Dual solutions of nanaofluid forced convective flow with heat transfer and porous media past a moving surface. (English) Zbl 07531192
Summary: The paper presents a numerical study to explore the possible similarity solutions as well as dual branch solutions to study the performance evaluation of various nanoparticles associated water as the base fluid in the case of steady two-dimensional forced convection boundary layer flow through a moving flat porous plate under external magnetic fields. We considered water as a base fluid embedded with the three different types of nanoparticles namely copper (Cu), alumina (\(\mathrm{Al_2O}_3\)) and titania (\(\mathrm{TiO}_2\)). The governing equations are simplified by similarity approach. The resulting equations are solved numerically and the numerical results are explored through graphs and tables and discussed in detail. The influences of problem parameters are discussed for the steady solution. The paper extends results of previous works by others authors contributing to increase the scientific knowledge on the subject. The skin friction coefficient and local Nusselt number on the plane are studied as functions of the problem parameters. The study reveals that the problem considered admits of upper and lower branch solutions for moving parameter \(\lambda\), magnetic parameter \(M\), the power law parameter \(n\), convection heat transfer \(b\) and nanoparticle volume fraction parameter \(\phi\).
MSC:
| 82-XX | Statistical mechanics, structure of matter |
References:
| [1] | P.M. Congedo, S. Collura, P.M. Congedo, Modeling and analysis of natural convection heat transfer in nanofluids, in: Proc. ASME Summer Heat Transfer Conf. Vol. 3, 2009, pp. 569-579. |
| [2] | Ghasemi, B.; Aminossadati, S. M., Natural convection heat transfer in an inclined enclosure filled with a water cuo nanofluid, Numer. Heat Transfer A, 55, 807-823 (2009) |
| [3] | Ho, C. J.; Chen, M. W.; Li, Z. W., Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity, Int. J. Heat Mass Transfer, 51, 4506-4516 (2008) · Zbl 1144.80317 |
| [4] | C.J. Ho, M.W. Chen, Z.W. Li, Effect on natural convection heat transfer of nanofluid in an enclosure due to uncertainties of viscosity and thermal conductivity, in: Proc. ASME/JSME Thermal Engng. Summer Heat Transfer Conf. HT Vol. 1 2007, pp. 833-841. |
| [5] | Hamad, M. A.A.; Pop, I.; Ismail, A. I., Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate, Nonlinear Anal. RWA, 12, 1338-1346 (2011) · Zbl 1402.76155 |
| [6] | Buongiorno, J., Convective transport in nanofluids, ASME J. Heat Transfer, 128, 240-250 (2006) |
| [7] | Hamad, M. A.A.; Pop, I., Scaling transformations for boundary layer flow near the stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects, Transp. Porous Media, 87, 25-39 (2011) |
| [8] | Hamad, M. A.A., Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field, Int. Comm. Heat Mass Transfer, 38, 487-492 (2011) |
| [9] | Khan, W. A.; Pop, I., Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat Mass Transfer, 53, 2477-2483 (2010) · Zbl 1190.80017 |
| [10] | Abu-Nada, E.; Chamkha, A. J., Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO-EG-water nanofluid, Int. J. Therm. Sci., 49, 2339-2352 (2010) |
| [11] | Teng, T. P.; Hung, Y. H.; Teng, T. C.; Mo, E. E.; Hsu, H. G., The effect of alumina/water nanofluid particle size on thermal conductivity, Appl. Therm. Eng., 30, 2213-2218 (2010) |
| [12] | Ho, C. J.; Liu, W. K.; Chang, Y. S.; Lin, C. C., Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study, Int. J. Therm. Sci., 49, 1345-1353 (2010) |
| [13] | Das, S. K.; Choi, S. U.S.; Yu, W.; Pradeep, T., Nanofluids: Science and Technology (2007), Wiley: Wiley New Jersey |
| [14] | Wang, X.-Q.; Mujumdar, A. S., Heat transfer characteristics of nanofluids: a review, Int. J. Therm. Sci., 46, 1-19 (2007) |
| [15] | Wang, X.-Q.; Mujumdar, A. S., A review on nanofluids - part I: theoretical and numerical investigations, Braz. J. Chem. Eng., 25, 613 (2008) |
| [16] | Wang, X.-Q.; Mujumdar, A. S., Heat transfer characteristics of nanofluids: A review, Int. J. Therm. Sci., 46, 1-19 (2007) |
