## THERMAL SCIENCE

International Scientific Journal

### HEAT TRANSFER ENHANCEMENT IN ROTATING DISK BOUNDARY LAYER

**ABSTRACT**

A generally admitted fact about the nanofluids is the expedition of heat transfer process in comparison to pure fluids. The calculation of enhanced rate of heat transfer depends strongly upon the nanofluid modeling. Following the experimental evidence most of the researchers assume the nanofluid to be a homogeneous mixture. However, this is a severe condition that results in underprediction of heat transfer rates. Due to the ongoing convection phenomena the nanoparticle concentration is actually non-homogeneous within the boundary layer because of the presence of concentration gradients. The objective of this study is to calculate the heat transfer enhancement in three dimensional boundary layer when the working fluid is a nanofluid. The rotating disk geometry, which perhaps serves as the bench mark for the three dimensional boundary layers, have been chosen for the purpose here. The non-homogeneous nanofluid modeling has been utilized and a percent increase in Nusselt number has been calculated. Detailed analyses of flow and heat transfer phenomena for nanofluids have been conducted under the influence of several physical parameters.

**KEYWORDS**

PAPER SUBMITTED: 2016-04-12

PAPER REVISED: 2016-11-05

PAPER ACCEPTED: 2016-11-09

PUBLISHED ONLINE: 2016-12-03

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**6**, PAGES [2467 - 2482]

