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ISSN Online: 2688-7231

ISBN Online: 978-1-56700-524-0

Proceedings of the 26thNational and 4th International ISHMT-ASTFE Heat and Mass Transfer Conference December 17-20, 2021, IIT Madras, Chennai-600036, Tamil Nadu, India
December, 17-20, 2021, IIT Madras, Chennai, India

Natural Convection from a Confined Sphere in Yield stress Fluids

Get access (open in a dialog) DOI: 10.1615/IHMTC-2021.380
pages 257-263


Laminar natural convection in a yield stress fluid filled in the annular region between two concentric spheres with a constant heat flux condition on the inner sphere and an isothermal temperature on the outer sphere was investigated numerically. The numerical results presented here span a wide range of parameters, Rayleigh number (102Ra ≤ 106), Prandtl number (30 ≤ Pr ≤ 100) and Bingham number (0 ≤ Bn ≤ Bnmax) illustrating the momentum and heat transfer characteristics in the steady regime. The effect of confinement has been investigated by varying the annular gap (gap ratio, B = inner sphere diameter, Di/ outer sphere diameter, Do) from 0.1-0.5. The finite element based numerical study shows that there exists a critical Bingham number (or yield stress) for each confinement beyond that fluid motion completely ceases and heat transfer occurs by conduction only. The critical Bingham number is strongly influenced by the values of B and it increases with Ra. The present results also confirm that beyond the critical Bingham number, heat transfer is governed solely by conduction where the average Nusselt number attains a constant limiting value dependent on B only. A dimensionless criterion in terms of Bn×Pr1/2 corresponding to the onset of the conduction limit has been established over the range of parameters. The results of yielded-unyielded zones, isotherms and streamlines have been analysed below the critical yield stress limit. Finally, the functional dependence of the average Nusselt number has been established for each confinement in terms of Rayleigh number, Prandtl number and Bingham number embraced in this work.