Combined effects of blockage and yield stress on drag and heat transfer from an in-line array of three spheres

References

• Schramm, L. L. Emulsions, Foams, Suspensions, and Aerosols: Microscience and Applications, 2nd ed.; Wiley-VCH, 2014.
   Google Scholar
• Ochowiak, M.; Broniarz-Press, L.; Rozanski, J. Rheology and Structure of Emulsions and Suspensions. J. Dispersion Sci. Technol. 2012, 33, 177–184.
   Web of Science ®Google Scholar
• Chhabra, R. P. Bubbles, Drops, and Particles in Non-Newtonian Fluids, 2nd ed.; CRC Press: Boca Raton, FL, 2006.
   Google Scholar
• Kermani, M. S.; Rahnama, M.; Djilali, N.; Jafari, S.; Javaran, E. J. Lattice Boltzmann Simulation of Particles Agglomeration and Rheology in a Particulate Flow. J. Dispersion Sci. Technol. 2018, 39, 777–791.
   Web of Science ®Google Scholar
• Rooki, R.; Ardejani, F. D.; Moradzadeh, A.; Norouzi, M. CFD Simulation of Rheological Model Effect on Cuttings Transport. J. Dispersion Sci. Technol. 2015, 36, 402–410.
   Web of Science ®Google Scholar
• Michaelides, E. E. Particles, Bubbles and Drops: Their Motion, Heat and Mass Transfer; World Scientific: Singapore, 2006.
   Google Scholar
• Maheshwari, A.; Chhabra, R. P.; Biswas, G. Effect of Blockage on Drag and Heat Transfer from a Single Sphere and an In-Line Array of Three Spheres. Powder Technol. 2006, 168, 74–83.
   Web of Science ®Google Scholar
• Lloyd, B.; Boehm, R. Flow and Heat Transfer Around a Linear Array of Spheres. Numer. Heat Transfer: Part A 1994, 26, 237–252.
   Web of Science ®Google Scholar
• Ramachandran, R. S.; Kleinstreuer, C.; Wang, T.-Y. Forced Convection Heat Transfer of Interacting Spheres. Numer. Heat Transfer: Part A 1989, 15, 471–487.
   Web of Science ®Google Scholar
• Liang, S.-C.; Hong, T.; Fan, L.-S. Effects of Particle Arrangements on the Drag Force of a Particle in the Intermediate Flow Regime. Int. J. Multiphase Flow 1996, 22, 285–306.
   Web of Science ®Google Scholar
• Beaulne, M.; Mitsoulis, E. Creeping Motion of a Sphere in Tubes Filled with Herschel-Bulkley Fluids. J. Non-Newt. Fluid Mech. 1997, 72, 55–71.
   Web of Science ®Google Scholar
• Vidya Sagar, T.; Patel, S. A.; Gupta, A. K.; Chhabra, R. P. Effects of Severe Blockage on Heat Transfer from a Sphere in Power-Law Fluids. Int. Commun. Heat Mass Transfer 2017, 84, 27–34.
   Web of Science ®Google Scholar
• Vidya Sagar, T.; Patel, S. A.; Gupta, A. K.; Chhabra, R. P. Effect of Confinement and Fluid Yield Stress on Settling Velocity and Heat Transfer from an Isothermal Sphere. J. Chem. Eng. Jpn. 2018 (in press).
   Web of Science ®Google Scholar
• Song, D.; Gupta, R. K.; Chhabra, R. P. Wall Effects on a Sphere Falling in Quiescent Power Law Fluids in Cylindrical Tubes. Ind. Eng. Chem. Res. 2009, 48, 5845–5856.
   Web of Science ®Google Scholar
• Song, D.; Gupta, R. K.; Chhabra, R. P. Effect of Blockage on Heat Transfer from a Sphere in Power-Law Fluids. Ind. Eng. Chem. Res. 2010, 49, 3849–3861.
