## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Numerical study of MHD mixed convective flow in a lid-driven enclosure filled with nanofluid saturated porous medium with center heater

**ABSTRACT**

This present numerical study explores the MHD mixed convective flow and heat transfer analysis in a square porous enclosure filled with nanofluid having center thin heater. The left and right walls of the enclosure are maintained at temperature Tc. The bottom wall is considered with a constant heat source whereas the remaining part of bottom wall and top wall are kept adiabatic. The finite volume method based on SIMPLE algorithm is used to solve the governing equations in order to investigate the effect of heater length, Hartmann number, Richardson number and Darcy number on the fluid flow and heat transfer characteristics inside the enclosure. A set of graphical results are presented in terms of streamlines, isotherms, mid height velocity profiles and average Nusselt numbers. The results reveal that heat transfer rate increases as heater length increases for increasing Darcy number and Richardson number. Among the two positions of heaters, larger enhancement of heat transfer is obtained for horizontal heater of maximum length. It is observed that, Hartmann number is a good control parameter for heat transfer in fluid flow through porous medium in enclosure. More over, Ag-water nanofluid has greater merit to be used for heat transfer enhancement. This problem may be occurred in designing cooling system for electronic equipment to maximize the efficiency with active and secured operational conditions.

**KEYWORDS**

PAPER SUBMITTED: 2017-11-05

PAPER REVISED: 2017-12-05

PAPER ACCEPTED: 2017-12-06

PUBLISHED ONLINE: 2018-01-07

- Bejan, A., et al., Porous and Complex Flow Structures in Modern Technologies, Springer, (2004), New York.
- Vafai, K., Handbook of Porous Media, Taylor and Francis, Second ed., (2005), New York.
- Ingham, D.B., Pop I., (Eds.), Transport Phenomena in Porous Media, Elsevier, (2005), Oxford.
- Nield, D., Bejan, A., Convection in Porous Media, Springer, 3rd ed., (2006), Berlin.
- Khanafer, K., Vafai, K., Double-Diffusive Mixed Convection in a Lid-Driven Enclosure Filled with a Fluid- Saturated Porous Medium, Numerical Heat Transfer, Part A, 42 (2002), pp. 465-486.
- Mahmud, S., Pop, I., Mixed Convection in a Square Vented Enclosure Filled with a Porous Medium, Int. J. Heat Mass Transfer, 49 (2006), pp. 2190-2206.
- Jaballah, S., et al., Numerical Simulation of Mixed Convection in a Channel Irregularly Heated and Partially Filled with a Porous Medium, J. Por. Media, 11 (2008), pp. 247-257.
- Basak, T., et al., A Peclet Number Based Analysis of Mixed Convection for Lid-Driven Porous Square Cavities with Various Heating of Bottom Wall, Int. Comm. Heat Mass Transfer, 39 (2012), pp. 657-664.
- Rahman, M.M., et al., Unsteady Mixed Convection in a Porous Media Filled Lid-Driven Cavity Heated by a Semi-Circular Heaters, Thermal Science, 19 (2015), pp. 1761-1768.
- Mittal, N., et al., Numerical Simulation of Mixed Convection in a Porous Medium Filled with Water / Al2O3 Nanofluid, Heat Transfer - Asian Research, 42 (2013), 1, pp. 46-59.
- Heydari, M.R., et al., Mixed Convection Heat Transfer in a Double Lid-Driven Inclined Square Enclosure Subjected to Cu-Water Nanofluid with Particle Diameter of 90 nm, Heat Transfer Research, 45 (2014), pp. 75-95.
- Kefayati, G.H.R., FDLBM Simulation of Magnetic Field Effect on Mixed Convection in a Two Sided Lid-Driven Cavity Filled with Non-Newtonian Nanofluid, Powder Technol., 280 (2015), pp. 135-153.
- Nayak, R.K., et al., Numerical Study on Mixed Convection and Entropy Generation of a Nanofluid in a Lid-Driven Square Enclosure, J. Heat Transfer, 138 (2016), pp. 012503-1 - 012503-11.
