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Research Papers: Natural and Mixed Convection

# Effects of Insulated and Isothermal Baffles on Pseudosteady-State Natural Convection Inside Spherical Containers

[+] Author and Article Information
Yuping Duan1

Department of Mechanical Engineering, Auburn University, 270 Ross Hall, Auburn, AL 36849-5341

Department of Mechanical Engineering, Auburn University, 270 Ross Hall, Auburn, AL 36849-5341

Department of Mechanical Engineering, Auburn University, 270 Ross Hall, Auburn, AL 36849-5341khodajm@auburn.edu

1

Currently with China Guodian Corp., Zhongneng Power-Tech Development Co., Ltd., Beijing, China.

2

At that time, a Ph.D. candidate in the Department of Aerospace Engineering, Sharif University of Technology, I.R. Iran; currently an Assistant Professor, Mechanical Engineering Department, Babol Noshirvani University of Technology, Babol, Iran.

J. Heat Transfer 132(6), 062502 (Apr 01, 2010) (10 pages) doi:10.1115/1.4000753 History: Received June 14, 2009; Revised November 11, 2009; Published April 01, 2010; Online April 01, 2010

## Abstract

The effects of insulated and isothermal thin baffles on pseudosteady-state natural convection within spherical containers were studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of $104$, $105$, $106$, and $107$, baffles with three lengths positioned at five different locations were investigated (120 cases). The fluid that is heated adjacent to the sphere rises replacing the colder fluid, which sinks downward through the stratified stable thermal layer. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid, thus causing oscillations in the temperature and flow fields. Due to flow obstruction (blockage or confinement) effect of baffles and also because of the extra heating afforded by the isothermal baffle, multi-cell recirculating vortices are observed. This additional heat is directly linked to creation of another recirculating vortex next to the baffle. In effect, hot fluid is directed into the center of the sphere disrupting thermal stratified layers. For the majority of the baffles investigated, the Nusselt numbers were generally lower than the reference cases with no baffle. The extent of heat transfer modification depends on Ra, length, and location of the extended surface. With an insulated baffle, the lowest amount of absorbed heat corresponds to a baffle positioned horizontally. Placing a baffle near the top of the sphere for high Ra number cases can lead to heat transfer enhancement that is linked to disturbance of the thermal boundary layer. With isothermal baffles, heat transfer enhancement is achieved for a baffle placed near the bottom of the sphere due to interaction of the counterclockwise rotating vortex and the stratified layer. For some high Ra cases, strong fluctuations of the flow and thermal fields indicating departure from the pseudosteady-state were observed.

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## Figures

Figure 8

Cyclic variation in the instantaneous area-averaged Nusselt number for case with an insulated baffle (L=0.25, θb=60 deg, and Ra=107)

Figure 9

Dependence of the time-averaged Nusselt number (Nuc) on Ra among cases with an insulated baffle (L=0.05) at various locations and the case without baffle

Figure 10

Dependence of the Nusselt number (Nuc) on θb among a case without baffle and the cases with a thin insulated baffle of different lengths for Ra=107

Figure 1

Schematic diagram of a spherical container with an insulated or isothermal thin baffle and its three-dimensional cutaway view

Figure 2

Pseudosteady-state streamline patterns (left half) and corresponding temperature contours (right half) for cases with no baffles (Ra=105 and 107)

Figure 3

Thermally stable and unstable flow structures

Figure 4

Pseudosteady-state streamline patterns and temperature contours for two insulated baffles (L=0.1 and 0.25) placed at various locations for Ra=105

Figure 5

Pseudosteady-state streamline patterns and temperature contours for two insulated baffles (L=0.1 and 0.25) placed at various locations for Ra=106

Figure 6

Pseudosteady-state streamline patterns and temperature contours with an insulated baffle (L=0.25) placed at θb=30 deg, 90 deg, and 150 deg for Ra=104, 106, and 107

Figure 7

Streamline patterns and temperature contours in one cycle (a–h with the time instants shown in Fig. 8) with an insulated baffle (L=0.25, θb=60 deg, and Ra=107)

Figure 13

Dependence of the time-averaged Nusselt number (Nuc) on Ra among cases with an isothermal baffle (L=0.25) at various locations and the case without baffle

Figure 14

Dependence of the time-averaged Nusselt number (Nuc) on θb among a case without baffle and the cases with a thin isothermal baffle of different lengths (L=0.05, 0.10, and 0.25) for Ra=107

Figure 11

Pseudosteady-state streamline patterns and temperature contours for two isothermal baffles (L=0.1 and 0.25) placed at various locations for Ra=106

Figure 12

Comparison of the pseudosteady-state streamline patterns and temperature contours due to insulated and isothermal baffles (Ra=107, L=0.25, and θb=150 deg)

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