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Heat transfer in laminar Couette flow laden with rigid spherical particles

  • M. Niazi Ardekani (a1), O. Abouali (a1) (a2), F. Picano (a3) and L. Brandt (a1)


We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations. In the simulations we use a direct-forcing immersed boundary method to account for the dispersed phase together with a volume-of-fluid approach to solve the temperature field inside and outside the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed in the literature. In addition, an average composite diffusivity can be used to approximate the effective diffusivity of the suspension in the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger, smoothly saturating at higher volume fractions. By phase-ensemble-averaging we identify the different mechanisms contributing to the total heat transfer and show that the increase of the effective conductivity observed at finite inertia is due to the increase of the transport associated with fluid and particle velocity. We also show that the contribution of the heat conduction in the solid phase to the total wall-normal heat flux reduces when increasing the particle Reynolds number, so that particles of low thermal diffusivity weakly alter the total heat flux in the suspension at finite particle Reynolds numbers. On the other hand, a higher particle thermal diffusivity significantly increases the total heat transfer.


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Ahuja, A. S. 1975 Augmentation of heat transport in laminar flow of polystyrene suspensions. I. Experiments and results. J. Appl. Phys. 46 (8), 34083416.
Ardekani, M. N., Costa, P., Breugem, W. P. & Brandt, L. 2016 Numerical study of the sedimentation of spheroidal particles. Intl J. Multiphase Flow 87, 1634.
Breedveld, V., Van Den Ende, D., Bosscher, M., Jongschaap, R. J. J. & Mellema, J. 2002 Measurement of the full shear-induced self-diffusion tensor of noncolloidal suspensions. J. Chem. Phys. 116 (23), 1052910535.
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3–4), 242251.
Breugem, W.-P. 2012 A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows. J. Comput. Phys. 231 (13), 44694498.
Chung, Y. C. & Leal, L. G. 1982 An experimental study of the effective thermal conductivity of a sheared suspension of rigid spheres. Intl J. Multiphase Flow 8 (6), 605625.
Costa, P., Boersma, B. J., Westerweel, J. & Breugem, W. P. 2015 Collision model for fully resolved simulations of flows laden with finite-size particles. Phys. Rev. E 92 (5), 053012.
Dan, C. & Wachs, A. 2010 Direct numerical simulation of particulate flow with heat transfer. Intl J. Heat Fluid Flow 31 (6), 10501057.
Feng, Z. G. & Michaelides, E. E. 2008 Inclusion of heat transfer computations for particle laden flows. Phys. Fluids 20 (4), 040604.
Feng, Z. G. & Michaelides, E. E. 2009 Heat transfer in particulate flows with direct numerical simulation (DNS). Intl J. Heat Mass Transfer 52 (3), 777786.
Fornari, W., Formenti, A., Picano, F. & Brandt, L. 2016a The effect of particle density in turbulent channel flow laden with finite size particles in semi-dilute conditions. Phys. Fluids 28, 033301.
Fornari, W., Picano, F. & Brandt, L. 2016b Sedimentation of finite-size spheres in quiescent and turbulent environments. J. Fluid Mech. 788, 640669.
Hashemi, Z., Abouali, O. & Kamali, R. 2014 Three dimensional thermal lattice Boltzmann simulation of heating/cooling spheres falling in a Newtonian liquid. Intl J. Therm. Sci. 82, 2333.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VoF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201225.
Incropera, F. P., Lavine, A. S., Bergman, T. L. & Dewitt, D. P. 2007 Fundamentals of Heat and Mass Transfer. Wiley.
Kempe, T. & Fröhlich, J. 2012 An improved immersed boundary method with direct forcing for the simulation of particle laden flows. J. Comput. Phys. 231 (9), 36633684.
Ladd, A. J. C. 1994a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285309.
