## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Entropy generation analysis of nanofluid natural convection in coaxial cylinders subjected to magnetic field

**ABSTRACT**

This paper concerns with the effect of a magnetic field on the entropy generation due to natural convection of Al2O3-water nanofluid flow between coaxial cylinders of aspect ratio H/D=2. The inner and outer cylinders are maintained at hot and cold temperatures, respectively. The top and bottom walls are thermally insulated. The finite volume method was used to discretize the mathematical equations. The present results are compared with those found in the literature, which reveal a very good agreement. The influence of dimensionless parameters such as Hartmann Ha number, Rayleigh Ra number, solid volume fraction of nanoparticules f and inclination angle of magnetic field on streamlines, isotherms contours, local entropy generation, mean Nusselt number , total entropy generation St, and Bejan number Be is discussed. The results show that the local entropy generation are strongly influenced by the application of magnetic field. The increase in heat transfer and entropy generation by adding the nanoparticles to the base fluid depends on the magnetic field strength and direction.

**KEYWORDS**

PAPER SUBMITTED: 2017-12-23

PAPER REVISED: 2018-02-20

PAPER ACCEPTED: 2018-03-01

PUBLISHED ONLINE: 2018-04-28

- Mahmoudi, A. H., et al., MHD Natural Convection and Entropy Generation in a Trapezoidal Enclosure Using Cu-water Nanofluid, Computers and Fluids, 72 (2013), Feb., pp. 46-62.
- Salari, M., et al., Effects of Circular Corners and Aspect-Ratio on Entropy Generation Due to Natural Convection of Nanofluid Flows in Rectangular Cavities, Thermal Science, 19 (2015), 5, pp. 1621-1632.
- Mahian, O., et al., Irreversibility Analysis of a Vertical Annulus Using TiO2/water Nanofluid with MHD Flow Effects, International Journal Heat and Mass Transfer, 64 (2013), Sep., pp. 671-679.
- Matin, M. H., Vaziri, S., Natural Convection of a Nanofluid Inside a Vertical Circular Enclosure Exposed to a Non-Uniform Heat Flux, International Communications in Heat and Mass Transfer, 76 (2016), Aug., pp. 337-347.
- Malvandi, A., et al., Effect of Magnetic Fields on Heat Convection Inside a Concentric Annulus Filled with Al2O3-water Nanofluid, Advanced Powder Technology, 25 (2014), 6, pp. 1817-1824.
- Battira, M., Bessaih, R., Radial and Axial Magnetic Fields Effects on Natural Convection in a Nanofluid-filled Vertical Cylinder, Journal of Applied Fluid Mechanics, 9 (2016), 1, pp. 407-418.
- Afrand, M., et al., Effect of Induced Electric Field on Magneto-Natural Convection in a Vertical Cylindrical Annulus Filled With Liquid Potassium, International Journal of Heat and Mass Transfer, 90 (2015), Nov., pp. 418-426.
- Sankar, M., et al., Effect of Magnetic field on Natural Convection in a Vertical Cylindrical Annulus, International Journal Engineering Science, 44 (2006), 20, pp. 1556-1570.
- Kakarantzas, S.C., et al., Magnetohydrodynamic Natural Convection in a Vertical Cylindrical Cavity with Sinusoidal Upper Wall Temperature, International Journal of Heat and Mass Transfer, 52 (2009), 1-2, pp. 250-259.
- Rashidi, M.M., et al., Numerical Investigation of Magnetic Field Effect on Mixed Convection Heat Transfer of Nanofluid in a Channel with Sinusoidal Walls, Journal of Magnetism and Magnetic Materials, 401 (2016), Mar., pp. 159-168.
- Sankar, M., Do, Y., Numerical Simulation of Free Convection Heat Transfer in a Vertical Annular Cavity with Discrete Heating, International Communications in Heat and Mass Transfer, 37 (2010), 6, pp. 600-606.
