Gravity-driven laminar film flow of power-law fluids along vertical walls

Andersson, Helge I.; Irgens, Fridtjov

doi:10.1016/0377-0257(88)85011-0

Cited by 53 publications

(39 citation statements)

References 18 publications

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“…They have particular significance in the original problem. Therefore, the resulting self-similar solution f ′ (η) and |f ′′ (0)| n for various values of the parameters, which are obtained by utilizing numerical and analytical methods, are always displayed in tables and figures in many references, for example, [4,5,8,9,13,16,17,19].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Exact self-similar solutions of the magnetohydrodynamic boundary layer system for power-law fluids

Zhang

Wang

2007

Z. angew. Math. Phys.

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In a particular self-similar case, the magnetohydrodynamic boundary layer system for an electrically conducting power-law fluid together with certain boundary conditions can be transformed into a boundary value problem for a third-order nonlinear ordinary differential equation, only whose (generalized) normal solutions possess the physical meaning of the original problem. Uniqueness, existence and nonexistence results are established for the problem. Representations are also given for all (generalized) normal solutions. (2000). 76A05, 76D10, 34B15. Mathematics Subject Classification

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Section: Formulation Of the Problemmentioning

confidence: 99%

Exact self-similar solutions of the magnetohydrodynamic boundary layer system for power-law fluids

Zhang

Wang

2007

Z. angew. Math. Phys.

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“…Accordingly, it has been extensively studied during the last decades. For details, see, for example, [1,2] and the references therein. The third-order nonlinear ordinary differential equation for f (η),…”

Section: Introductionmentioning

confidence: 99%

“…with boundary conditions f (0) = 0, f (0) = 0, f (+∞) = 1, (1.2) arises just in the study of gravity-driven laminar film flow of power-law fluids along vertical walls and was deduced by Andersson and Irgens in [1]. Here n > 0 is the power-law index of the fluid, β := 2n+1 n+1 , ξ > 0 a dimensionless constant, and f (η) denotes the dimensionless stream function.…”

Section: Introductionmentioning

confidence: 99%

“…Here the physical meaning of each letter can be found in [1] and hence is omitted, since all letters emerging the above formula, excluding n and ξ, will never be used in the following.…”

Section: Introductionmentioning

confidence: 99%

“…In the paper [1], the boundary layer problem (1.1) -(1.2) has been solved only numerically for n = 0.5, 1.0, 1.5, 2.0, and ξ = 1.5. The resulting similarity solutions for the dimensionless velocity f (η) are displayed in a figure, while some characteristic boundary parameters, including f (0), are given in a table.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A boundary layer problem arising in gravity-driven laminar film flow of power-law fluids along vertical walls

Zhang

Wang

Shi

2004

Z. angew. Math. Phys.

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A rigorous mathematical analysis is given for a boundary layer problem for a thirdorder nonlinear ordinary differential equation, which arises in gravity-driven laminar film flow of power-law fluids along vertical walls. Firstly, the problem is transformed into a singular nonlinear two-point boundary value problem of second order. Next, the latter is proved to have a unique positive solution, for which some estimates are established. Finally, the result above-mentioned is turned over to the original problem. The conclusion of this paper is that the boundary layer problem has a unique normal solution if the power-law index is less than or equal to one and a generalized normal solution if the power-law index is greater than one. Also the asymptotic behavior of the normal solution at the infinity is displayed. Mathematics Subject Classification (2000). 76A05, 76D10, 34B15.

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Falling film flow of a viscoelastic fluid along a wall

Miao

Aubry

et al. 2013

Math Methods in App Sciences

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In this paper, we study the heat transfer in the fully developed flow of a viscoelastic fluid, a slag layer, down a vertical wall. A new constitutive relation for the stress tensor of this fluid is proposed, where the viscosity depends on the volume fraction, temperature, and shear rate. For the heat flux vector, we assume the Fourier's law of conduction with a constant thermal conductivity. The model is also capable of exhibiting normal stress effects. The governing equations are non-dimensionalized and numerically solved to study the effects of various dimensionless parameters on the velocity, temperature, and volume fraction. The effect of the exponent in the Reynolds viscosity model is also discussed. The different cases of shear-thinning and shear-thickening, cooling and heating, are compared and discussed. The results indicate that the viscous dissipation and radiation (at the free surface) cause the temperature to be higher inside the flow domain.

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Gravity-driven laminar film flow of power-law fluids along vertical walls

Cited by 53 publications

References 18 publications

Exact self-similar solutions of the magnetohydrodynamic boundary layer system for power-law fluids

Exact self-similar solutions of the magnetohydrodynamic boundary layer system for power-law fluids

A boundary layer problem arising in gravity-driven laminar film flow of power-law fluids along vertical walls

Falling film flow of a viscoelastic fluid along a wall

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