School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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The cone–disk apparatus consists of a cone that touches the disk at its apex and is used in medical evices, viscosimeters, conical diffusers, etc. Theoretically, a three-dimensional flow of a nanofluid in a conical gap of a cone–disk apparatus is studied for four different physical configurations. Buongiorno nanofluid model, consisting of thermophoresis and Brownian diffusion mechanisms, is used to describe the convective heat transport of the nanofluid. The continuity equation, the Navier–Stokes momentum equation, the heat equation, and the conservation of nanoparticle volume fraction equation constitute the governing system for the flow of nanofluids. The Lie group approach is used to obtain self-similar equations. Solutions are computed for an appropriate rotational Reynolds number and four different gap angles to examine flow, mass, and heat transport features. The skin friction coefficients and torque are computed and analyzed. Multivariate nonlinear regression analysis is also performed. A co-rotating disk and cone configuration has been shown to produce less torque due to the increased centrifugal force. Of the four cone–disk apparatus configurations, the maximum heat/mass transport occurs for a rotating disk with a static cone for all selected gap angles, and the least drag in the radial direction is attained for a rotating cone with a static disk. In addition, there is a minimal drag along the tangential direction for the counter-rotating disk and cone configuration. Brownian diffusion and thermophoresis of the nanoparticles lead to a higher fluid temperature and, thus, lower Nusselt numbers are obtained.


© 2022 Author(s). Published under an exclusive license by AIP Publishing. Original published version available at

Publication Title

Physics of Fluids



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Mathematics Commons



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