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Effect of buoyancy-assisted flow on convection from an isothermal spheroid in power-law fluids

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Abstract

In this work, the coupled momentum and energy equations have been solved to elucidate the effect of aiding-buoyancy on the laminar mixed-convection from a spheroidal particle in power-law media over wide ranges of the pertinent parameters: Richardson number, 0≤Ri≤5; Reynolds number, 1≤Re≤100; Prandtl number, 1≤Pr≤100; power-law index, 0.3≤n≤1.8, and aspect ratio, 0.2≤e≤5 for the case of constant thermo-physical properties. New results for the velocity and temperature fields are discussed in terms of the streamline and isotherm contours, surface pressure and vorticity contours, drag coefficient, local and surface averaged Nusselt number. The effect of particle shape on the flow is seen to be more pronounced in the case of oblates (e < 1) than that for prolates (e > 1). The propensity for wake formation reduces with the rising values of power-law index, Richardson number and slenderness of the body shape (e > 1). Also, the drag coefficient is seen to increase with the Richardson number and power-law index. All else being equal, the Nusselt number shows a positive dependence on the Richardson number and Reynolds number and an inverse dependence on the power-law index and aspect ratio of the spheroid. Limited results were also obtained by considering the exponential temperature dependence of the power-law consistency index. This factor can increase the values of the average Nusselt number by up to ~10-12% with reference to the corresponding values for the case of the constant thermo-physical properties under otherwise identical conditions. Finally, the present values of the Nusselt number have been consolidated in the form of Colburn j-factor as a function of the modified Reynolds and Prandtl numbers for each value of the aspect ratio (e). The effect of the temperature dependent viscosity is included in this correlation in terms of a multiplication factor.

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

    Anoop K. Gupta & Rajendra Prasad Chhabra

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  1. Anoop K. Gupta
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  2. Rajendra Prasad Chhabra
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Correspondence to Rajendra Prasad Chhabra.

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Gupta, A.K., Chhabra, R.P. Effect of buoyancy-assisted flow on convection from an isothermal spheroid in power-law fluids. Korea-Aust. Rheol. J. 28, 87–110 (2016). https://doi.org/10.1007/s13367-016-0009-4

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  • DOI: https://doi.org/10.1007/s13367-016-0009-4

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