Numerical analysis of MHD double diffusive nano-fluid convection in a cavity using FEM

Numerical analysis of MHD double diffusive nano-fluid convection in a cavity using FEM

P. Nithish Reddy K. Murugesan V. Koushik 

Mechanical Engineering Department, Sreenidhi Institute of Science and Technology, Hyderabad 501301, India

Mechanical & Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247667, India

Corresponding Author Email: 
dr.nithish.reddy@gmail.com
Page: 
589-612
|
DOI: 
https://doi.org/10.3166/ACSM.42.589-612
Received: 
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Accepted: 
|
Published: 
31 December 2018
| Citation

OPEN ACCESS

Abstract: 

In this paper double diffusive convection phenomenon in a cavity subjected to magnetic field is studied. Various investigations are conducted on heat and mass transfer rates in the cavity filled with water based nano fluid containing different nano particles including Ag, Cu and TiO2. The side walls of the cavity are differentially heated and concentrated while both the top and bottom walls are kept adiabatic to heat and mass flow. Galerkin’s weighted residual finite element method is used to solve the conservation equations namely vorticity transport equation, velocity Poisson equations, energy and mass balance equations. Maxwell-Garnett model is used for evaluating thermal conductivity ratio and Brinkman model is used in predicting the effective viscosity. Numerical investigations are carried out on the effect of parameters like magnetic field intensity, particle volume fraction, type of nano particles and thermal Rayleigh number on heat and mass transfer rates in the system. The effect of inclusion of nano particles at different levels of magnetic field intensities is studied and results obtained with different nano particles with variation in Hartmann number are compared. It is observed that maximum of 71% and 78% loss is observed in Nusselt and Sherwood numbers respectively with increment in Hartmann number from 0 to 100.The gain or loss in the ratio of Nusselt of nano fluid to that of base fluid tend to increase with increase in intensity of magnetic field and particle volume fraction

Keywords: 

double diffusive convection, magnetic field, nano fluid, and cavity

1. Introduction
2. Governing equations
3. Solution methodology
4. Results and discussion
5. Conclusion
Nomenclature
  References

Abu-Nada E., Oztop H. (2009). Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid. International Journal of Heat and Fluid Flow, Vol. 30, No. 4, pp. 669-678. http://doi.org/10.1016/j.ijheatfluidflow.2009.02.001

Akbarinia A., Behzadmehr A. (2007). Numerical study of laminar mixed convection of a nanofluid in horizontal curved tubes. Applied Thermal Engineering, Vol. 27, No. 8-9, pp. 1327-1337. http://doi.org/10.1016/j.applthermaleng.2006.10.034.

Al-Amiri A. M., Khanafar K. M., Pop I. (2007). Numerical simulation of a combined thermal mass transport in a square lid-driven cavity. International Journal of Thermal Sciences, Vol. 46, No. 7, pp. 662-671. http://doi.org/10.1016/j.ijthermalsci.2006.10.003

Alchaar S., Vasseur P., Bilgen E. (2007). Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field. ASME Journal of Heat Transfer, Vol. 117, No. 3, pp. 668-673. http://doi.org/10.1115/1.2822628

Ashorynejad H. R., Mohamad A. A., Sheikholeslami M. (2013). Magnetic field effects on natural convection flow of a nanofluid in a horizontal cylindrical annulus using Lattice Boltzmann Method. International Journal of Thermal Sciences, Vol. 64, pp. 240–250. http://doi.org/10.1016/j.ijthermalsci.2012.08.006

Beghein C., Haghighat F., Allard F. (1992). Numerical study of double-diffusive natural convection in a square cavity. International Journal of Heat and Mass Transfer, Vol. 35, No. 4, pp. 833–846. http://doi.org/10.1016/0017-9310(92)90251-M

Bourantas G., Loukopoulos V. (2014). MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid. International Journal of Heat and Mass Transfer, Vol. 79, pp. 930–944. http://doi.org/10.1016/j.ijheatmasstransfer.2014.08.075