   Web of Science ®Google Scholar
• Song, D.; Gupta, R. K.; Chhabra, R. P. Drag on a Sphere in Poiseuille Flow of Shear-Thinning Power-Law Fluids. Ind. Eng. Chem. Res. 2011, 50, 13105–13115.
   Web of Science ®Google Scholar
• Song, D.; Gupta, R. K.; Chhabra, R. P. Heat Transfer to a Sphere in Tube Flow of Power-Law Liquids. Int. J. Heat Mass Transfer 2012, 55, 2110–2121.
   Web of Science ®Google Scholar
• Krishnan, S.; Kannan, A. Effects of Particle Blockage and Eccentricity in Location on the Non-Newtonian Fluid Hydrodynamics Around a Sphere. Ind. Eng. Chem. Res. 2012, 51, 14867–14883.
   Web of Science ®Google Scholar
• Gupta, A. K.; Chhabra, R. P. Spheroids in Viscoplastic Fluids: Drag and Heat Transfer. Ind. Eng. Chem. Res. 2014, 53, 18943–18965.
   Web of Science ®Google Scholar
• Zhang, G.; Li, M.; Li, J.; Yu, M.; Qi, M.; Bai, Z. Wall Effects on Spheres Settling Through Non-Newtonian Fluid Media in Cylindrical Tubes. J. Dispersion Sci. Technol. 2015, 36, 1199–1207.
   Web of Science ®Google Scholar
• Das, P. K.; Gupta, A. K.; Nirmalkar, N.; Chhabra, R. P. Effect of Confinement on Forced Convection from a Heated Sphere in Bingham Plastic Fluids. Korea-Aust. Rheol. J. 2015, 27, 75–94.
   Web of Science ®Google Scholar
• Atapattu, D. D.; Chhabra, R. P.; Uhlherr, P. H. T. Wall Effect for Spheres Falling at Small Reynolds Number in a Viscoplastic Medium. J. Non-Newt. Fluid Mech. 1990, 38, 31–42.
   Web of Science ®Google Scholar
• Yu, Z.; Wachs, A. A Fictitious Domain Method for Dynamic Simulation of Particle Sedimentation in Bingham Fluids. J. Non-Newt. Fluid Mech. 2007, 145, 78–91.
   Web of Science ®Google Scholar
• Dhole S. D.; Chhabra R. P.; Eswaran V. Forced Convection Heat Transfer from a Sphere to Non‐Newtonian Power Law Fluids. AIChE J. 2006, 52, 3658–3667.
   Web of Science ®Google Scholar
• Nirmalkar, N.; Chhabra, R. P.; Poole, R. J. Effect of Shear-Thinning Behavior on Heat Transfer from a Heated Sphere in Yield-Stress Fluids. Ind. Eng. Chem. Res. 2013, 52, 13490–13504.
   Web of Science ®Google Scholar
• Nirmalkar, N.; Chhabra, R. P.; Poole, R. J. Numerical Predictions of Momentum and Heat Transfer Characteristics from a Heated Sphere in Yield-Stress Fluids. Ind. Eng. Chem. Res. 2013, 52, 6848–6861.
   Web of Science ®Google Scholar
• Daugan, S.; Talini, L.; Herzhaft, B.; Peysson, Y.; Allain, C. Sedimentation of Suspensions in Shear-Thinning Fluids. Oil Gas Sci. Technol. 2004, 59, 71–80.
   Google Scholar
• Daugan, S.; Talini, L.; Herzhaft, B.; Allain, C. Aggregation of Particles Settling in Shear-Thinning Fluids. Eur. Phys. J. E 2002, 9, 55–62.
   PubMed Web of Science ®Google Scholar
• Zhu, C.; Lam, K.; Chu, H.-H.; Tang, X.-D.; Liu, G. Drag Forces of Interacting Spheres in Power-Law Fluids. Mech. Res. Commun. 2003, 30, 651–662.
