THE EFFECT OF VARIATION OF BASE FLUID ON NATURAL CONVECTION IN CAVITY FILLED WITH NAOFLUID IN THE PRESENCE OF MAGNETIC FIELD

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1 THE EFFECT OF VARIATION OF BASE FLUID ON NATURAL CONVECTION IN CAVITY FILLED WITH NAOFLUID IN THE PRESENCE OF MAGNETIC FIELD Salma H. RADWAN 1*, Mohamed TEAMAH 2, Mohamed M. ABO ELAZM 3, Wael El-MAGHLANY 4 1,3 Arab Academy for Science and Technology and Maritime Transport, Egypt 2,4 Faculty of Engineering, Alexandria University, Egypt * Corresponding Author: Salma H. Radwan Abstract The present study examines the natural convection in a cavity filled with Nanofluid and influenced by a magnetic field and different types of base fluid will be examined. Steady state laminar regime is considered and the transport equations for continuity, momentum, energy are solved. The numerical results are examined for the effect of Hartmann number and Prandtl number on the iso-contours of streamline and temperature. In addition, the predicted results for average Nusselt are presented for various parametric conditions. Keywords: Nanofluids, magnetic field, cavity, natural convection 1. Introduction A nanofluid is a suspension of particles in a conventional base fluid which enormously enhances the heat transfer characteristics of the original fluid. Heat transfer fluids such as water, mineral oil and ethylene glycol play an important role in many industrial processes, including power generation, chemical processes, heating or cooling processes, and microelectronics. The critical initiative is to seek the solid additives having thermal conductivities several hundreds of times higher than those of convectional fluids. An inventive idea is to add solid particles in the fluid for improving the thermal conductivity of a fluid. Many types of particles, such as metallic, non-metallic and polymeric can be suspended into fluids to form slurries. However, the usual slurries, with suspended particles in the order of millimeters or even micrometers may cause some severe problems. Nanofluids are suspensions of nanoparticles in a base fluid. Nanoparticles 2016 RS Publication, rspublicationhouse@gmail.com Page 344

2 are made up of stable metals, metal oxides or carbon in several forms. The size of the nanoparticles informs some characteristics to these fluids, including greatly improved energy, momentum, mass transfer, as well as reduced tendency for sedimentation and erosion of the containing surfaces. Nanofluids are being examined for many applications, such as cooling, manufacturing chemical and pharmaceutical processes, medical treatments, etc. Most researchers claim that the suspension of nanoparticles with high thermal conductivity to the base fluid results in an increase of the thermal performance of the resultant nanofluid [1-7].There has been an interest to understand the flow behavior and the heat transfer mechanism of enclosures which are filled with electrically conducting fluids and are in the influence of a magnetic field [8-9]. 2. Problem description Fig.1. A schematic diagram of the physical model. A schematic diagram of the cavity filled with nanofluid is represented in figure1. The cavity bounded by two isothermal vertical walls and by two horizontal adiabatic walls. A magnetic field with strength Bo is applied in the horizontal direction. It is assumed that the base fluid and the nanoparticles are in thermal equilibrium, the nanofluid is Newtonian and incompressible, the flow is steady and laminar and the nanoparticles used are copper. The equations that govern the conservation of mass, momentum and energy can be written in a dimensionless form as follows [10]: (1) (2) 2016 RS Publication, rspublicationhouse@gmail.com Page 345

3 (3) (4) The dimensionless boundary conditions for vertical walls are: U=V=0 and =1 at X=0 (Left wall), U=V=0 and =0 at X=L (right wall), U =V = =0 at Y = 0 and Y = 1. The effective density of the nanofluid is: (5) Where, is the solid volume fraction of the nanofluid. The thermal diffusivity of nanofluid is: (6) Where is the heat capacitance of the nanofluid and is given by The thermal expansion coefficient of the nanofluid is: Applied models for the effective viscosity and thermal conductivity of nanofluid [16]: Effective viscosity: Effective Thermal conductivity: For the present study, FORTRAN code is used to solve numerically the differential equations that govern fluid motion with the corresponding boundary conditions. (7) (8) (9) (10) The local Nusselt number on the left hot wall can be defined as: The average Nusselt number is obtained by integrating the above local Nusselt number over the hot vertical wall: (11) (12) 2016 RS Publication, rspublicationhouse@gmail.com Page 346

