Numerical modelling of shear thickening fluid in nanosilica dispersion

Chauhan, Vimal; Bhalla, Neelanchali Asija; Danish, Mohammad

doi:10.21595/vp.2019.21123

Cited by 6 publications

(6 citation statements)

References 7 publications

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“…It was shown there that, strictly speaking, the self-similar formulation of the problem of flow and heat transfer is valid and leads to accurate calculation results only at small conicity angles up to 4°. At large conicity angles, separate boundary layers inevitably appear on both surfaces [which is also confirmed by the results of Chauhan et al (2019)], so the self-similar formulation can only be HFF 33,11 used rather for a qualitative assessment of transport processes. For small conicity angles up to 4°, it is enough to use the self-similar heat transfer equation without the inclusion of radial heat conduction because with its inclusion, the Nusselt numbers change by a maximum of 1.5%.…”

Section: Introductionmentioning

confidence: 73%

Improved asymptotic expansion method for laminar fluid flow and heat transfer in conical gaps with disks rotating

Shevchuk

2023

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Purpose The purpose of this paper was to study laminar fluid flow and convective heat transfer in a conical gap at small conicity angles up to 4° for the case of disk rotation with a fixed cone. Design/methodology/approach In this paper, the improved asymptotic expansion method developed by the author was applied to the self-similar Navier–Stokes equations. The characteristic Reynolds number ranged from 0.001 to 2.0, and the Prandtl numbers ranged from 0.71 to 10. Findings Compared to previous approaches, the improved asymptotic expansion method has an accuracy like the self-similar solution in a significantly wider range of Reynolds and Prandtl numbers. Including radial thermal conductivity in the energy equation at small conicity angle leads to insignificant deviations of the Nusselt number (maximum 1.23%). Practical implications This problem has applications in rheometry to experimentally determine viscosity of liquids, as well as in bioengineering and medicine, where cone-and-disk devices serve as an incubator for nurturing endothelial cells. Social implications The study can help design more effective devices to nurture endothelial cells, which regulate exchanges between the bloodstream and the surrounding tissues. Originality/value To the best of the authors’ knowledge, for the first time, novel approximate analytical solutions were obtained for the radial, tangential and axial velocity components, flow swirl angle on the disk, tangential stresses on both surfaces, as well as static pressure, which varies not only with the Reynolds number but also across the gap. These solutions are in excellent agreement with the self-similar solution.

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Section: Introductionmentioning

confidence: 73%

Improved asymptotic expansion method for laminar fluid flow and heat transfer in conical gaps with disks rotating

Shevchuk

2023

HFF

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“…As the conicity angle γ increases above 4°, the flow in the conical gap loses the properties of Couette flows, whereas separate boundary layers appear on the disk and cone. In experiments (Chauhan et al , 2019), it was found that at a relatively large gap height, a pattern is observed that differs from the Couette flow. At the minimum local radii at which the measurements were made, the profile of the tangential velocity in the gap is still linear.…”

Section: Mathematical Model Of Fluid Flowmentioning

confidence: 99%

“…Validation of these theoretical solutions and their comparison with experiments have not been performed, so the practical application of the results of these studies is questionable. Chauhan et al (2019) performed experiments on the flow of a nonNewtonian fluid in a cone-and-disk device supplemented by numerical simulations. In this geometry, the cone did not touch the surface of the disk with its apex, which provided an additional overall height of the gap with a conicity angle of about 6°.…”

Section: Introductionmentioning

confidence: 99%

“…Chauhan et al (2019) performed experiments on the flow of a nonNewtonian fluid in a cone-and-disk device supplemented by numerical simulations. In this geometry, the cone did not touch the surface of the disk with its apex, which provided an additional overall height of the gap with a conicity angle of about 6°.…”

Section: Introductionmentioning

confidence: 99%

“…However, from a physical point of view, the flow structure at large conicity angles naturally differs from Couette flows. At large conicity angles (or a relatively large gap height, as, for example, in Chauhan et al (2019), separate boundary layers appear on both surfaces, between which there is a flow core with the potential flow in it. The self-similar solution becomes obviously inapplicable for large conicity angles.…”

Section: Introductionmentioning

confidence: 99%

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Concerning the effect of radial thermal conductivity in a self-similar solution for rotating cone-disk systems

Shevchuk

2022

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Purpose Thus, the purposes of this study are to study the limits of applicability of the self-similar solution to the problem of fluid flow, heat and mass transfer in conical gaps with small conicity angles, to substantiate the impossibility of using a self-similar formulation of the problem in the case of large conicity angles and to substantiate the absence of the need to take into account the radial thermal conductivity in the energy equation in its self-similar formulation for the conicity angles up to 4°. Design/methodology/approach In the present work, an in-depth and extended analysis of the features of fluid flow and heat transfer in a conical gap at small angles of conicity up to 4° is performed. The Couette-type flow arising, in this case, was modeled using a self-similar formulation of the problem. A detailed analysis of fluid flow calculations using a self-similar system of equations showed that they provide the best agreement with experiments than other known approaches. It is confirmed that the self-similar system of flow and heat transfer equations is applicable only to small angles of conicity up to 4°, whereas, at large angles of conicity, this approach becomes unreasonable and leads to significantly inaccurate results. The heat transfer process in a conical gap with small angles of conicity can be modeled using the self-similar energy equation in the boundary layer approximation. It was shown that taking into account the radial thermal conductivity in the self-similar energy equation at small conicity angles up to 4° leads to maximum deviations of the Nusselt number up to 1.5% compared with the energy equation in the boundary layer approximation without taking into account the radial thermal conductivity. Findings It is confirmed that the self-similar system of fluid flow equations is applicable only for small conicity angles up to 4°. The inclusion of radial thermal conductivity in the model unnecessarily complicates the mathematical formulation of the problem and at small conicity angles up to 4° leads to insignificant deviations of the Nusselt number (maximum 1.5%). Heat transfer in a conical gap with small conicity angles up to 4° can be modeled using the self-similar energy equation in the boundary layer approximation. Originality/value This paper investigates the question of the validity of taking into account the radial heat conduction in the energy equation.

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