0
Technical Brief

# Effect of Magnetic Field on Natural Convection and Entropy Generation in Al2O3/Water Nanofluid-Filled Enclosure With Twin Protruding Heat Sources

[+] Author and Article Information
Prasanth Anand Kumar Lam

Fluid Mechanics Laboratory,
Department of Applied Mechanics,
Chennai 600036, India
e-mail: prasanth62@gmail.com

K. Arul Prakash

Fluid Mechanics Laboratory,
Department of Applied Mechanics,
Chennai 600036, India
e-mail: arulk@iitm.ac.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received November 4, 2015; final manuscript received November 16, 2016; published online February 28, 2017. Assoc. Editor: Ranganathan Kumar.

J. Thermal Sci. Eng. Appl 9(2), 024502 (Feb 28, 2017) (12 pages) Paper No: TSEA-15-1313; doi: 10.1115/1.4035810 History: Received November 04, 2015; Revised November 16, 2016

## Abstract

In this paper, the effect of magnetic field on natural convection of Al2O3/water nanofluid in an enclosure containing twin protruding heat sources placed on top and bottom walls arranged in-line and staggered manner is presented. For this purpose, coupled equations governing fluid flow and heat transfer are solved in Cartesian framework using streamline upwind/Petrov–Galerkin (SUPG) finite element method. Numerical computations are performed to predict the fluid flow, heat transfer, and entropy generation for a wide range of Hartmann number (0.0 $≤$ Ha $≤$ 100.0), Rayleigh number ($103≤Ra≤106$), and nanoparticle volume fraction ($0.0≤ϕ≤0.1$). The simulated results indicate that, for both in-line and staggered arrangement, the entropy generation due to heat transfer is significant along isothermal surfaces, whereas entropy generation due to fluid friction is higher at no-slip walls and along the regions of contact between adjacent recirculation cells. For both in-line and staggered arrangement, increase in global total entropy generation and average Nusselt number along top and bottom heat sources is obtained with decreasing Ha and increasing Ra. Furthermore, for both in-line and staggered arrangement, variation in global total entropy generation and average Nusselt number along top and bottom heat sources with increasing nanoparticle volume fraction, depend on both Ha and Ra.

<>

## References

Sparrow, E. , and Cess, R. , 1961, “ The Effect of a Magnetic Field on Free Convection Heat Transfer,” Int. J. Heat Mass Transfer, 3(4), pp. 267–274.
Rudraiah, N. , Barron, R. , Venkatachalappa, M. , and Subbaraya, C. , 1995, “ Effect of a Magnetic Field on Free Convection in a Rectangular Enclosure,” Int. J. Eng. Sci., 33(8), pp. 1075–1084.
Sathiyamoorthy, M. , and Chamkha, A. , 2010, “ Effect of Magnetic Field on Natural Convection Flow in a Liquid Gallium Filled Square Cavity for Linearly Heated Side Wall(s),” Int. J. Therm. Sci., 49(9), pp. 1856–1865.
Choi, S. U. , and Eastman, J. , 1995, “ Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Argonne National Laboratory, Lemont, IL, Technical Report No. ANL/MSD/CP--84938.
Khanafer, K. , Vafai, K. , and Lightstone, M. , 2003, “ Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids,” Int. J. Heat Mass Transfer, 46(19), pp. 3639–3653.
Anilkumar, S. , and Kuzhiveli, B. T. , 2009, “ Numerical Study of Natural Convective Heat Transfer in a Two-Dimensional Cavity With Centrally Located Partition Utilizing Nanofluids,” ASME J. Therm. Sci. Eng. Appl., 1(3), p. 031004.
Ho, C. , Liu, W. , Chang, Y. , and Lin, C. , 2010, “ Natural Convection Heat Transfer of Alumina-Water Nanofluid in Vertical Square Enclosures: An Experimental Study,” Int. J. Therm. Sci., 49(8), pp. 1345–1353.
Tayebi, T. , Chamkha, A. J. , Djezzar, M. , and Bouzerzour, A. , 2016, “ Natural Convective Nanofluid Flow in an Annular Space Between Confocal Elliptic Cylinders,” ASME J. Therm. Sci. Eng. Appl., 9(1), p. 011010.
Bouhalleb, M. , and Abbassi, H. , 2016, “ Numerical Investigation of Heat Transfer by CuO-Water Nanofluid in Rectangular Enclosures,” Heat Transfer Eng., 37(1), pp. 13–23.
Putra, N. , Roetzel, W. , and Das, S. , 2003, “ Natural Convection of Nano-Fluids,” Heat Mass Transfer, 39(8–9), pp. 775–784.
Ternik, P. , 2015, “ Conduction and Convection Heat Transfer Characteristics of Water-Au Nanofluid in a Cubic Enclosure With Differentially Heated Side Walls,” Int. J. Heat Mass Transfer, 80, pp. 368–375.
Ghodsinezhad, H. , Sharifpur, M. , and Meyer, J. P. , 2016, “ Experimental Investigation on Cavity Flow Natural Convection of Al2O3 Water Nanofluids,” Int. Commun. Heat Mass Transfer, 76, pp. 316–324.
Ghasemi, B. , Aminossadati, S. , and Raisi, A. , 2011, “ Magnetic Field Effect on Natural Convection in a Nanofluid-Filled Square Enclosure,” Int. J. Therm. Sci., 50(9), pp. 1748–1756.
Mahmoudi, A. H. , Pop, I. , Shahi, M. , and Talebi, F. , 2013, “ MHD Natural Convection and Entropy Generation in a Trapezoidal Enclosure Using Cu-Water Nanofluid,” Comput. Fluids, 72, pp. 46–62.
Mejri, I. , and Mahmoudi, A. , 2015, “ MHD Natural Convection in a Nanofluid-Filled Open Enclosure With a Sinusoidal Boundary Condition,” Chem. Eng. Res. Des., 98, pp. 1–16.
Mahmoudi, A. H. , Shahi, M. , Shahedin, A. M. , and Hemati, N. , 2011, “ Numerical Modeling of Natural Convection in an Open Cavity With Two Vertical Thin Heat Sources Subjected to a Nanofluid,” Int. Commun. Heat Mass Transfer, 38(1), pp. 110–118.
Aminossadati, S. , and Ghasemi, B. , 2011, “ Natural Convection of Water-CuO Nanofluid in a Cavity With Two Pairs of Heat Source-Sink,” Int. Commun. Heat Mass Transfer, 38(5), pp. 672–678.
Mahmoudi, A. H. , Pop, I. , and Shahi, M. , 2012, “ Effect of Magnetic Field on Natural Convection in a Triangular Enclosure Filled With Nanofluid,” Int. J. Therm. Sci., 59, pp. 126–140.
Lam, P. A. K. , and Prakash, K. A. , 2014, “ A Numerical Study on Natural Convection and Entropy Generation in a Porous Enclosure With Heat Sources,” Int. J. Heat Mass Transfer, 69, pp. 390–407.
Brooks, A. N. , and Hughes, T. J. R. , 1982, “ Streamline Upwind/Petrov–Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier–Stokes Equations,” Comput. Methods Appl. Mech. Eng., 32(1–3), pp. 199–259.
Prakash, K. , Biswas, G. , and Kumar, B. , 2007, “ Numerical Prediction of Fluid Flow and Heat Transfer in the Target System of an Axisymmetric Accelerator-Driven Subcritical System,” J. Heat Transfer, 129(4), pp. 582–588.
Lam, P. A. K. , and Prakash, K. A. , 2015, “ A Numerical Investigation of Heat Transfer and Entropy Generation During Jet Impingement Cooling of Protruding Heat Sources Without and With Porous Medium,” Energy Convers. Manage., 89, pp. 626–643.
Lam, P. A. K. , and Prakash, K. A. , 2016, “ Thermodynamic Investigation and Multi-Objective Optimization for Jet Impingement Cooling System With Al2O3/Water Nanofluid,” Energy Convers. Manage., 111, pp. 38–56.