- Sheikholeslami, M., Influence of Lorentz forces on nanofluid flow in a porous cavity by means of non- Darcy model, Engineering Computations, 34 (8) (2017) pp. 2651-2667.
- Sheikholeslami, M., Rokni, H.B., Simulation of nanofluid heat transfer in presence of magnetic field: A review, International Journal of Heat and Mass Transfer, 115 (2017) pp. 1203-1233.
- 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) pp.1039-1049.
- Oztop, H.F., Dagtekin, I., Bahloul, A., Comparision of Position of a Heated Thin Plate Located in a Cavity for Natural Convection, Int. Comm. Heat Mass Transfer, 31(1) (2004) pp. 121-132.
- Dogan, M., Sivrioglu, M., Experimental Investigation of Mixed Convection Heat Transfer from Longitudinal Fins in a Horizontal Rectangular Channel: In Natural Convection Dominated Flow Regimes, Energy Conversion and Management, 50 (2009), pp. 2513-2521.
- Islam, A.W., et al., Mixed Convection in a Lid Driven Square Cavity with an Isothermally Heated Square Blockage Inside, Int. J. Heat Mass Transfer, 55 (2012), pp. 5244-5255.
- Kalteh, M., et al., Numerical Solution of Nanofluid Mixed Convection Heat Transfer in a Lid-Driven Square Cavity with Triangular Heat Source, Powder Technol. 253 (2014), pp. 780-788.
- Rahman, M.M., et al., MHD Mixed Convection with Joule Heating Effect in a Lid-Driven Cavity with a Heated Semi-Circular Source Using the Finite Element Technique, Numerical Heat Transfer, Part A, 60 (2011), pp. 543-560.
- Selimefendigil, F., Oztop, H.F., Numerical Study of MHD Mixed Convection in a Nanofluid Filled Lid Driven Square Enclosure with a Rotating Cylinder, Int. J. Heat Mass Transfer, 78 (2014), pp. 741-754.
- Abu-Nada, E., Dissipative Particle Dynamics Simulation of Combined Convection in a Vertical Lid Driven Cavity with a Comer Heater, Int. J. Therm. Sci., 92 (2015), pp. 72-84.
- Rahman, M. M., et al., Unsteady mixed convection in a porous media filled lid-driven cavity heated by a semi-circular heaters, Thermal Science, 19 (2015) 5, pp. 1761-1768
- Gangawane, K.M., Computational Analysis of Mixed Convection Heat Transfer Characteristics in Lid-Driven Cavity Containing Triangular Block with Constant Heat Flux: Effect of Prandtl and Grashof numbers, Int. J. Heat Mass Transfer, 105 (2017), pp. 34-57.
- Sheikholeslami, M., Sadoughi, M.K., Simulation of CuO-water nanofluid heat transfer enhancement in presence of melting surface, Int. Comm. Heat Mass Transfer, 116 (2018) pp. 909-919.
- Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, (2004) USA.
- Nithyadevi, N., Rajarathinam, M., Effect of Inclination Angle and Magnetic Field on Convection Heat Transfer for Nanofluid in a Porous Cavity, Journal of Applied Fluid Mechanics, 9 (5) (2016), pp. 2347-2358.
- Umadevi, P., Nithyadevi, N., Magneto-convection of Water-based Nanofluids inside an enclosure having Uniform Heat Generation and Various Thermal Boundaries, Journal of the Nigerian Mathematical Society, 35 (2016) pp. 82-92.
- Nithyadevi, N., et al., Effects of inclination angle and non-uniform heating on mixed convection of a nanofluid filled porous enclosure with active mid-horizontal moving, International Journal of Heat and Mass Transfer, 104 (2017) 1217-1228.
- Mahmoodi, M., Numerical Simulation of Free Convection of Nanofluid in a Square Cavity with an Inside Heater, Int. J. Therm. Sci., 50 (2011), pp. 2161-2175.
- Ghasemi, B., et al., Magnetic Field Effect on Natural Convection in a Nanofluid-Filled Square Enclosure, Int. J. Therm. Sci., 50 (2011), pp. 1748-1756.
- Cheng, T. S., Liu, W. H., Effect of Temperature Gradient Orientation on the Characteristics of Mixed Convection Flow in a Lid-Driven Square Cavity, Comput. Fluids, 39 (2010), pp. 965-978.