapping grids

MHD mixed convective radiative flow of Eyring‐Powell fluid over an oscillatory stretching sheet using bivariate spectral method on overlapping grids

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