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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Imprimir: 1940-2503
ISSN En Línea: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2016015847
pages 73-98

EFFECT OF PRANDTL NUMBER ON FREE CONVECTION IN NEWTONIAN AND POWER-LAW FLUIDS FROM A CYLINDER ADJACENT TO AN ADIABATIC WALL

A. K. Baranwal
Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India
S. A. Patel
Department of Chemical Engineering, Indian Institute of Technology Ropar, Rupnagar 140001, India
Rajenda P. Chhabra
Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India; Department of Chemical Engineering, Indian Institute of Technology Ropar, Rupnagar 140001, India

SINOPSIS

Steady two-dimensional natural convection heat transfer from a horizontal cylinder situated above or beneath an adiabatic wall is numerically studied. The governing differential equations have been solved over wide ranges of dimensionless parameters, namely, Grashof number (10 ≤ Gr ≤ 104), Prandtl number (5 ≤ Pr ≤ 100) and power-law index (0.2 ≤ n ≤ 1), for a range of gaps between the cylinder and the adiabatic wall, ΙH/DΙ = 0.05, 0.2, 0.5, 0.9, 1.1, 1.5, 3, and 5. Limited results were also obtained for large values of (H/D) ≥ 3000 to approach the unconfined cylinder limit. Detailed discussion of the momentum and heat transfer phenomena is presented in terms of the streamlines, velocity field, isotherms, and the Nusselt number. The effect of the Prandtl number is more pronounced when the cylinder is close to the wall and this effect gradually diminishes as the gap increases. The average Nusselt number shows a positive dependence on the values of the Grashof and Prandtl numbers. With reference to the value of the Nusselt number for an unconfined cylinder, the presence of the adiabatic wall, above or below the cylinder, has an adverse influence on heat transfer. Indeed, the influence of the wall persists up to large values of the gap between the wall and the cylinder. The present results on the average Nusselt number have been reconciled in the form of a single correlation for the both top and bottom confinements.


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