Brinkman H. C. (1952). The viscosity of concentrated suspensions and solution. The Journal of Chemical Physics, Vol. 20, No. 4, pp. 571-581. http://doi.org/ 10.1063/1.1700493

Chamkha A. J., Al-Naser H. (2002). Hydromagnetic double-diffusive convection in a rectangular enclosure with uniform side heat mass fluxes opposing temperature concentration gradients. International Journal of Thermal Sciences, Vol. 41, pp. 936-948. http://doi.org/10.1016/S1290-0729(02)01386-8

Chamkha A. J., Al-Naser H. (2002). Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature concentration gradients. International Journal of Heat and Mass Transfer, Vol. 45, pp. 2465–2483. http://doi.org/10.1016/S0017-9310(01)00344-1

Chaves C. A., Lamas W. Q., Nunes L., Camargo J. R., Grandinetti F. J. (2015). Notes on steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous media. ASME Journal of Heat Transfer, Vol. 137, No. 7, pp. 074501-074508. http://doi.org/10.1115/1.4029878

Chen S., Tolke J., Krafczyk M. (2010). Numerical investigation of double-diffusive (natural) convection in vertical annuluses with opposing temperature concentration gradients. International Journal of Heat and Fluid Flow, Vol. 31, pp. 217–226. http://doi.org/10.1016/j.ijheatfluidflow.2009.12.013

Corcione M., Grignaffini S., Quintino A. (2015). Correlations for the double-diffusive natural convection in square enclosures induced by opposite temperature concentration gradients. International Journal of Heat and Mass Transfer, Vol. 81, pp. 811–819. http://doi.org/10.1016/j.ijheatmasstransfer.2014.11.013

Drew D. A., Passman S. L. (1999). Theory of MulticomponentFluids, Springer, http://doi.org/ 101007/b97678

Emery A. F. (1963). The effect of a magnetic field upon the free convection of a conducting fluid. ASME Journal of Heat Transfer, Vol. 85, No. 2, pp. 119-124. http://doi.org/10.1115/1.3686025

Ghasemi B., Aminossadati S. M., Raisi A. (2011). Magnetic field effect on natural convection in a nanofluid-filled square enclosure. International Journal of Thermal Sciences, Vol. 50, pp. 1748–1756. http://doi.org/10.1016/j.ijthermalsci.2011.04.010

Ghernaout B., Bouabdallah S., Benchatti A., Bessaih R. (2014). Effect of the buoyancy ratio on oscillatory double-diffusive convection in binary mixture. Numerical Heat Transfer Part A: Applications, Vol. 66, No. 8, pp. 928-946. http://doi.org/10.1080/10407782.2014.892386

Jenaa S. K., Mahapatra S. K., Sarkar A., Chamkhac A. J. (2015). Thermo-solutal buoyancy-opposed free convection of a binary Ostwald–De Waele fluid inside a cavity having partially-active vertical walls. Journal of the Taiwan Institute of Chemical Engineers, Vol. 51, pp. 9–19. http://doi.org/10.1016/j.jtice.2015.01.007

Kefayati G. H. R. (2013). Effect of a magnetic source on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann Method. International Journal of Heat and Mass Transfer, Vol. 40, pp. 67–77. http://doi.org/10.1016/j.icheatmasstransfer.2012.10.024

Kefayati G. H. R. (2016). Simulation of heat transfer and entropy generation of MHD natural convection of non-Newtonian nanofluid in an enclosure. International Journal of Heat and Mass Transfer, Vol. 92, pp. 1066–1089. http://doi.org/10.1016/j.ijheatmasstransfer.2015.09.078

Kumar D. S., Murugesan K., Gupta A. (2010). Numerical analysis of interaction between inertial and thermosolutal buoyancy forces on convective heat transfer in a lid-driven cavity. Journal of Heat Transfer, Vol. 132, No. 11, pp. 112501. http://doi.org/10.1115/1.4002029

Kumar D. S., Murugesan K., Thomas H. R. (2011). Effect of the aspect ratio of a heated block on the interaction between inertial thermosolutal buoyancy forces in a lid- driven cavity. Numerical Heat Transfer, Part A: Applications, Vol. 60, No. 7, pp. 604-628. http://doi.org/10.1080/10407782.2011.609094

Lee J. W., Hyun J. M. (1997). Double-diffusive convection in a rectangle with opposing horizontal temperature and concentration gradients. International Journal of Heat and Mass Transfer, Vol. 33, pp. 1619–1632. http://doi.org/10.1016/0017-9310(90)90018-p

Ma C. (2009). Lattice BGK simulations of double diffusive natural convection in a rectangular enclosure in the presences of magnetic field heat source. Nonlinear Anal Real World, Vol. 10, pp. 2666-2678. http://doi.org/10.1016/j.nonrwa.2008.07.006

Mahapatra T. R., Pal D., Mondal S. (2013). Effects of buoyancy ratio on double-diffusive natural convection in a lid-driven cavity. International Journal of Heat and Mass Transfer, Vol. 57, pp.771–785. http://doi.org/10.1016/j.ijheatmasstransfer.2012.10.028

Mahmoudi A., Mejri I., Abbassi M. A., Omri A. (2015). Analysis of MHD natural convection in a nanofluid-filled open cavity with non-uniform boundary condition in the presence of uniform heat generation/absorption. Powder Technology, Vol. 269, pp. 275–289. http://doi.org/10.1016/j.powtec.2014.09.022

Mahmoudi A., Mejri I., Abbassi M. A., Omri A. (2014). Analysis of the entropy generation in a nanofluid-filled cavity in the presence of magnetic field and uniform heat generation/absorption. Journal of Molecular Liquids, Vol. 198, pp. 63–77. http://doi.org/10.1016/j.molliq.2014.07.010

Maiga S. E. B., Palm S. J., Nguyen C. T., Roy G., Galanis N. (2005). Heat transfer enhancement by using nanofluids in forced convection flows. International Journal of Heat and Fluid Flow, Vol. 26, No. 4, pp. 530-546. http://doi.org/10.1016/j.ijheatfluidflow.2005.02.004

Motevasel M., Nazar A. R. S., Jamialahmadi M. (2017). Experimental investigation of turbulent flow convection heat transfer of MgO/water nanofluid at low concentrations–Prediction of aggregation effect of nanoparticles. International Journal of Heat and Technology, Vol. 35, No. 4, pp. 755-764. http://doi.org/10.18280/ijht.350409

Nazari M., Louhghalam L., Kayhani M. H. (2015). Lattice Boltzmann simulation of double diffusive natural convection in a square cavity with a hot square obstacle. Chinese Journal of Chemical Engineering, Vol. 23, pp. 22–30. http://doi.org/10.1016/j.cjche.2014.10.008

Nishimura T., Wakamatsu M., Morega A. M. (1998). Oscillatory double diffusive convection in a rectangular enclosure with combined horizontal temperature concentration gradients. International Journal of Heat and Mass Transfer, Vol. 41, pp. 1601-1611. http://doi.org/10.1016/S0017-9310(97)00271-8

Qin Q., Za, X., Tian Z. F. (2014). High accuracy numerical investigation of double-diffusive convection in a rectangular enclosure with horizontal temperature concentration Gradients. International Journal of Heat and Mass Transfer, Vol. 71, pp. 405–423. http://doi.org/10.1016/j.ijheatmasstransfer.2013.12.035

Reddy N., Murugesan K. (2017). Numerical investigations on the advantage of nano fluids under DDMC in a lid driven cavity, Wiley. Heat transfer- Asian Research, Vol. 46, No. 7, pp. 1065-1086. http://doi.org/10.1002/htj.21260

Reddy N., Murugesan K. (2017). Magnetic field influence on double diffusive natural convection in a square cavity-A numerical study. Taylor and Fransis, Numerical Heat Transfer, Vol. 71, No. 4, pp. 448-475. http://doi.org/10.1080/10407782.2016.1277922 

Reddy N., Murugesan K. (2017). Numerical study of double diffusive convection in a lid driven cavity with linearly salted side walls. Journal of Applied Fluid mechanics, Vol. 10, No. 1, pp. 69-79. http://doi.org/10.18869/acadpub.jafm.73.238.26231

Ren Q., Chan C. L. (2016). Numerical study of double-diffusive convection in a vertical cavity with Soret Dufour effects by lattice Boltzmann method on GPU. International Journal of Heat and Mass Transfer, Vol. 93, pp. 538-553. http://doi.org/10.1016/j.ijheatmasstransfer.2015.10.031

Seki M., Kawamura H., and Sanokawa K. (1979). Natural convection of mercury in a magnetic field parallel to the gravity. ASME Journal of Heat Transfer, Vol. 101, No. 2, pp. 227-232. https://doi.org/10.1115/1.3450951

Selimefendigil F., Oztop H. F. (2014). Numerical study of MHD mixed convection in a nanofluid filled lid driven square enclosure with a rotating cylinder. International Journal of Heat and Mass Transfer, Vol. 78, pp. 741–754. http://doi.org/10.1016/j.ijheatmasstransfer.2014.07.031

Sheikholeslami M., Gorji-Bandpy M., Ganji D. D. (2014). Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid. Powder Technology, Vol. 254, pp. 82-93. http://doi.org/10.1016/j.powtec.2013.12.054

Siddiqa S., Hossain M. A., Saha S. C. (2012). Double diffusive magneto-convection fluid flow in a strong cross magnetic field with uniform surface heat mass flux. ASME Journal of Heat Transfer, Vol. 134, No. 11, pp.114506-1. http://doi.org/10.1115/1.4007130

Singh P., Kumar M. (2015). Mass transfer in MHD flow of alumina water nanofluid over a flat plate under slip conditions. Alexandria Engineering Journal, Vol. 54, pp. 383-387. http://doi.org/10.1016/j.aej.2015.04.005

Sourtiji E., Gorji-Bandpy M., Ganji D. D., Seyyedi S. M. (2014). Magnetohydrodynamic buoyancy-driven heat transfer in a cylindrical–triangular annulus filled by Cu– water nanofluid using CVFEM. Journal of Molecular Liquids, Vol. 196, pp. 370–380. http://doi.org/10.1016/j.molliq.2014.04.017

Teamah M. A. (2008). Numerical simulation of double diffusive natural convection in rectangular enclosure in the presences of magnetic field heat source. International Journal of Thermal Sciences, Vol. 47, pp. 237-248. http://doi.org/10.1016/j.ijthermalsci.2007.02.003

Vasanthakumari R., Pondy P. (2018). Mixed convection of silver and titanium dioxide nanofluids along inclined stretching sheet in presence of MHD with heat generation and suction effect. Mathematical Modelling of Engineering Problems, Vol. 5, No. 2, pp. 123-129. http://doi.org/10.18280/mmep.050210

Venkatachalapa M., Younghae D., Sankar M. (2011). Effect of magnetic field on the heat mass transfer in a vertical annulus. International Journal of Engineering Science, Vol. 49, No. 3, pp. 262-278. http://doi.org/10.1016/j.ijengsci.2010.12.002

Xu B., Li B. Q., Stock D. E. (2006). An experimental study of thermally induced convection of molten gallium in magnetic fields. International Journal of Heat and Mass Transfer, Vol. 49, pp. 2009–2019. http://doi.org/10.1016/j.ijheatmasstransfer.2005.11.033