Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Natural convection and heat transfer in a rotating fluid sphere with uniform heat source and axial gravity. The origin of the Cartesian coordinate system is located at the center of the sphere. The dimensional constant angular velocity, axial gravity and uniform heat source are defined by Ω = Ω 3 i 3, g = g 3 i 3, and Q v, respectively. Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Spectral element method mesh with 256 nonregular hexahedra macroelements with polynomial expansion of order 6. The origin of the Cartesian coordinate system is located at the center of the quasi-sphere. Left panel: discretization of the bounding spherical surface. Right panel: an interior view of the mesh. Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / SEM GLL points distribution in the quasi-sphere. Left panel: x 2 - x 3 meridional plane. Right panel: GLL points on the bounding spherical surface at three positions of the x 1 axis (directed out of the page), (i) external circle at x 1 = 0 (meridional plane), (ii) middle circle at x 1 = 0.7, and (iii) internal circle at x 1 = Circles: SEM-GLL points. Continuous line: perfect sphere with radius Order of the polynomial equal to 6. Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Nonsteady heat conduction within a quasi-sphere with homogeneous and constant heat source. Dimensionless temperature distribution along the radial direction. Left panel: polynomial interpolation p of order 6. Right panel: polynomial interpolation p of order 8. Continuous line: analytical solution for a perfect sphere, see Eqs. (6) and (7). Circles: SEM method results. At t = 1, the steady state condition is reached. Dimensional values: ΔT = Q v R 2 /6k = K, Q v = 1000 W/m 3, R = m, k = 1 W/m-K, α = 1 m 2 /s. Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Natural convection in a fluid sphere for different Ra numbers without rotation Ta = 0. Meridional fields of vorticity (left column), pressure (middle column), and temperature (right column). (a): Ra = 10, (b): Ra = 1 × 10 3, (c): Ra = 1 × 10 4, (d): Ra = 1 × 10 5, (e): Ra = 5 × 10 5, (f): Ra = 1 × 10 6, and (g): Ra = 1 × Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Dimensionless maximum temperature T max in the fluid sphere (left panel) and average Nusselt number Nu¯ (right panel) as functions of the Taylor number Ta and the Rayleigh number Ra. The convection coefficient h, used to obtain Nu¯, has been calculated from the energy balance (see Eqs. (12) and (13)). (i) ○ Ra = 10, (ii) * Ra = 1 × 10 3, (iii) □ Ra = 1 × 10 4, (iv) Δ Ra = 1 × 10 5, (v) ⋆ Ra = 1 × 10 6, and (vi) ⋄ Ra = 1 × Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Average Nusselt number as a function of the Ra and Ta numbers. The convection coefficient h, used to obtain Nu¯, has been calculated from the energy balance (see Eqs. (12) and (13)). (i) ○ Ta = 0, (ii) □ Ta = 1600, (iii) Δ Ta = 6400, and (iv) ⋆ Ta = 14,400. Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Meridional convective vorticity fields with rotation. First column (left): Ta = 0, second column: Ta = 1600, third column: Ta = 6400, and fourth column (right): Ta = 14,400. (a): Ra = 10, (b): Ra = 1 × 10 3, (c): Ra = 1 × 10 4, (d): Ra = 1 × 10 5, (e): Ra = 1 × 10 6, and (f): Ra = 1 × Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Meridional convective temperature fields with rotation. Same caption as Fig. 8. Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Dimensionless meridional (x 2, x 3 ) vorticity (i 1 component) in a fluid (quasi sphere) for Ra = 10. Left panel: Ta = Middle panel: Ta = Right panel: Ta = 14,400. Bold line represents the average vorticity equal to zero, and a measure of the thickness of the Ekman boundary layer δ E. Figure Legend:

Date of download: 7/9/2016 Copyright © ASME. All rights reserved. From: Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity J. Heat Transfer. 2013;135(4): doi: / Dimensionless Ekman boundary layer thickness δ E, and thermal boundary layer thickness δ T in terms of the Ra number. Left panel: Ta = 6400, δ E ≈ (continuous line). Right panel: Ta = 14,400, δ E ≈ (continuous line). ○: δ T at the north pole region, □: δ T at the equatorial region. Figure Legend: