Analytical solutions for the free-draining flow of a Carreau-Yasuda fluid on a vertical plate

Peralta, Juan Manuel; Meza, Barbara Erica del Valle; Zorrilla, Susana

doi:10.1016/j.ces.2017.05.002

Cited by 37 publications

(19 citation statements)

References 19 publications

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“…Since, for a shear-thinning fluid, μ 1 < 0 and hence J 1 < 0, the general results (43) and (44) show that, in agreement with the results for Carreau and Ellis fluids described in Sec. IV, the effect of weakly non-Newtonian behavior is always to make the rivulet smaller; in Eq.…”

Section: A General Resultssupporting

confidence: 77%

“…Notable among the limited number of previous studies of non-Newtonian rivulet flow are those by Rosenblat [3], who extended the pioneering work of Towell and Rothfeld [1] to study uniform rivulet flow of a viscoelastic fluid, Wilson et al [13], who extended the pioneering work of Smith [2] and Duffy and Moffatt [9] to study nonuniform rivulet flow of a power-law fluid, Balmforth et al [12] and Wilson et al [14], who studied rivulet flow of a viscoplastic material, Yatim et al [25], who studied unsteady nonuniform rivulet flow of a power-law fluid, and Al Mukahal et al [33,34], who studied locally uniform rivulet flow of a power-law fluid. However, despite a growing body of work on free surface flow of fluids with various non-Newtonian rheologies (see, for example, the recent work by Jossic et al [38] on thin-film flow of an Ellis fluid, Tshehla [39] on thin-film flow of a Carreau fluid, Kheyfets and Kieweg [40] on thin-film flow of an Ellis fluid, Pritchard et al [41] on thin-film flow of a generalized Newtonian fluid, Fomin et al [42] on non-Newtonian rimming flow, and Peralta et al [43] on thin-film flow of a Carreau-Yasuda fluid) there is very little work on rivulet flow of fluids with other than the theoretically convenient but highly idealised power-law rheology. Hence, in an attempt to begin to redress this imbalance, in the present work we consider rivulet flow of fluids with more realistic non-Newtonian rheologies, specifically generalized Newtonian fluids.…”

Section: Introductionmentioning

confidence: 99%

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Rivulet flow of generalized Newtonian fluids

2018

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Steady unidirectional gravity-driven flow of a uniform thin rivulet (i.e., a rivulet with small transverse aspect ratio) of a generalized Newtonian fluid down a vertical planar substrate is considered. The parametric solution for any generalized Newtonian fluid whose viscosity can be expressed as a function of the shear rate and the explicit solution for any generalized Newtonian fluid whose viscosity can be expressed as a function of the extra stress are obtained. These general solutions are used to describe rivulet flow of Carreau and Ellis fluids, highlighting the similarities and differences between the behavior of these two fluids. In addition, the general behavior of rivulets of nearly Newtonian fluids and of rivulets with small or large prescribed flux as well as the behavior of rivulets of strongly shear-thinning Carreau and Ellis fluids are also described. It is found that whereas the monotonic dependence of the viscosity of a Carreau fluid on its three nondimensional parameters and of an Ellis fluid on two of its three nondimensional parameters leads to the expected dependence of the behavior of the rivulet on these parameters (namely, that increasing the viscosity of the fluid leads to a larger rivulet), the nonmonotonic dependence of the viscosity of an Ellis fluid on the nondimensional parameter that measures the degree of shear thinning leads to a more complicated dependence of the behavior of the rivulet on this parameter. In particular, it is also found that when the maximum extra stress in the rivulet is sufficiently large a rivulet of an Ellis fluid in the strongly shear-thinning limit in which this parameter becomes large comprises two regions with different viscosities. In the general case of nonzero viscosity in the limit of large extra stress the two regions have different constant viscosities, whereas in the special case of zero viscosity in the limit of large extra stress one region has constant viscosity and the other has a nonconstant power-law viscosity, leading to a pluglike velocity profile with large magnitude in the narrow central region of the rivulet.

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Section: A General Resultssupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Rivulet flow of generalized Newtonian fluids

2018

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“…(41) has proven to converge quickly to roots that are real and with physical meaning. [3][4][5] Based on Eqs. (37) and (40), a useful additional and convenient way to calculate QW is…”

Section: G Local Film Thicknessmentioning

confidence: 99%

“…In this sense, efforts in previous works have been made in order to obtain analytical expressions for the main outputs (velocity, flow rate, and film thickness) that describe the film draining flow on regular geometries, such as vertical plates. [2][3][4][5] During free draining, the shear flow of the film-forming material is due mainly to gravity forces that generate the movement of the film. The energy that must be supplied to maintain the relative motion of a fluid under simple shear, and that is often considered to be a dissipated power, is usually referred to as viscous dissipation.…”

Section: Introductionmentioning

confidence: 99%

Draining of films on a quasivertical plate using viscous dissipation

2019

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This work focused on obtaining an improved and expanded general theoretical analysis of a two-dimensional film draining on a quasivertical plate, solving rigorous mass, momentum, and energy balances. A dimensional analysis and scaling was used to simplify the mathematical description, and a generalized Newtonian fluid was assumed as the film-forming material. A new quantity that governs the draining flow and film characteristics, called viscous dissipation, was proposed as part of the novel analytical expressions obtained in this work. Velocity profile, average velocity, flow rate, and local and average film thickness expressions can be obtained, allowing to simplify the overall calculation complexity and to find new potential analytical expressions using more complex rheological models.

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“…Pal and Mondal [1] investigated MHD flow of heat transfer over a stretching The Carreau-Yasuda model is one of the most important subclass of rheological fluid models, extended form of Carreau [26] improved by Yasuda [27]. Recent analysis have exposed that analytic solution for Carreau-Yasuda fluid flow was calculated by Peralta et al [28]. Salahuddin et al [29] calculated an approximate solution for squeezed flow of Carreau-Yasuda fluid due to a sensor surface.…”

Section: Introductionmentioning

confidence: 99%

Impact of enhancing diffusion on Carreau–Yasuda fluid flow over a rotating disk with slip conditions

Khan

Salahuddin

Malik

2019

J Braz. Soc. Mech. Sci. Eng.

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The present study is devoted to acquire non-similar solutions for the behavior of slip conditions on the steady MHD Carreau-Yasuda fluid flow over a rotating disk. In order to examine the heat transfer phenomena, superior form of Fourier's law is used and the conductivity of the fluid is assumed to be changeable. The nonlinear partial differential equations leading the flow and thermal field are written in the non-dimensional ordinary differential form by using suitable transformations. The non-dimensional set of coupled ordinary differential equations is solved using the RK method. The impact of various non-dimensional physical parameters on velocity and temperature fields is explored. The numerical results of resistant force in terms of the skin friction coefficient are revealed graphically for various physical parameters involved in the problem. Keywords MHD • Slip conditions • Generalized Fourier's law • Variable thermal conductivity • Carreau-Yasuda fluid model • Rotating disk • Shooting method List of symbols C f , C g Skin friction coefficient We Weissenberg number d Fluid parameter n Power law index d * T. Salahuddin

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Analytical solutions for the free-draining flow of a Carreau-Yasuda fluid on a vertical plate

Cited by 37 publications

References 19 publications

Rivulet flow of generalized Newtonian fluids

Rivulet flow of generalized Newtonian fluids

Draining of films on a quasivertical plate using viscous dissipation

Impact of enhancing diffusion on Carreau–Yasuda fluid flow over a rotating disk with slip conditions

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