Mixed Convection Boundary Layer Flow from a Vertical Cone in a Porous Medium Filled with a Nanofluid

Authors: Ezzah Liana Ahmad Fauzi, Syakila Ahmad, Ioan Pop

Abstract:

The steady mixed convection boundary layer flow from a vertical cone in a porous medium filled with a nanofluid is numerically investigated using different types of nanoparticles as Cu (copper), Al2O3 (alumina) and TiO2 (titania). The boundary value problem is solved by using the shooting technique by reducing it into an ordinary differential equation. Results of interest for the local Nusselt number with various values of the constant mixed convection parameter and nanoparticle volume fraction parameter are evaluated. It is found that dual solutions exist for a certain range of mixed convection parameter.

Keywords: boundary layer, mixed convection, nanofluid, porous medium, vertical cone.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081331

References:

[1] D. A. Nield, and A. Bejan, Convection in Porous Media. 3rd ed. New York : Springer, 2006.
[2] D.B. Ingham, and I. Pop, Transport Phenomena in Porous Media. vol 3, Oxford : Elsevier, 2005.
[3] I. Pop, and D. B. Ingham, Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media. Oxford : Pergamon, 2001.
[4] A. Bejan, I. Dincer, S. Lorente, A. F. Miguel, A. H. Reis, Porous and Complex Flow Structure in Modern Technologies. New York : Springer, 2004.
[5] P. Vadasz, Emerging Topics in Heat and Mass Transfer in Porous Media. New York : Springer, 2008.
[6] S. U. S. Choi, "Enhancing thermal conductivity of fluids with nanoparticles," in Developments and Applications of Non-Newtonian Flows, vol. 231, D. A. Siginer, and H. P. Wang (eds.). ASME MD, 1995, pp. 99-105.
[7] S. K. Das, S. U. S. Choi, andW. Yu, Nanofluids, Sciences and Technology. New Jersey : Wiley, 2007.
[8] X. -Q. Wang, and A. S. Mujumdar, "Heat transfer characteristics of nanofluids," International Journal of Thermal Sciences, vol. 46, pp. 1- 9, 2007.
[9] E. Abu-Nada, and H. F. Oztop, "Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid," International Journal Heat Fluid Flow, vol. 30, pp. 669-678, 2009.
[10] K. Khanafer, K. Vafai, and M. Lightstone, "Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids," International Journal Heat Mass Transfer, vol. 46, pp. 3639-3663, 2003.
[11] K. Sadik, and A. Pramuanjaroenkij, "Review of convective heat transfer enhancement with nanofluids," International Journal Heat Mass Transfer, vol. 52, pp. 3187-3196, 2009.
[12] J. Buongiorno, "Convective transport in nanofluids," ASME Journal Heat Transfer, vol. 128, pp. 240-250, 2006.
[13] X. -Q. Wang, and A. S. Mujumdar, "A review on nanofluids-Part II: experiments and applications," Brazilian Journal Chemical Engineering, vol. 25, pp. 631-648, 2008.
[14] S. Kakac┬©, and A. Pramuanjaroenkij, "Review of convective heat transfer enhancement with nanofluids," International Journal Heat Mass Transfer, vol. 52, pp. 3187-3196, 2009.
[15] J. H. Lee, S. H. Lee, C. J. Choi, S. P. Jang, and S. U. S. Choi, "A review of thermal conductivity data, mechanics and models for nanofluids," International Journal Micro-Nano Scale Transport, vol. 1, pp. 269-322, 2010.
[16] J. Eagen, R. Rusconi, R. Piazza, and S. Yip, "The classical nature of thermal conduction in nanofluids," ASME Journal Heat Transfer, vol. 132, pp. 102402, 2010.
[17] J. Fan, and L. Wang, "Review of heat conduction in nanofluids," ASME Journal Heat Transfer, vol. 133, pp. 040801, 2011.
[18] S. Ahmad, and I. Pop, "Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids," International Communications in Heat Mass Transfer, vol. 37, pp. 987- 991, 2010.
[19] R. Nazar, L. Tham, I. Pop, and D.B. Ingham, "Mixed convection boundary layer flow from a horizontal circular cylinder embedded in a porous medium filled with a nanofluid," Transport in Porous Media, vol. 86, pp.517-536, 2010.
[20] P. Cheng, T.T. Le, and I. Pop, "Natural convection of a Darcian fluid about a cone," International Communications in Heat and Mass Transfer, vol. 12, pp. 705717, 1985.
[21] Ching-Yang Cheng, "Nonsimilar boundary layer analysis of doublediffusive convection from a vertical truncated cone in a porous medium with variable viscosity," Applied Mathematics and Computation, vol. 212, pp. 185-193, 2009.
[22] R. K. Tiwari, and M. K. Das, "Heat transfer augmentation in a twosided lid-driven differentially heated square cavity utilizing nanofluids," International Journal Heat Mass Transfer, vol. 50, pp. 2002-2018, 2007.
[23] H. C. Brinkman, "The viscosity of concentrated suspensions and solutions," Journal Chemistry Physics, vol. 20, pp. 571-581, 1952.
[24] H. F. Oztop, and E. Abu Nada, "Numerical study of natural convection in partically heated rectangular enclosure filled with nanofluids," International Journal Heat Fluid Flow, vol. 29, pp. 1326-1336, 2008.