- Maxwell, J. C., Treatise on Electricity and Magnetism, Oxford University Press, London, 1904.
- Keblinski, P., Philpot, S. R., Choi, S. U. S., Eastman, J. A., Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), International Journal of Heat and Mass Transfer, 45 (2002), pp. 855-863.
- Choi, S. U. S., Enhancing thermal conductivity of fluids with nanoparticle in developments and applications of Non-Newtonian flows, eds. D. A. Siginer, H. P. Wang, ASME Fluids Engineering Division, San Francisco, CA, 231 (1995), pp. 99-103.
- Buongiorno, J., Convective transport in nanofluids, Journal of Heat Transfer, 128 (2006), pp. 240-250.
- Tiwari, R. K., Das, M. K., Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, International Journal of Heat and Mass Transfer, 50 (2007), pp. 2002-2018.
- Buschmann, M. H., Nanofluid in thermosyphons and heat pipes: overview of recent experiments and modelling approaches, International Journal of Heat and Mass Transfer, 52 (2009), pp. 3187-3196.
- Rea, U., Meckrell, T., Hu, L., Buongiorno, J., Laminar convective heat transfer and viscous pressure loss of almunia-water and zirconia-water nanofluids, International Journal of Heat and Mass Transfer, 52 (2009), pp. 2042- 2048.
- Magia, S. E. B., Nugyen, C. T., Glains, N., Roy, G., Heat transfer behaviors of nanofluids in uniformly heated tube, Supperlattices Microstructure, 35 (2004), pp. 543-557.
- Merhi, D., Lamaire, E., Bossis, G., Moukalled, F., Particle migration in concentrated suspensions flowing between rotating plates: investigations of diffusion flux coefficients, Journal of Rheology, 49 (2005), pp. 1429-1448.
- Avramenko, A. A., Bilnov, D. G., Shevchuk, I. V., Self-similar analysis of fluid flow and heat-mass transfer of nanofluids in boundary layer, Physics of Fluids, 23 (2011), pp. 1-8.
- Avramenko, A. A., Bilnov, D. G., Shevchuk, I. V., Kuznetsov, A. V., Symmetry analysis and self-similar forms of fluid flow and heat-mass transfer in turbulent boundary layer flow of a nanofluid, Physics of Fluids, 24 (2012), pp. 1-20.
- Frank, M., Aderson, D., Weeks, E. R., Morris, J. F., Particle migration in pressure driven flow of a Brownian suspension, Journal of Fluid Mechanics, 493 (2003), pp. 363-378.
- Ding, Y. L., Wen, D., et al., Particle migration in a flow of nanoparticles suspensions, Powder Technology, 149 (2005), pp. 84-92.
- Avramenko, A. A., Shevchuk, I. V., Tyrinov, A. L., Bilnov, D. G., Heat transfer at film condensation of stationary vapor with nanoparticles near a vertical plate, Applied Thermal Engineering, 73 (1) (2014), pp. 389-396.
- Avramenko, A. A., Shevchuk, I. V., Tyrinov, A. L., Bilnov, D. G., Heat transfer at film condensation of moving vapor with nanoparticles near a flat surface, International Journal of Heat and Mass Transfer, 82 (2015), pp. 316-324.
- Avramenko, A. A., Shevchuk, I. V., Tyrinov, A. L., Bilnov, D. G., Heat transfer in stable film boiling of nanofluid over a vertical surface, International Journal of Heat and Mass Transfer, 92 (2015), pp. 106-118.
- Shevchuk, I. V., Convective Heat and Mass Transfer in Rotating Disk Systems, Springer-Verlag, Berlin Heidelberg, 2009.
- Lingwood, R. J., Absolute instability of the boundary layer on a rotating disk, Journal of Fluid Mechanics, 299 (1995), pp. 17-33.
- Pier, B., Finite-amplitude crossflow vortices, secondary instability and transition in the rotating-disk boundary layer, Journal of Fluid Mechanics, 487 (2003), pp. 315-343.
- Carpenter, P. W., & Thomas, P. J., Flow over a compliant rotating disks, Journal of Engineering Mathematics, 57 (2007), pp. 303-315.
- Davies, C., & Carpenter, P. W., Global behaviour corresponding to the absolute instability of the rotating-disk boundary layer, Journal of Fluid Mechanics, 486 (2003), pp. 287-329.
- Imayama, S., Experimental study of the rotating-disk boundary layer flow. Ph. D. thesis, Linne FLOW Centre, KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden.
- Karman, T. V., Uber laminaire und turbulente reibung, Z. Angew. Math. Mech., 1 (1921), pp. 233-252.
- Cochran, W. G., The flow due to a rotating disk, Mathematical proceedings of the Cambridge Philosophical Society, 30 (1934), pp. 365-375.
- Benton, E. R., On the flow due to a rotating disk, Journal of Fluid Mechanics, 24 (1966), pp. 781-800.
- Mehmood, A., Ali, A., Takhar, H. S., Anwar Beg, O., Islam, M. N., Vilson, L. S., Unsteady von Karman swirling flow: Analytic study using the homotopy method, International Journal of Applied Mathematics and Mechanics, 6 (2) (2010), pp. 67-84.
- Attia, H. A., Hassan, A. L. A., On hydromagnetic flow due to a rotating disk, Applied Mathematical Modelling, 28 (2004), pp. 1007-1014.
- Bachok, N., Ishak, A., Pop, I.., Flow and heat transfer over a rotating porous disk in nanofluid, Physica B, 406 (2011), pp. 1767-1772.
- Turkyilmazoglu, M., Nanofluid flow and heat transfer due to a rotating disk, Comp. Phy., 94 (2014), pp. 139-146.
- Rashidi, M. M., Abelman, S., Freidooni, N., Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid, International Journal of Heat and Mass Transfer, 62 (2013), pp. 515-525.
- Yin, C., Zheng, L., Zhang, C., Zhang, X., Flow and heat transfer of nanofluids over a rotating porous disk with velocity slip and temperature jump, Z. Naturforsch. A, 70 (2015), pp. 351-.
- Liu, I. C., Wan, H. H., Liu, C. N., Flow and heat transfer of nanofluids near a rotating disk, Advanced Martial Research, 664 (2013), pp. 859-865.
- Minkowycz, W. J., et al., Nanoparticles heat transfer and fluid flow, CRC Press, Taylor & Franics Group, Boca Raton, London, New York 2013.
- Einstein, A., Eine neue bestimmung der molekuldimensionen, Annalen der Physik, Leipzig, 19 (1906), pp. 289-306.
- Brikmann, H. C.,The viscosity of concentrated suspensions and solutions, Journal of Chemical Physics, 20 (1952), pp. 571-581.
- Batchelor, G., The effect of Brownian motion on the bulk stress in a suspension of spherical particles, Journal of Fluid Mechanics, 83(1977), pp. 97-117.
- Lundgren, T., Slow flow through stationary random beds and suspension of spheres, Journal of Fluid Mechanics, 51 (1972), pp. 273-299.
- Maxwell, J. C. A., Treatise on electricity and magnetism, Calrendon Press, Oxford,UK, 2nd edition 1881.
- Brugeman, D. A. G., Berechnung verschiedener physikalischer konstanten von hetrogenen substanzen, I. Dielektrizitatskonstanten und lietfahigkiten der mischkorper aus isotropen substanzen, Annalan der Physik, Leipzig, 24(1935), pp. 636-679.