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Technical Brief

Effects of Uniform Heat Flux and Velocity-Slip Conditions at Interface on Heat Transfer Phenomena of Smooth Spheres in Newtonian Fluids

[+] Author and Article Information
Rahul Ramdas Ramteke

Department of Chemical Engineering,
Indian Institute of Technology Guwahati,
Guwahati, Assam 781039, India

Nanda Kishore

Department of Chemical Engineering,
Indian Institute of Technology Guwahati,
Guwahati, Assam 781039, India
e-mail: nkishore@iitg.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 15, 2016; final manuscript received April 6, 2017; published online May 23, 2017. Assoc. Editor: Ravi Prasher.

J. Heat Transfer 139(10), 104501 (May 23, 2017) (6 pages) Paper No: HT-16-1386; doi: 10.1115/1.4036598 History: Received June 15, 2016; Revised April 06, 2017

The effects of the uniform heat flux and a linear velocity-slip on the heat transfer phenomena of spheres in Newtonian fluids are numerically investigated using semi-implicit marker and cell (SMAC) method implemented on a staggered grid arrangement in spherical coordinates. The solver is thoroughly benchmarked through domain independence, grid independence, and comparison with literature. Further extensive results are obtained in the range of conditions as: Reynolds number, Re = 0.1–200; Prandtl number, Pr = 1–100; and dimensionless slip number, λ = 0.01–100. The results are presented and discussed such that the isotherm contours and the local and average Nusselt numbers of isoflux spheres with velocity-slip at the interface are compared with their isothermal spheres counterparts under identical conditions. Briefly, the results indicate that the average Nusselt numbers of isoflux spheres are large compared to those of isothermal spheres under identical conditions. Finally, an empirical correlation is developed for the average Nusselt numbers of the spheres in Newtonian fluids with velocity-slip and the uniform heat flux conditions along the fluid–solid sphere interface.

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Figures

Grahic Jump Location
Fig. 1

Schematic of heat transfer between isoflux spheres and unbounded fluids

Grahic Jump Location
Fig. 2

Isotherm contours around spheres at Re = 50 and Pr = 50 with constant surface temperature (upper half) and uniform heat flux (lower half) boundary conditions at surface: (a) λ = 0.1, (b) λ = 1, (c) λ = 5, and (d) λ = 10

Grahic Jump Location
Fig. 3

Isotherm contours around spheres at Re = 200 and Pr = 50 with constant surface temperature (upper half) and uniform heat flux (lower half) boundary conditions at surface: (a) λ = 0.1, (b) λ = 1, (c) λ = 5, and (d) λ = 10

Grahic Jump Location
Fig. 4

Nulocal of spheres at Re = 50 with constant wall temperature and uniform heat flux boundary conditions at the surface: (a) λ = 0.01, (b) λ = 0.1, (c) λ = 1, (d) λ = 5, (e) λ = 10, and (f) λ = 100

Grahic Jump Location
Fig. 5

Nuavg of isoflux spheres in Newtonian fluids with velocity-slip at the interface: (a) Re = 1, (b) Re = 20, (c) Re = 50, and (d) Re = 200

Grahic Jump Location
Fig. 6

Nuavg of isoflux and isothermal spheres in Newtonian fluids with velocity-slip at the interface: (a) Re = 1, (b) Re = 20, (c) Re = 50, and (d) Re = 200

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