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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

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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, 102 ≤ Ra ≤ 106; Prandtl number, 20 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 103, 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.

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology, Kanpur, 208016, India

    Anoop Kumar Gupta, Sanjay Gupta & Rajendra Prasad Chhabra

  2. Department of Chemical Engineering, National University of Singapore, Singapore, 119077, Singapore

    Anoop Kumar Gupta

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  1. Anoop Kumar Gupta
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Correspondence to Rajendra Prasad Chhabra.

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Gupta, A.K., Gupta, S. & Chhabra, R.P. Natural convection in Bingham plastic fluids from an isothermal spheroid: Effects of fluid yield stress, viscous dissipation and temperature-dependent viscosity. Korea-Aust. Rheol. J. 29, 163–184 (2017). https://doi.org/10.1007/s13367-017-0018-y

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