Ladd, A. J. C. 1994b Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311339.
Lambert, R. A., Picano, F., Breugem, W.-P. & Brandt, L. 2013 Active suspensions in thin films: nutrient uptake and swimmer motion. J. Fluid Mech. 733, 528557.
Lashgari, I., Picano, F., Breugem, W. P. & Brandt, L. 2014 Laminar, turbulent, and inertial shear-thickening regimes in channel flow of neutrally buoyant particle suspensions. Phys. Rev. Lett. 113 (25), 254502.
Lashgari, I., Picano, F., Breugem, W. P. & Brandt, L. 2016 Channel flow of rigid sphere suspensions: particle dynamics in the inertial regime. Intl J. Multiphase Flow 78, 1224.
Leal, L. G. 1973 On the effective conductivity of a dilute suspension of spherical drops in the limit of low particle Péclet number. Chem. Engng Commun. 1 (1), 2131.
Madanshetty, S. I, Nadim, A. & Stone, H. A. 1996 Experimental measurement of shear-induced diffusion in suspensions using long time data. Phys. Fluids 8 (8), 20112018.
Marchioro, M., Tanksley, M. & Prosperetti, A. 1999 Mixture pressure and stress in disperse two-phase flow. Intl J. Multiphase Flow 25 (6), 13951429.
Maxwell, J. C. 1904 A Treatise on Electricity and Magnetism, 3rd edn, vol. 1. Clarendon.
Metzger, B., Rahli, O. & Yin, X. 2013 Heat transfer across sheared suspensions: role of the shear-induced diffusion. J. Fluid Mech. 724, 527552.
Nielsen, L. E. 1974 The thermal and electrical conductivity of two-phase systems. Ind. Engng Chem. Fundam. 13 (1), 1720.
Picano, F., Breugem, W. P. & Brandt, L. 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463487.
Picano, F., Breugem, W. P., Mitra, D. & Brandt, L. 2013 Shear thickening in non-Brownian suspensions: an excluded volume effect. Phys. Rev. Lett. 111 (9), 098302.
Pietrak, K. & Wisniewski, T. S. 2015 A review of models for effective thermal conductivity of composite materials. J. Power Technol. 95 (1), 1424.
Roma, A. M., Peskin, C. S. & Berger, M. J. 1999 An adaptive version of the immersed boundary method. J. Comput. Phys. 153 (2), 509534.
Shin, S. & Lee, S. H. 2000 Thermal conductivity of suspensions in shear flow fields. Intl J. Heat Mass Transfer 43 (23), 42754284.
Sohn, C. W. & Chen, M. M. 1981 Microconvective thermal conductivity in disperse two-phase mixtures as observed in a low velocity Couette flow experiment. Trans. ASME J. Heat Transfer 103 (1), 4751.
Souzy, M., Yin, X., Villermaux, E., Abid, C. & Metzger, B. 2015 Super-diffusion in sheared suspensions. Phys. Fluids 27 (4), 041705.
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129149.
Ström, H. & Sasic, S. 2013 A multiphase DNS approach for handling solid particles motion with heat transfer. Intl J. Multiphase Flow 53, 7587.
Sun, B., Tenneti, S., Subramaniam, S. & Koch, D. L. 2016 Pseudo-turbulent heat flux and average gas-phase conduction during gas–solid heat transfer: flow past random fixed particle assemblies. J. Fluid Mech. 798, 299349.
Tavassoli, H, Kriebitzsch, S. H. L., van der Hoef, M. A., Peters, E. A. J. F. & Kuipers, J. A. M. 2013 Direct numerical simulation of particulate flow with heat transfer. Intl J. Multiphase Flow 57, 2937.
Uhlmann, M. 2005 An immersed boundary method with direct forcing for simulation of particulate flow. J. Comput. Phys. 209 (2), 448476.
Wang, L., Koch, D. L., Yin, X. & Cohen, C. 2009 Hydrodynamic diffusion and mass transfer across a sheared suspension of neutrally buoyant spheres. Phys. Fluids 21 (3), 033303.
Zhang, Q. & Prosperetti, A. 2010 Physics-based analysis of the hydrodynamic stress in a fluid–particle system. Phys. Fluids 22 (3), 033306.
Zydney, A. L & Colton, C. K 1988 Augmented solute transport in the shear flow of a concentrated suspension. Physico-Chem. Hydrodyn. 10 (1), 7796.
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Heat transfer in laminar Couette flow laden with rigid spherical particles

  • M. Niazi Ardekani (a1), O. Abouali (a1) (a2), F. Picano (a3) and L. Brandt (a1)


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