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Research Papers: Forced Convection

# Direct Numerical Simulation of Forced Convective Heat Transfer From a Heated Rotating Sphere in Laminar Flows

[+] Author and Article Information
Zhi-Gang Feng

Department of Mechanical Engineering,
University of Texas at San Antonio,
San Antonio, TX 78249
e-mail: zhigang.feng@utsa.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 3, 2013; final manuscript received December 8, 2013; published online February 18, 2014. Assoc. Editor: William P. Klinzing.

J. Heat Transfer 136(4), 041707 (Feb 18, 2014) (8 pages) Paper No: HT-13-1334; doi: 10.1115/1.4026307 History: Received July 03, 2013; Revised December 08, 2013

## Abstract

The laminar forced convection of a heated rotating sphere in air has been studied using a three-dimensional immersed boundary based direct numerical simulation method. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the rotating sphere, a moving Lagrangian grid is used, which tracks the rotational motion of the particle. A force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between the sphere and fluid. This numerical method is validated by comparing simulation results with analytical solutions of heat diffusion problem and other published experimental data. The flow structures and the mean Nusselt numbers for flow Reynolds number ranging from 0 to 1000 are obtained. We compared our simulation results of the mean Nusselt numbers with the correlations from the literature and found a good agreement for flow Reynolds number greater than 500; however, a significant discrepancy arises at flow Reynolds number below 500. This leads us to develop a new equation that correlates the mean Nusselt number of a heated rotating sphere for flows of $0≤Re≤500$.

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## Figures

Fig. 1

Conceptual DNS-IB model of a solid particle immersed in a fluid

Fig. 2

Setup of Cartesian coordinates for a heated sphere of radius a rotating at angular velocity ω in a viscous fluid

Fig. 3

Comparisons of the mean Nusselt number of the unsteady diffusion of a sphere obtained by analytical solution and numerical simulation

Fig. 4

Snapshots of temperature contours from both numerical (right half side of each plot) and analytical solution (left half side of each plot) at time t = 0.25 (left), t = 0.75 (middle), and t = 1.5 (right)

Fig. 5

Simulation results and exact solution of dimensionless temperature in the radial direction

Fig. 6

The effect of grid spacing to the simulated mean Nusselt number at Re = 500

Fig. 7

The effect of time step δt to the simulated mean Nusselt number at Re = 500

Fig. 10

Isosurfaces for dimensionless temperature ranging from 1.0 to 0.1 at t = 50

Fig. 8

Visualizations of a rotating sphere in air at Re = 500. (a) Isosurface for fluid velocity magnitude of v = 0.2 colored in terms of temperature scale; (b) top view of flow streamlines; and (c) side view of flow streamlines.

Fig. 9

Velocity vectors on two slices passing through the center of the sphere at t = 50. (a) a horizontal slice or equatorial plane and (b) a vertical slice.

Fig. 11

Simulation results of time evolution of the mean Nusselt numbers for Re≤1000

Fig. 12

Flow velocity magnitude contours (top row) and temperature contours (bottom row) on vertical slices (x-y plane) at t = 40. Left: Re = 100; middle: Re = 200; right: Re = 500.

Fig. 13

Comparison of present simulation results with correlations found in the literature and the new correlation for Re≤500

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