The Flow of a Variable Viscosity Fluid down an Inclined Plane with a Free Surface

Tshehla, M. S.

doi:10.1155/2013/754782

Cited by 27 publications

(17 citation statements)

References 13 publications

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“…Eqs. (12) and (13) are expected to be necessarily small so it might approach to zero, coming about that an arrangement of ordinary differential equations is simplified [39]. Therefore, the first level of truncation or the local similarity solution is attractive for calculation but indicates the numerical outcomes of unclear accuracy.…”

Section: Local Non-similar Solution Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Local non-similar solutions of convective flow of Carreau fluid in the presence of MHD and radiative heat transfer

Sardar

Khan

Ahmad

2019

J Braz. Soc. Mech. Sci. Eng.

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In this research article we studied a realistic methodology to inspect the non-similar solutions for the two-dimensional steady Carreau fluid flow in the presence of applied magnetic field and mixed convection within the sight of infinite shear rate viscosity. With the help of local non-similar method, we presented the nonlinear PDEs for the flow and heat transfer analysis. The leading PDEs are converted into an system of nonlinear ODEs by using the local non-similarity method. The final resulting non-dimensional set of coupled nonlinear PDEs is then solved with the help of bvp4c function in MATLAB. This investigation discover numerous physical aspects of flow and heat transfer. Major outcomes in the form of velocity enhancement and temperature reduction for the higher values of buoyancy parameter () are observed. On the other hand, for increasing values of N R the temperature of the fluid increases, while for larger values of suction/injection parameter the temperature of the fluid reduces. Parallel variation of buoyancy parameter and Weissenberg number shows a slight difference regarding local similar and local non-similar solution while computing the local skin friction number. The enhancement in buoyancy parameter causes enhancement in local skin friction as well as local Nusselt number. Additionally this investigation is validated through a comparison with previous results and found a good correlation with the previous results.

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Section: Local Non-similar Solution Methodsmentioning

confidence: 99%

“…Furthermore, the numerical inspection of flow and heat transfer in cylindrical-type axes was exposed by Lauriat and Khellaf [12]. The Carreau fluid effects with inclined sheet were discovered by Tshehla [13]. Abbasi et al [14] revealed the MHD Carreau fluid flow in curved channel.…”

Section: Introductionmentioning

confidence: 99%

Local non-similar solutions of convective flow of Carreau fluid in the presence of MHD and radiative heat transfer

Sardar

Khan

Ahmad

2019

J Braz. Soc. Mech. Sci. Eng.

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“…Noor et al 3 explained the thermophoretic flow on a slanted sheet. Tshehla 4 discussed the flow of the fluid on a slanted plate. Besides, non-Newtonian fluid flow through slanted sheet was investigated by Bognár et al 5 Moreover, Hamza et al 6 examined the flow over an inclined surface by using the finite difference technique.…”

Section: Introductionmentioning

confidence: 99%

Energy and mass transport of micropolar nanofluid flow over an inclined surface with Keller‐Box simulation

et al. 2020

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In this article, micropolar nanofluid boundary layer flow over a slanted stretching surface with Soret and Dufour effect is studied. The inclined stretching surface in this study is considered permeable and linear. In this problem, the Buongiorno model is considered for thermal efficiencies of fluid flow in the existence of Brownian movement and thermophoresis properties. The nonlinear problem for Micropolar Nanofluid flow over the slanted channel is developed to think about the heat and mass exchange phenomenon by incorporating portent flow factors to strengthened boundary layers. In this study, nonlinear partial differential equations are converted to nonlinear ordinary differential equations by utilizing appropriate similarity transformations then elucidated the numerical outcomes by the Keller-Box technique. An examination of the setup results is performed with accessible outcomes and perceived in a good settlement without involved impacts. Numerical and graphical outcomes are additionally displayed in tables and charts.

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“…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%

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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The Flow of a Variable Viscosity Fluid down an Inclined Plane with a Free Surface

Cited by 27 publications

References 13 publications

Local non-similar solutions of convective flow of Carreau fluid in the presence of MHD and radiative heat transfer

Local non-similar solutions of convective flow of Carreau fluid in the presence of MHD and radiative heat transfer

Energy and mass transport of micropolar nanofluid flow over an inclined surface with Keller‐Box simulation

Rivulet flow of generalized Newtonian fluids

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