4 3. Code Validation In order to check on the accuracy of the numerical method employed for the solution of the problem considered in the present study, The present computation is validated in contradiction of the results of Pirmohammadi and Ghassemi [11] for the average Nusselt number in the presence of nanofluid is represented in Fig.2.The Figure shows good agreement between the present code and their results. 4. Results Fig.2. Variation of average Nusselt number with Hartmann number (Ha) for different Ra for =0.03 and Pr = 6.2 (water-al 2 O 3 The effects of different base fluid on the streamlines and isotherms are presented in Fig.4 for different Hartmann number (0 Ha 60) and Prandtl number (Pr =0.01, 6.2, 100) with Rayleigh number (Ra= 10 5 ) and solid volume fraction =0.03and the nanoparticles used are copper. The results showed that at Ha=0, the strength of streamlines increase with the increase of Prandtl number and this is due to the strengthening of the convection flow field at higher Rayleigh numbers and the strong buoyant flows. In the presence of magnetic field due to the suppression of the convective circulating flows by the stronger magnetic field, it decreases as the Hartmann number increases. The isotherms are affected by variations in the Hartmann number. Changing the Fig. 3. The average Nusselt number at different Ha and Pr, for =0.03 and Ra =10 5 Hartmann number has an obvious effect on the Nusselt number at Ra=10 5 which is shown in fig.3, where the buoyant flows are significantly influenced by the magnetic field. So, the nusselt number decreases with increasing magnetic field and increases with increasing Prandl number RS Publication, rspublicationhouse@gmail.com Page 347

5 Isotherms Ha=60 Streamlines Isotherms Ha=0 Streamlines International Journal of Advanced Scientific and Technical Research Issue 6 volume 3, May June 2016 Pr=0.01 Pr=6.2 Pr=100 Ψmin=0.5 Ψmax=7 Ψmin=0.5 Ψmax=13 Ψmin=0.5 Ψmax=14.5 Ψmin=0.2 Ψmax=2.5 Ψmin=0.2 Ψmax=2.4 Ψmin=0.2 Ψmax=2.3 Fig. 4. The streamlines and isotherms at different Ha and Pr, for =0.03 and Ra = RS Publication, rspublicationhouse@gmail.com Page 348

6 5. References [1] A.G.A. Nnanna, Experimental model of temperature-driven nanofluid, Journal of Heat Transfer 129 (2007) [2] H.F. Oztop, E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow 29 (2008) [3] S.M. Aminossadati, B. Ghasemi, Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure, European Journal of Mechanics, B/Fluids 28 (2009) [4] A.K. Santra, S. Sen, N. Chakraborty, Study of heat transfer characteristics of copperwater nanofluid in a differentially heated square cavity with different viscosity models, Journal of Enhanced Heat Transfer 15 (2008) [5] C.J. Ho, M.W. Chen, Z.W. Li, Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity, International Journal of Heat and Mass Transfer 51 (2008) [6] Z. Alloui, P. Vasseur, M. Reggio, Natural convection of nanofluids in a shallow cavity heated from below, International Journal of Thermal Sciences 50 (2011) [7] C.J. Ho, W.K. Liu, Y.S. Chang, C.C. Lin, Natural convection heat transfer of aluminawater nanofluid in vertical square enclosures: an experimental study, International Journal of Thermal Sciences 49 (2010) [8] Yahyazadeh, H., et al, Evaluation of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field by the differential transformation method, Thermal science 16 (2012), 5, PP [9] M.A. Teamah, Numerical simulation of double diffusive natural convection in rectangular enclosure in the presences of magnetic field and heat source, International Journal of Thermal Sciences 47(2008), 3, PP [10] B. Ghasemi, S.M. Aminossadati, Brownian motion of nanoparticles in a triangular enclosure with natural convection, International Journal of Thermal Sciences,49 (6) (2010) PP [11] S.M. Aminossadati, A. Kargar, B. Ghasemi, Magnetic field effect on natural convection in a nanofluid-filled square enclosure, International Journal of Thermal Sciences, 50 (2011) PP RS Publication, rspublicationhouse@gmail.com Page 349