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Numerical Investigation of the Effect of Unsteadiness on Three-Dimensional Flow of an Oldroyb-B Fluid.

Motsa SS, Makukula ZG, Shateyi S - PLoS ONE (2015)

Bottom Line: The modified approach involves seeking solutions that are expressed as bivariate Lagrange interpolating polynomials and applying pseudo-spectral collocation in both independent variables of the governing PDEs.Numerical analysis of the error and convergence properties of the method are also discussed.One of the benefits of the proposed method is that it is computationally fast and gives very accurate results after only a few iterations using very few grid points in the numerical discretization process.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa.

ABSTRACT
A spectral relaxation method used with bivariate Lagrange interpolation is used to find numerical solutions for the unsteady three-dimensional flow problem of an Oldroyd-B fluid with variable thermal conductivity and heat generation. The problem is governed by a set of three highly coupled nonlinear partial differential equations. The method, originally used for solutions of systems of ordinary differential equations is extended to solutions of systems of nonlinear partial differential equations. The modified approach involves seeking solutions that are expressed as bivariate Lagrange interpolating polynomials and applying pseudo-spectral collocation in both independent variables of the governing PDEs. Numerical simulations were carried out to generate results for some of the important flow properties such as the local skin friction and the heat transfer rate. Numerical analysis of the error and convergence properties of the method are also discussed. One of the benefits of the proposed method is that it is computationally fast and gives very accurate results after only a few iterations using very few grid points in the numerical discretization process.

No MeSH data available.


Related in: MedlinePlus

Effect of β2 on f′′(0, ξ).β = 0.5, β1 = 0.1 ϵ = 0.4, Pr = 2, S = 0.2.
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pone.0133507.g007: Effect of β2 on f′′(0, ξ).β = 0.5, β1 = 0.1 ϵ = 0.4, Pr = 2, S = 0.2.

Mentions: The effect of the flow parameters on the velocity and temperature profiles are not presented in this study since at any fixed time they are qualitatively similar to those presented in the study done by Shehzad et al. [14] for the equivalent steady state flow case. Hence we show the effect of the flow parameters on the skin friction coefficients and Nusselt number for varying time values. The effects of the ratio parameter β and the Deborah numbers β1 and β2 on the local skin friction coefficient along x−, −f′′(0, ξ) are presented in Figs 5–7. The skin friction coefficient along x− is seen to be a decreasing function of time as seen across all Figs 5–7.


Numerical Investigation of the Effect of Unsteadiness on Three-Dimensional Flow of an Oldroyb-B Fluid.

Motsa SS, Makukula ZG, Shateyi S - PLoS ONE (2015)

Effect of β2 on f′′(0, ξ).β = 0.5, β1 = 0.1 ϵ = 0.4, Pr = 2, S = 0.2.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4510369&req=5

pone.0133507.g007: Effect of β2 on f′′(0, ξ).β = 0.5, β1 = 0.1 ϵ = 0.4, Pr = 2, S = 0.2.
Mentions: The effect of the flow parameters on the velocity and temperature profiles are not presented in this study since at any fixed time they are qualitatively similar to those presented in the study done by Shehzad et al. [14] for the equivalent steady state flow case. Hence we show the effect of the flow parameters on the skin friction coefficients and Nusselt number for varying time values. The effects of the ratio parameter β and the Deborah numbers β1 and β2 on the local skin friction coefficient along x−, −f′′(0, ξ) are presented in Figs 5–7. The skin friction coefficient along x− is seen to be a decreasing function of time as seen across all Figs 5–7.

Bottom Line: The modified approach involves seeking solutions that are expressed as bivariate Lagrange interpolating polynomials and applying pseudo-spectral collocation in both independent variables of the governing PDEs.Numerical analysis of the error and convergence properties of the method are also discussed.One of the benefits of the proposed method is that it is computationally fast and gives very accurate results after only a few iterations using very few grid points in the numerical discretization process.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa.

ABSTRACT
A spectral relaxation method used with bivariate Lagrange interpolation is used to find numerical solutions for the unsteady three-dimensional flow problem of an Oldroyd-B fluid with variable thermal conductivity and heat generation. The problem is governed by a set of three highly coupled nonlinear partial differential equations. The method, originally used for solutions of systems of ordinary differential equations is extended to solutions of systems of nonlinear partial differential equations. The modified approach involves seeking solutions that are expressed as bivariate Lagrange interpolating polynomials and applying pseudo-spectral collocation in both independent variables of the governing PDEs. Numerical simulations were carried out to generate results for some of the important flow properties such as the local skin friction and the heat transfer rate. Numerical analysis of the error and convergence properties of the method are also discussed. One of the benefits of the proposed method is that it is computationally fast and gives very accurate results after only a few iterations using very few grid points in the numerical discretization process.

No MeSH data available.


Related in: MedlinePlus