   Web of Science ®Google Scholar
• Riddle, M. J.; Narvaez, C.; Bird, R. B. Interactions between Two Spheres Falling Along Their Line of Centers in a Viscoelastic Fluid. J. Non-Newt. Fluid Mech. 1977, 2, 23–35.
   Web of Science ®Google Scholar
• Allen, E.; Uhlherr, P. H. T. Nonhomogeneous Sedimentation in Viscoelastic Fluids. J. Rheol. 1989, 33, 627–638.
   Web of Science ®Google Scholar
• Liu, B. T.; Muller, S. J.; Denn, M. M. Interactions of Two Rigid Spheres Translating Collinearly in Creeping Flow in a Bingham Material. J. Non-Newt. Fluid Mech. 2003, 113, 49–67.
   Web of Science ®Google Scholar
• Jie, P.; Zhu, K.-Q. Drag Force of Interacting Coaxial Spheres in Viscoplastic Fluids. J. Non-Newt. Fluid Mech. 2006, 135, 83–91.
   Web of Science ®Google Scholar
• Thompson, R. L.; Soares, E. J. Viscoplastic Dimensionless Numbers, J. Non-Newt. Fluid Mech. 2016, 238, 57–64.
   Web of Science ®Google Scholar
• Bercovier, M.; Engelman, M. A. A Finite-Element Method for Incompressible Non-Newtonian Flows. J. Comput. Phys. 1980, 36, 313–326.
   Web of Science ®Google Scholar
• O’Donovan, E. J.; Tanner, R. I. Numerical Study of the Bingham Squeeze Film Problem. J. Non-Newt. Fluid Mech. 1984, 15, 75–83.
   Web of Science ®Google Scholar
• Papanastasiou, T. C. Flows of Materials with Yield. J. Rheol. 1987, 31, 385–404.
   Web of Science ®Google Scholar
• Glowinski, R.; Wachs, A. On the Numerical Simulation of Viscoplastic Fluid Flow. In Handbook of Numerical Analysis; Glowinski, R., Xu, J., Eds.; Elsevier: North Holland, 2011; pp 483–717.
   Google Scholar
• Huilgol, R. R.; Kefayati, G. H. R. Natural Convection Problem in a Bingham Fluid Using the Operator-Splitting Method. J. Non-Newt. Fluid Mech. 2015, 220, 22–32.
   Web of Science ®Google Scholar
• Mitsoulis, E.; Tsamopoulos, J. Numerical Simulations of Complex Yield-Stress Fluid Flows. Rheol. Acta 2017, 56, 231–258.
   Web of Science ®Google Scholar
• Dimakopoulos, Y.; Pavlidis, M.; Tsamopoulos, J. Steady Bubble Rise in Herschel–Bulkley Fluids and Comparison of Predictions via the Augmented Lagrangian Method with Those via the Papanastasiou Model. J. Non-Newt. Fluid Mech. 2013, 200, 34–51.
   Web of Science ®Google Scholar
• Saramito, P. A Damped Newton Algorithm for Computing Viscoplastic Fluid Flows. J. Non-Newt. Fluid Mech. 2016, 238, 6–15.
   Web of Science ®Google Scholar
• Macosko, C. W. Rheology: Principles, Measurements, and Applications; Wiley-Blackwell: New York, 1994.
   Google Scholar
• Roache, P. J. Verification and Validation in Computational Science and Engineering; Hermosa: Albuquerque, NM, 2009.
   Google Scholar
• Liu, B. T.; Muller, S. J.; Denn, M. M. Convergence of a Regularization Method for Creeping Flow of a Bingham Material about a Rigid Sphere. J. Non-Newt. Fluid Mech. 2002, 102, 179–191.
   Web of Science ®Google Scholar
• Atapattu, D. D.; Chhabra, R. P.; Tiu, C.; Uhlherr, P. H. T. The Effect of Cylindrical Boundaries for Spheres Falling in Fluids Having a Yield Stress. Proc. 9th Australasian Fluid Mech. Conference, Auckland, 1986; pp 584–588.
   Google Scholar