Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Physical model with coordinate system and boundary conditions

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Radial and axial velocity profiles at the centerlines calculated with four grids at Ha=100, τL=1, ω=0.5, and εW=1

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Comparisons of streamlines ((a) and (b)), +Δψ=6.8,−Δψ=0.11 and isotherms ((c) and (d)), ΔT=0.1 for Ri=1: (a) and (c) result of Ref. [34] and (b) and (d) this study

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Comparisons of streamlines ((a) and (b)), +Δψ=1.3,−Δψ=0.89 and isotherms ((c) and (d)), ΔT=0.1 for Ri=0.05: (a) and (c) result of Ref. [34] and (b) and (d) this study

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Comparison of mean equivalent conductivity variation with Richardson number for Re=100

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Comparisons of nondimensional radial heat flux distribution at the outer wall of a finite concentric cylindrical enclosure

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Streamlines with τL=0.1, ω=0.5, and εW=1: (a) Ha=0, (b) Ha=10, (c) Ha=50, and (d) Ha=100

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Isotherms with τL=0.1, ω=0.5, and εW=1: (a) Ha=0, (b) Ha=10, (c) Ha=50, and (d) Ha=100

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Streamlines (top row) and isotherms (bottom row) with Ha=100, ω=0.5, and εW=1: (i) τL=0.1, (ii) τL=1.0, and (iii) τL=10

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Streamlines (top row) and isotherms (bottom row) with Ha=100, τL=1.0, and εW=1: (i) ω=0, (ii) ω=0.5, and (iii) ω=1.0

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Streamlines (top row) and isotherms (bottom row) with Ha=100, τL=1.0, and ω=0.5: (i) εW=0.2, (ii) εW=0.6, and (iii) εW=1.0

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Effects of Hartmann number on Nusselt number for τL=0.1, ω=0.5, and εW=1

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Effects of optical thickness on Nusselt number for Ha=100, ω=0.5, and εW=1

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Effects of scattering albedo on Nusselt number for Ha=100, τL=1.0, and εW=1

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus J. Heat Transfer. 2016;138(6):062501-062501-13. doi:10.1115/1.4032609 Figure Legend: Effects of emissivity of walls on Nusselt number for Ha=100, τL=1.0, and ω=0.5