A dimensionless heat transfer coefficient for free convection that is more appropriate than Nusselt number

Arakeri, JH and Kumar, N and Mahapatra, O (2024) A dimensionless heat transfer coefficient for free convection that is more appropriate than Nusselt number. In: Physics of Fluids, 36 (8).

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Abstract

Heat transfer in flows created by buoyancy, or natural convection, is a widely studied topic across various disciplines spanning natural flows as well as those with engineering applications. The convective heat transfer rate on a surface is commonly represented by the Nusselt number (Nu), a ratio of convective to diffusive transport, expressed often as R a n P r m , where R a is the Rayleigh number, the buoyancy forcing parameter, and P r the Prandtl number. Motivated by the observation that n � 1 / 3 for turbulent convection, which implies the heat flux is independent of the length scale ( L , characteristic length related to the geometry), we propose an alternate and physically more meaningful non-dimensional heat transfer parameter, denoted by C q . C q is derived using only the near wall variables and does not contain L . For n = 1 / 3 , C q is constant. Even for laminar convection, where n � 1 / 4 , C q � R a � 1 / 12 , a weak function of R a . We show that for natural convection over several geometries and a wide range of Ra, the C q values within a narrow range while the corresponding Nu values span several orders of magnitude. We also show that C q is akin to the non-dimensional representation of wall shear stress, skin friction coefficient C f . We believe that just like C f , C q will be an equally useful non-dimensional measure of heat transfer in natural convection flows. © 2024 Author(s).

Item Type:	Journal Article
Publication:	Physics of Fluids
Publisher:	American Institute of Physics
Additional Information:	The copyright for this article belongs to publisher.
Keywords:	Heat transfer coefficients; Laminar flow; Natural convection; Nusselt number; Prandtl number; Shear flow; Shear stress; Skin friction; Turbulent flow, Buoyancy forcing; Characteristic length; Convective heat transfer rates; Diffusive transport; Engineering applications; Heat transfer co-efficients; Length scale; Natural flow; Rayleigh number; Turbulent convection, Buoyancy
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	15 Sep 2024 05:37
Last Modified:	15 Sep 2024 05:37
URI:	http://eprints.iisc.ac.in/id/eprint/86078

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