Coupled systems mechanics

  • 제9권3호
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  • Pages.219-235
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  • 2020
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
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Natural convection of nanofluid flow between two vertical flat plates with imprecise parameter

  • Biswal, U. (Department of Mathematics, National Institute of Technology Rourkela) ;
  • Chakraverty, S. (Department of Mathematics, National Institute of Technology Rourkela) ;
  • Ojha, B.K. (Department of Mathematics, National Institute of Technology Rourkela)
  • 투고 : 2019.07.29
  • 심사 : 2019.12.14
  • 발행 : 2020.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

Natural convection of nanofluid flow between two vertical flat plates has been analyzed in uncertain environment.Anon-Newtonian fluid SodiumAlginate (SA) as base fluid and nanoparticles ofCopper(Cu) are taken into consideration. In thepresentstudy,we have takennanoparticle volume fraction as an uncertain parameterin terms offuzzy number. Fuzzy uncertainties are controlled by r-cut and parametric concept. Homotopy PerturbationMethod (HPM) has been used to solve the governing fuzzy coupleddifferential equationsforthe titled problem.Forvalidation, presentresults are comparedwith existingresultsforsome special casesviz. crisp case andthey are foundto be ingood agreement.

키워드

과제정보

The 1st author is thankful to the Council of Scientific and Industrial Research (CSIR), New Delhi, India for the support and funding to carry out the present research work.

참고문헌

  1. Bakar, N.A.A., Bachok, N. and Arifin, N.M. (2016), "Boundary layer flow and heat transfer in nanofluid over a stretching sheet using buongiorno model and thermophysical properties of nanoliquids", Ind. J. Sci. Technol., 9, 31.
  2. Biswal, U., Chakraverty, S. and Ojha, B. (2019), "Natural convection of non-Newtonian nanofluid flow between two vertical parallel plates", Int. J. Numer. Meth. Heat Fluid Flow, 29(6), 1984-2008. https://doi.org/10.1108/HFF-06-2018-0302.
  3. Brinkman, H.C. (1952), "The viscosity of concentrated suspensions and solutions", J. Chem. Phys., 20(4), 571-571. https://doi.org/10.1063/1.1700493.
  4. Chakraverty, S. and Nayak, S. (2012), "Fuzzy finite element method for solving uncertain heat conduction problems", Coupl. Syst. Mech., 1(4), 345-360. http://dx.doi.org/10.12989/csm.2012.1.4.345.
  5. Chakraverty, S. and Nayak, S. (2017), Neutron Diffusion: Concepts and Uncertainty Analysis for Engineers and Scientists, CRC Press, Taylor and Francis, Boca Raton, Florida.
  6. Chakraverty, S. and Perera, S. (2018), Recent Advances in Applications of Computational and Fuzzy Mathematics, Springer, Singapore.
  7. Chakraverty, S., Tapaswini, S. and Behera, D. (2016), Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications, John Wiley & Sons.
  8. Chakraverty, S., Tapaswini, S. and Behera, D. (2016), Fuzzy Differential Equations and Applications for Engineers and Scientists, CRC Press.
  9. Ellahi, R., Hassan, M. and Zeeshan, A. (2015), "Study of natural convection MHD nanofluid by means of single and multi-walled carbon nanotubes suspended in a salt-water solution", IEEE Tran. Nanotechnol., 14(4), 726-734. https://doi.org/10.1109/TNANO.2015.2435899.
  10. Garoosi, F., Jahanshaloo, L., Rashidi, M.M., Badakhsh, A. and Ali, M.E. (2015), "Numerical simulation of natural convection of the nanofluid in heat exchangers using a Buongiorno model", Appl. Math. Comput., 254, 183-203. https://doi.org/10.1016/j.amc.2014.12.116.
  11. Hanss, M. (2005), Applied Fuzzy Arithmetic: an Introduction with Engineering Applications.
  12. Hatami, M. and Ganji, D.D. (2014), "Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods", Case Stud. Therm. Eng., 2, 14-22. https://doi.org/10.1016/j.csite.2013.11.001.
  13. He, J.H. (1999), "Homotopy perturbation technique", Comput. Meth. Appl. Mech. Eng., 178(3-4), 257-262. https://doi.org/10.1016/S0045-7825(99)00018-3.
  14. He, J.H. (2005), "Application of homotopy perturbation method to nonlinear wave equations", Chaos Solit. Fract., 26(3), 695-700. https://doi.org/10.1016/j.chaos.2005.03.006.
  15. He, J.H. (2006), "Homotopy perturbation method for solving boundary value problems", Phys. Lett. A, 350(1-2), 87-88. https://doi.org/10.1016/j.physleta.2005.10.005.
  16. Karunakar, P. and Chakraverty, S. (2017), "Comparison of solutions of linear and non-linear shallow water wave equations using homotopy perturbation method", Int. J. Numer. Meth. Heat Fluid Flow, 27(9), 2015-2029. https://doi.org/10.1108/HFF-09-2016-0329.
  17. Karunakar, P. and Chakraverty, S. (2018), "2-D shallow water wave equations with fuzzy parameters", Recent Advances in Applications of Computational and Fuzzy Mathematics, Springer, Singapore.
  18. Mandal, A. and Maity, D. (2019), "Seismic analysis of dam-foundation-reservoir coupled system using direct coupling method", Coupl. Syst. Mech., 8(5), 393-414. https://doi.org/10.12989/csm.2019.8.5.393.
  19. Maxwell, J.C. (1881), A Treatise on Electricity and Magnetism, Vol. 1, Clarendon Press.
  20. Nayak, S. and Chakraverty, S. (2018), Interval finite element method with MATLAB, Academic Press.
  21. Rajagopal, K.R. and Na, T.Y. (1985), "Natural convection flow of a non-Newtonian fluid between two vertical flat plates", Acta Mechanica, 54(3-4), 239-246. https://doi.org/10.1007/BF01184849.
  22. Rao, T.D. and Chakraverty, S. (2017), "Modeling radon diffusion equation in soil pore matrix by using uncertainty based orthogonal polynomials in Galerkin's method", Coupl. Syst. Mech., 6(4), 487-499. https://doi.org/10.12989/csm.2017.6.4.487.
  23. Sheikholeslami, M. and Seyednezhad, M. (2018), "Simulation of nanofluid flow and natural convection in a porous media under the influence of electric field using CVFEM", Int. J. Heat Mass Transf., 120, 772-781. https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.087.
  24. Sus, C. and Eastman, J.A. (1995), "Enhancing thermal conductivity of fluids with nanoparticles", International Mechanical Engineering Congress and Exhibition (IMECE), San Francisco.
  25. Ziabakhsh, Z. and Domairry, G. (2009), "Analytic solution of natural convection flow of a non-Newtonian fluid between two vertical flat plates using homotopy analysis method", Commun. Nonlin. Sci. Numer. Simul., 14(5), 1868-1880. https://doi.org/10.1016/j.cnsns.2008.09.022.
  26. Ziaolhagh, S.H., Goudarzi, M. and Sani, A.A. (2016), "Free vibration analysis of gravity dam-reservoir system utilizing 21 node-33 Gauss point triangular elements", Coupl. Syst. Mech., 5(1), 59-86. https://doi.org/10.12989/csm.2016.5.1.059.