Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Test cases of SSD problems with forced convection heat transfer: (a) cylindrical quote flow and (b) diffuser

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Test cases of SSD problems with natural convection and conjugate heat transfer: (a) natural convection in a concentric annulus and (b) conjugate heat transfer test case

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Test cases of SSD problems with mixed convection heat transfer

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: The computational grid used in this study

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Local coordinates in a typical quadrilateral element

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: The flowchart of the direct design algorithm

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Schematic of the ball spine algorithm used in 2D SSD problems: (a) internal flow problems and (b) external flow problems

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: The flowchart of the BSA

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Heat flux distributions for initial and target geometries in the cylindrical Couette flow problem

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Results of the first test case at Re = 100: (a) convergence histories, (b) shape evolutions during several iterations, and (c) a comparison between designed and target geometry

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Results of the second test case at Re=50 and Pr=7.02 : (a) initial and target heat flux distributions, (b) initial and computed geometries corresponding to the defined heat flux distributions, (c) streamlines and isotherms in the designed geometry in case of S*=0.4, and (d) comparison of the computational cost between direct design approach and the BSA method with equal under-relation value (ω for direct design and C for BSA)

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Results of the third test case at Ra=103 and Pr=0.71 : (a) initial and target heat flux distributions along the outer cylinder, (b) shape evolutions corresponding to the direct design with ω=0.5, (c) comparing the convergence rate of the direct design approach with the BSA method with equal under-relation value (ω for direct design and C for BSA), and (d) the contour of dimensionless temperature (right half) and streamlines (left half) in the designed geometry

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Results of the forth test case at θs=0.85, kf/ks=0.1, Pr = 0.71: (a) computed shapes for different Reynolds numbers and (b) comparing the convergence rate of the direct design approach with the BSA method at Re = 20 with equal under-relation value (ω for direct design and C for BSA)

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Surface Shape Design in Different Convection Heat Transfer Problems Via a Novel Coupled Algorithm J. Heat Transfer. 2017;140(2):021702-021702-15. doi:10.1115/1.4037581 Figure Legend: Results of the fifth test case at Ri = 1, Gr = 104 and Re = 100: (a) initial and target heat flux distributions along the bottom surface, (b) shape evolutions during several iterations corresponding to the direct design with ω=0.6, and (c) convergence rate of the direct design approach for various values of under-relaxation factor