- Kakarantzas, S.C., et al., Natural Convection of Liquid Metal in a Vertical Annulus with Lateral and Volumetric Heating in the Presence of a Horizontal Magnetic Field, International Journal of Heat and Mass Transfer, 54 (2011), 15-16, pp. 3347-3356.
- Pourmohamadian et al., Investigating the Effect of Brownian Motion Models on Heat Transfer and Entropy Generation in Nanofluid Forced Convection, Thermal Science, 19 (2015), pp. 161-1632.
- Bessaïh, R., et al., Hydrodynamics and Heat Transfer in Disk Driven Rotating Flow Under Axial Magnetic Field, International Journal of Transport Phenomena, 5 (2003), Dec., pp. 259-278.
- Sankar, M., et al., Effect of Magnetic Field on the Buoyancy and Thermocapillary Driven Convection of an Electrically Conducting Fluid in an Annular enclosure, International Journal of Heat and Fluid Flow, 32 (2011), 2, pp. 402-412.
- Kakarantzas, S.C., et al., MHD Liquid Metal Flow and Heat Transfer Between Vertical Coaxial Cylinders Under Horizontal Magnetic Field, International Journal of Heat and Fluid Flow, 65 (2017), Jun., pp. 342-351.
- Gelfgat, A.Y., et al., Effect of Axial Magnetic Field on Three-Dimensional Instability of Natural Convection in a Vertical Bridgman Growth Configuration, Journal of Crystal Growth, 230 (2001), 1-2, pp. 63-72.
- Sheikholeslami, M., et al., MHD Effects on Nanofluid with Energy and Hydrothermal Behavior Between Two Collateral Plates: Application of New Semi Analytical Technique, Thermal Science, 21 (2017), 5,pp. 2081-2093.
- Chamkha, A., et al., Entropy Generation and Natural Convection of CuO-Water Nanofluid in C-Shaped Cavity under Magnetic Field, Entropy, 18,50 (2016), 2, pp. 1-18.
- Ismael, M., et al., Conjugate Heat Transfer and Entropy Generation in a Cavity Filled with Nanofluid-Saturated Porous Media and Heated by a Triangular Solid, Journal of the Taiwan Institute of Chemical Engineers, 59 (2015), Feb. , pp. 1-14.
- Sheikholeslami, M., Seyednezhad, M., Simulation of Nanofluid Flow and Natural Convection in a Porous Media under the Influence of electric fields Using CVFEM, International Journal of Heat and Mass Transfer, 120 (2018), May., pp. 772-781.
- Sheikholeslami, M., Bhatti, M., M., Forced Convection of Nanofluid in Presence of constant Magnetic Field Considering shape effects of Nanoparticles, International Journal of Heat and Mass Transfer, 111 (2017), Aug., pp. 1039-1049.
- Sheikholeslami, M., Numerical Simulation of Magnetic Nanofluid Natural Convection in Porous Media , Physics Letters A, 381 (2017), 5, pp. 494-503.
- Sheikholeslami, M., Numerical Investigation of Nanofluid Free Convection Under the Influence of Electric Field in a Porous Enclosure, Journal of Molecular Liquids, 249 (2018), Jan., pp. 1212-1221.
- Sheikholeslami, M., et al., Numerical Simulation of Nanofluid Forced Convection Heat Transfer Improvement in Existence of Magnetic Field using Lattice Boltzmann method, International Journal of Heat and Mass Transfer, 108 (2017), B, pp. 1870-1883.
- Brinkman, H.C., The Viscosity of Concentrated Suspensions and Solution, Journal of Chemical Physics, 20 (1952), 4, pp. 571-581.
- Maxwell, J.C., A Treatise on Electricity and Magnetism, Vol. 2, Oxford University, Cambridge, UK,1873, 54.
- Patankar, S.V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New-York, 1980.
- Kumar, R., Kalam M.A., Laminar Thermal Convection Between Vertical Co-axial Isothermal Cylinders, International Journal of Heat and Mass Transfer, 34 (1991), 2, pp. 513-524.
- Selimefendigil, F., Öztop, H. F., Conjugate Natural Convection in a Nanofluid Filled Partitioned Horizontal Annulus Formed by Two Isothermal Cylinder Surfaces Under Magnetic Field, International Journal of Heat and Mass Transfer, 108 (2017), A, pp. 156-171.