On some non-linear shear flows of non-Newtonian fluids

Pascal, J. P.; Pascal, H.

doi:10.1016/0020-7462(95)00018-j

Cited by 27 publications

(21 citation statements)

References 6 publications

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“…Eq. (2) is called "Gorter-Melling law" and has been employed in nonlinear heat conduction [20], nonlinear flows of nonNewtonian fluids [21], etc. The properties of Eq.…”

Section: The Mathematical Modelmentioning

confidence: 99%

A Study for Boronizing Process within Nonextensive Thermostatistics

Kayacan

Şahin

Tastan

2010

MCA

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Abstract-In this study, diffusion mechanism of the boronizing process of AISI 1040 has been investigated. A nonlinear diffusion equation, which was proposed earlier, has been employed and compared with the experimental data. An interesting property of the diffusion equation used here is that it establishes a connection between the diffusion process and nonextensivity. The theoretical model also exhibits a possible connection between the exponents appeared in the differential equation and the entropic index. In this manner, the possible effects of nonextensivity on the boronizing process have been shown theoretically. We believe that a diffusion equation based on the nonextensive formalism is first applied to the boronizing process in literature.

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“…Eq. (2) is called "Gorter-Melling law" and has been employed in nonlinear heat conduction [20], nonlinear flows of nonNewtonian fluids [21], etc. The properties of Eq.…”

Section: The Mathematical Modelmentioning

confidence: 99%

A Study for Boronizing Process within Nonextensive Thermostatistics

Kayacan

Şahin

Tastan

2010

MCA

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“…Obviously, the power exponent n determines the deviation level from the normal constitutive model (Newtonian fluids). The generalized power law diffusion model has been utilized to address some typical nonlinear diffusion processes such as shear flow and heat transfer of non-Newtonian power law fluids by Zheng 36 and Pascal et al 37,38 The advantage that such theories can characterize the typical shear-thinning and shear-thickening performances of non-Newtonian fluids by modulating the power exponent n adequately, while the rheological relationships of some real complex fluids such as carboxymethyl cellulose (CMC) solutions and polyvinyl alcohol (PVA) were used to verify the value range of n experimentally. [39][40][41][42] With such motivation, we introduce in this work a generalized nonlinear diffusion model to remodel the rheological and heat-conduction constitutive relations of a micropolar fluid.…”

Section: Introductionmentioning

confidence: 99%

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

et al. 2017

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The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system. Published by AIP Publishing.

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“…For illustrative purposes, here we will investigate the diffusion of a rectilinear vortex in an unbounded power-law fluid, for which the vorticity u>z(R,t) satisfies the relation dv v n = OR + R ' = Ule = or, in terms of angular velocity fi, we have U>z = ^dR F rom relations (12), (16), and (17) we can write (64) in the form…”

Section: R>l(t)mentioning

confidence: 99%

“…In this case (18) Consequently, from (12), (16), and (23) we obtain n = e~6t where C* is also an integration constant. …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Similarity solutions to rotating Couette flow of non-Newtonian fluids in the presence of a magnetic field

Pascal¹,

Pascal²

1996

Quart. Appl. Math.

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Abstract.We study the rotating Couette flow of conducting power law fluids in the presence of a magnetic field. We analyze the coupled effects of the rheology and the magnetic field on the angular velocity and shear stress distributions for the case when an infinite long cylinder rotates in an unbounded fluid. For shear thickening fluids our exact similarity solutions exhibit traveling wave characteristics determining the existence of a moving shear front. We investigate the electrorheological effect on the propagation of the shear disturbances front.

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On some non-linear shear flows of non-Newtonian fluids

Cited by 27 publications

References 6 publications

A Study for Boronizing Process within Nonextensive Thermostatistics

A Study for Boronizing Process within Nonextensive Thermostatistics

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

Similarity solutions to rotating Couette flow of non-Newtonian fluids in the presence of a magnetic field

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