NDLI: Natural convection in Bingham plastic fluids from an isothermal spheroid: Effects of fluid yield stress, viscous dissipation and temperature-dependent viscosity

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Natural convection in Bingham plastic fluids from an isothermal spheroid: Effects of fluid yield stress, viscous dissipation and temperature-dependent viscosity

Content Provider	Springer Nature Link
Author	Gupta, Anoop Kumar Gupta, Sanjay Chhabra, Rajendra Prasad
Copyright Year	2017
Abstract	In this work, the buoyancy-induced convection from an isothermal spheroid is studied in a Bingham plastic fluid. Extensive results on the morphology of approximate yield surfaces, temperature profiles, and the local and average Nusselt numbers are reported to elucidate the effects of the pertinent dimensionless parameters: Rayleigh number, 10$^{2}$ ≤ Ra ≤ 10$^{6}$; Prandtl number, 20 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 10$^{3}$, and aspect ratio, 0.2 ≤ e ≤ 5. Due to the fluid yield stress, fluid-like (yielded) and solid-like (unyielded) regions coexist in the flow domain depending upon the prevailing stress levels vis-a-vis the value of the fluid yield stress. The yielded parts progressively grow in size with the rising Rayleigh number while this tendency is countered by the increasing Bingham and Prandtl numbers. Due to these two competing effects, a limiting value of the Bingham number (Bn $_{max}$) is observed beyond which heat transfer occurs solely by conduction due to the solid-like behaviour of the fluid everywhere in the domain. Such limiting values bear a positive dependence on the Rayleigh number (Ra) and aspect ratio (e). In addition to this, oblate shapes (e < 1) foster heat transfer with respect to spheres (e = 1) while prolate shapes (e > 1) impede it. Finally, simple predictive expressions for the maximum Bingham number and the average Nusselt number are developed which can be used to predict a priori the overall heat transfer coefficient in a new application. Also, a criterion is developed in terms of the composite parameter Bn∙Gr-$^{1/2}$ which predicts the onset of convection in such fluids. Similarly, another criterion is developed which delineates the conditions for the onset of settling due to buoyancy effects. The paper is concluded by presenting limited results to delineate the effects of viscous dissipation and the temperature-dependent viscosity on the Nusselt number. Both these effects are seen to be rather small in Bingham plastic fluids.
Starting Page	163
Ending Page	184
Page Count	22
File Format	PDF
ISSN	1226119X
Journal	Korea-Australia Rheology Journal
Volume Number	29
Issue Number	3
e-ISSN	20937660
Language	English
Publisher	Korean Society of Rheology, Australian Society of Rheology
Publisher Date	2017-09-02
Publisher Place	Seoul, Melbourne
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	natural convection fluid yield stress Bingham number aspect ratio temperature-dependent viscosity Brinkman number Characterization and Evaluation of Materials Polymer Sciences Soft and Granular Matter, Complex Fluids and Microfluidics Mechanical Engineering Food Science
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Materials Science

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