## Figures

Fig. 1

Computational domain with boundary conditions (solid line: in-line arrangement, dashed line: staggered arrangement)

Fig. 2

Comparison of (a) streamlines, (b) isotherms, (c) v-velocity along vertical midplane, (d) temperature along vertical midplane, (e) local Nusselt number, and (f) average Nusselt number along hot vertical wall for a square enclosure with Al2O3/water nanofluid with Ghasemi et al. [13]

Fig. 3

Effect of Ha on (a) streamlines and (b) isotherms during natural convection of Al2O3/water nanofluid filled enclosure with built in heat sources on top and bottom walls placed in (i) in-line and (ii) staggered arrangement

Fig. 4

Effect of Ha on entropy generation contours due to (a) heat transfer irreversibility (Sθ) and (b) fluid friction irreversibility (Sψ) during natural convection of Al2O3/water nanofluid-filled enclosure with built-in heat sources placed in (i) in-line and (ii) staggered arrangement

Fig. 5

Effect of Ha on local Nusselt number distribution along the periphery of the heat sources at Ra = 105 and ϕ  = 0.03 in Al2O3/water nanofluid filled enclosure with built-in heat sources placed in (i) in-line and (ii) staggered arrangement

Fig. 6

Variation of surface-averaged Nusselt number ratio for: (a) bottom heat source (NuB¯*) and (b) top heat source (NuT¯*) and global entropy generation ratio due to (c) heat transfer (Sθ¯*) and (d) fluid friction (Sψ¯*) with Hartmann number and Rayleigh number at ϕ  = 0.0 in Al2O3/water nanofluid-filled enclosure with built in heat sources placed both in (i) in-line and (ii) staggered arrangement

Fig. 7

Variation of surface-averaged Nusselt number ratio with nanoparticle volume fraction and Hartmann number at different values of Rayleigh number (Ra = 104, 105 and 106) for both (a) bottom heat source (NuB¯**) and (b) top heat source (NuT¯**) in Al2O3/water nanofluid-filled enclosure with built in heat sources placed both in (i) in-line and (ii) staggered arrangement

Fig. 8

Variation of global entropy generation ratio for (a) heat transfer (Sθ¯**) and (b) fluid friction (Sψ¯**) with nanoparticle volume fraction and Hartmann number at different values of Rayleigh number (Ra = 104, 105, and 106) in Al2O3/water nanofluid-filled enclosure with built in heat sources placed both in (i) in-line and (ii) staggered arrangement

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections