univerge site banner
Review Article | Open Access | Int. J. Mat. Math. Sci., 2020; 2(2), 29-38. | doi: 10.34104/ijmms.020.029038

MHD Free Convective Heat Transfer in a Triangular Enclosure Filled with Copper-Water Nanofluid

Tarikul Islam* Mail Img Orcid Img ,
Nahida Akter Mail Img Orcid Img ,
Nusrat Jahan Mail Img Orcid Img

Abstract

Two-dimensional time-independent free convective flow and temperature flow into a right-angled triangle shape cavity charged by Cu-H2O nanofluid has been performed. The horizontal side of the enclosure is warmed uniformly T=Th whilst the standing wall is cooled at low-temperature T=Tc and the hypotenuse of the triangular is insulated. The dimensionless non-linear governing PDEs have been solved numerically by employing the robust PDE solver the Galerkin weighted residual finite element technique. An excellent agreement is founded between the previous, and present studies. The outcomes are displayed through streamlined contours, isotherm contours, and local and average Nusselt numbers for buoyancy-driven parameter Rayleigh number, Hartmann number, and nanoparticles volume fraction. The outcomes show that the temperature flow value significantly changes for the increases of Rayleigh number, Hartmann number, and nanoparticles volume fraction. The average Nusselt number is increased for the composition of nanoparticles whereas diminishes with the increase of the Hartmann number. 

INTRODUCTION

Temperature transfer and fluid flow of nanofluids into the triangle shape enclosure have a wide applications in numerous industrial and engineering systems like heat exchangers, fire prevention, solar collectors, home ventilation systems, and refrigeration units etc.  -water,  -water, and  -water are very common nanofluids. These nanofluids are used widely for the augmentation of temperature transfer. Enhancement of warmed-up conductivity into nanofluids was studied by Choi and Eastman (1995). Manca et al. (2010) performed heat transfer in nanofluids. Influence of external magnetic field on natural convective flow into rectangle shape enclosure using warmed up and cooled neighbor walls was investigated by Ece and Buyuk (2006). Convective temperature disposal within a cavity heated partially was performed by Ozotop and Abu-Nada (2008). Free convective temperature flow value into nanofluids within an inclined was performed by Ghasemi and Aminossadati (2009). Impact of inclined angle using copper-water nanofluids within an enclosure was investigated Abu-Nada et al. (2009). Varol et al. (2007) investigated free convectional flow within a triangle shape cavity using isothermal heater. Numerical computations of FEM on convectional temperature flow into nanofluids within a rectangle shape enclosure was performed by Rahman et al. (2009). FEM numerical computations on free convection into nanofluids within a triangle shape cavity in account of both uniform and non-uniform warmed boundary condition was investigated by Basak et al. (2008). A comprehensive review on convectional flow was researched Kamiyo et al. (2010). Aydin and Yesiloz (2011) investigated usual convectional flow into a quadrantal enclosure using warmed and cooled neighbor walls. 

Magnetic field which creates an external force on the thermal and energy systems that highly attack the liquid flow and temperature flowing.  Sheikholeslami et al. (2014) researched about CuO-water nanofluid effect on convectional flow taking into account Lorentz force in flow domain. Computational study using Al2O3-water nanofluids on natural convectional flow was investigated by Rashmi et al. (2011). Bhardwaj and Dalal (2013) investigated convectional temperature flow as well as entropy generation into a right-angled shape triangle cavity. Natural convectional flow into a nanofluid using horizontal warmed plate was studied by Arani et al. (2011). Combined convectional flow and temperature flow characteristics into lid-driven square enclosure using heated blocks was investigated by Boulahia et al. (2016). Magneto hydro dynamics free convectional temperature transfer into nanofluid within isosceles triangle shape cavity was performed by Rahman et al. (2016). Convectional temperature flow into nanofluid within a triangular shape cavity was performed by Uddin et al. (2018). 

From the literature review, the principle intention is to investigate the temperature flow and fluid flow within a right-angled triangle shape cavity charged by copper-water nanofluid. The impact of Rayleigh number, volume fraction of nanoparticles and Hartmann number are performed numerically and discussed them from physical point of view.

CONCLUSION

We have investigated numerically free convectional flow as well as temperature flow of a right-angled triangle charged by cupper-water nanofluid considering with the help of Galerkin weighted residual finite element analysis. The influence of various parameter are presented using streamline contours, isotherm contours, and Nusselt number and interpreted. The following main findings are listed:

i. Rayleigh number play significant roll on flow field and temperature transfer value.

ii. The fluid flow enhances for rising Rayleigh number whereas diminishes for rising Hartmann number. 

iii. Low Hartmann number and higher Rayleigh number conform better temperature transfer value. 

iv. Additional nanoparticles significantly improves temperature flow. 

v. Average Nusselt number augments for upper Rayleigh number whereas diminishes for rising Hartmann number.

NOMENCLATURE 

magnitude of magnetic field

specific heat at constant pressure 

gravitational acceleration 

Hartmann number

thermal conductivity 

length of the enclosure

average Nusselt number

dimensional pressure

dimensionless pressure

Prandtl number

Rayleigh number

fluid temperature 

velocity component 

dimensionless velocity component 

coordinates 

 Dimension less horizontal coordinate 

Greek symbols

thermal diffusivity 

thermal expansion coefficient 

solid volume fraction

dynamic viscosity 

kinematic viscosity 

non-dimensional temperature

density 

electric conductivity 

stream function

Subscript

heat surface

cold surface

nanofluid

nanoparticle

Base fluid

ACKNOWLEDGEMENT

The author is very grateful to the editor and reviewers.

CONFLICT OF INTERESTS

The authors declare no conflict of interest.

Article References:

  1. Abu-Nada, E., and Oztop H., (2009). Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid. Int. J. Heat fluid Flow, 30, 669-678.  https://doi.org/10.1016/j.ijheatfluidflow.2009.02.001 
  2. Arani A., Mahmoodi M., and Amini M., (2011). Free convection in a nanofluid filled square cavity with horizontal heated plate. Defect und Diffusion Forum, 312-315, 433-438. https://doi.org/10.4028/www.scientific.net/DDF.312-315.433   
  3. Aydin O., and Yesiloz G., (2011). Natural convection in a quadrantal cavity heated and cooled on adjacent walls. ASME J. Heat Transfer, 133(5), 1-7.https://doi.org/10.1115/1.4003044 
  4. Basak T., Roy S., Babu S.K., and Balakrishnan A.R, (2008).  Finite element analysis of natural convection flow in an isosceles triangular enclosure due to uniform and non-uniform heating at the side walls. Int. J. Heat Mass Transfer, 51(17-18), 4496-4506.https://doi.org/10.1016/j.ijheatmasstransfer.2007.12.018  
  5. Bhardwaj S., and Dalal A., (2013). Analysis of natural convection heat transfer and entropy generation inside right-angled triangular enclosure. Int. J. Heat Mass tran., 65, 500-513.https://doi.org/10.1016/j.ijheatmasstransfer.2013.06.020 
  6. Boulahia Z., Wakif A., and Sehaqui R., (2016). Numerical investigation of mixed convection heat transfer of nanofluid in a lid-driven square cavity with three triangular heating blocks.International Journal of Computer Applications, 143(6), 0975-8887. https://doi.org/10.5120/ijca2016910227  
  7. Choi S.U.S., and Eastman J.A. (1995). Enhan-cing thermal conductivity of fluids with nanoparticles. Int. Mech. Eng. Cong. and Expo, ASME, San Francisco, USA. 196515. 
  8. Ece M.C., and E. Buyuk, (2006). Natural convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls. Fluid Dynamics. Res., 38, 564-590.https://doi.org/10.1016/j.fluiddyn.2006.04.002 
  9. Ghasemi B., and Aminossadati S.M., (2009). Natural convection heat transfer in an inclined enclosure filled with a water-Cuo nanofluid. Numer. Heat Transfer A, 55, 807-823. https://doi.org/10.1080/10407780902864623 
  10. Islam S, Islam MS, and Mandal S. (2020). One dimensional heat transfer through a uniform plane wall by using finite volume method, Aust. J. Eng. Innov. Technol., 2(2), 24-30. https://doi.org/10.34104/ajeit.020.024030 
  11. Kamiyo O.M., Angeli D., Barozzi G.S., Collins M.W., Olunloyo V.O.S., and Talabi S.O.A., (2010). Comprehensive review of natural convection in triangular enclosures.  Applied Mech. Rev., 63, 060801-13. https://doi.org/10.1115/1.4004290 
  12. Manca O., Jaluria Y., and Poulikakos D. (2010). Heat transfer in nanofluids. Advances in Mech. Eng. Art. ID 380826, 2010, Pp. 1-2. https://doi.org/10.1155/2010/380826 
  13. Oztop H.F., and Abu-Nada E. (2008). Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat F. Flow, 29, 1326-1336.https://doi.org/10.1016/j.ijheatfluidflow.2008.04.009 
  14. Rahman M.M., Alim M.A., and Mamun M.A.H., (2009). Finite element analysis of mixed convection in a rectangular cavity with a heat conducting horizontal circular cylinder. Nonlinear Anal. Model. Control, 14(2), 217-247. https://www.journals.vu.lt/nonlinear-analysis/article/view/14522/13451  
  15. Rahman M.M., Alam M.S, Al-Salti N., and Eltayeb I.A. (2016).  Hydromagnetic natural convective heat transfer flow in an isosceles triangular cavity filled with nanofluid using two component nonhomogeneous model. Int. J. of Thermal Sciences, 107, 272-288. https://doi.org/10.1016/j.ijthermalsci.2016.04.009 
  16. Rashmi W., Ismail A.F., Khalid M., and FaridahY. (2011). CFD studies on natural convection heat transfer of Al2O3-water nanofluids. Heat Mass Transfer, 47, 1301-1310.https://doi.org/10.1007/s00231-011-0792-x  
  17. Sheikholeslami M., Bandpy M.G., Ellahi R., and Zeeshan A. (2014). Simulation of MHD CuO-water nanofluid flow and convective heat transfer considering Lorentz forces. J Magn. Magn. Mater., 369, 69-80. https://doi.org/10.1016/j.jmmm.2014.06.017 
  18. Yesiloz G., and Aydin O. (2013). Laminar natural convection in right-angled triangular enclosures heated and cooled on adjacent walls. International Journal of Heat and Mass Transfer, 60, 365-374. https://doi.org/10.1016/j.ijheatmasstransfer.2013.01.009 
  19. Uddin M.J., and Hoque A.F., (2018). Convective heat transfer flow of nanofluid in an isosceles triangular shaped enclosure with an uneven bottom wall. Chemical Engineering Transactions, 66, 403-408. https://doi.org/10.3303/CET1866068 
  20. Varol Y., Oztop H.F., and Yilmaz T., (2007). Natural convection in triangular enclosures with protruding isothermal heater. Int. J. Heat Mass Transfer, 50(13-14), 2451-2462.https://doi.org/10.1016/j.ijheatmasstransfer.2006.12.027 
  21. Zienkiewicz O.C., and Taylor R.L., (1991). The finite element method. 4th ed. McGraw-Hill. https://trove.nla.gov.au/version/40313901  

Article Info:

Academic Editor

Dr. Toansakul Tony Santiboon, Professor, Curtin University of Technology, Bentley, Australia.

Received

March 11, 2020

Accepted

April 22, 2020

Published

April 29, 2020

Article DOI: 10.34104/ijmms.020.029038

Corresponding author

Tarikul Islam*

Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, Bangladesh

Cite this article

Islam T., Akter N., and Jahan N. (2020). MHD free convective heat transfer in a triangular enclosure filled with Copper-water nanofluid, Int. J. Mat. Math. Sci., 2(2), 29-38. https://doi.org/10.34104/ijmms.020.029038 

Views
448
Download
1254
Citations
Badge Img
Share