| [17] | Kakaç, S.; Pramuanjaroenkij, A., Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transfer, 52, 3187-3196 (2009) · Zbl 1167.80338 |
| [18] | Yoo, J. S., Dual steady solutions in natural convection between horizontal concentric cylinders, Int. J. Heat Fluid Flow, 17, 587-593 (1996) |
| [19] | Xu, H.; Liao, S. J., Dual solutions of boundary layer flow over an upstream moving plate, Commun. Nonlinear Sci. Numer. Simul., 13, 350-358 (2008) · Zbl 1131.35066 |
| [20] | Bachok, N.; Ishak, A.; Pop, I., Boundary-layer flow of nanofluids over a moving surface in a flowing fluid, Int. J. Therm. Sci., 49, 1663-1668 (2010) |
| [21] | Ahmad, S.; Pop, I., Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids, Int. Commun. Heat Mass Transfer, 37, 987-991 (2010) |
| [22] | Uddin, M. J.; Khan, W. A.; Ismail, A. I., MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition, PLoS One, 7, Article e49499 pp. (2012) |
| [23] | Ali, M. E., The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface, Int. J. Therm. Sci., 45, 60-69 (2006) |
| [24] | Ishak, A.; Nazar, R.; Pop, I., Magnetohydrodynamic (MHD) flow of a micropolar fluid towards a stagnation point on a vertical surface, Comput. Math. Appl., 56, 3188-3194 (2008) · Zbl 1165.76309 |
| [25] | Abdel-wahed, Mohamed; Emam, Tarek, MHD boundary layer behaviour over a moving surface in a nanofluid under the influence of convective boundary conditions, J. Mech. Eng., 63, 119-128 (2017) |
| [26] | Ishak, A.; Nazar, R.; Pop, I., Boundary layer on a moving wall with suction and injection, Chin. Phys. Lett., 8, 2274 (2007) |
| [27] | Magyari, E., The moving plate thermometer, Int. J. Therm. Sci., 47, 1436-1441 (2008) |
| [28] | Merkin, J. H., A note on the solution of a differential equation arising in boundary-layer theory, J. Engrg. Math., 18, 31-36 (1984) · Zbl 0532.76038 |
| [29] | Ishaq, Mohammad; Shah, Syed Inayat Ali; Ali, Gohar; Khan, Hamid; Muhammad, Sher; Hussain, Syed Asif, Radiative thin film flow of incompressible eyring powell nanofluid with magnetohydrodynamics and variable heat transfer on porous stretching sheet, J. Nanofluids, 8, 1213-1221 (2019) |
| [30] | Hoernel, J. D., On the similarity solutions for a steady MHD equation, Commun. Nonlinear Sci. Numer. Simul., 13, 1353-1360 (2008) · Zbl 1221.76222 |
| [31] | Pal, D.; Mondal, H., Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge, Appl. Math. Comput., 212, 194-208 (2008) · Zbl 1200.76172 |
| [32] | Ziabakhsh, Z.; Domairry, G.; Ghazizadeh, H. R., Analytical solution of the stagnation-point flow in a porous medium by using the homotopy analysis method, J. Taiwan Inst. Chem. Eng., 40, 91-97 (2009) |
| [33] | Ziabakhsh, Z.; Domairry, G.; Bararnia, H.; Babazadeh, H., Analytical solution of flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium, J. Taiwan Inst. Chem. Eng., 41, 22-28 (2010) |
| [34] | Aziz, A., A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Commun. Nonlinear Sci. Numer. Simul., 14, 1064-1068 (2009) |
| [35] | Magyari, E., Comment on a similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition by A. Aziz, Commun. Nonlinear Sci. Numer. Simul.. Commun. Nonlinear Sci. Numer. Simul., Commun. Nonlinear Sci. Numer. Simul., 16, 599-601-1068 (2011) |
| [36] | Tiwari, R. K.; Das, M. K., Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer, 50, 2002-2018 (2007) · Zbl 1124.80371 |
| [37] | Schlichting, H.; Gersten, K., Boundary Layer Theory (2000), Springer: Springer NewYork · Zbl 0940.76003 |
| [38] | Oztop, H. F.; Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow, 29, 1326-1336 (2008) |
| [39] | Ishak, A., Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition, Appl. Math. Comput., 217, 837-842 (2010) · Zbl 1432.76090 |
| [40] | Afzal, N., Falkner-Skan equation for flow past a stretching surface with suction or blowing: analytical solutionsappl, Math. Comp., 217, 2724-2736 (2010) · Zbl 1342.76042 |
| [41] | Weidman, P. D.; Kubitschek, D. G.; Davis, A. M.J., The effect of transpiration on self-similar boundary layer flow over moving surfaces, Internat. J. Engrg. Sci., 44, 730-737 (2006) · Zbl 1213.76064 |
| [42] | Merrill, K.; Beauchesne, M.; Previte, J.; Paullet, J.; Weidman, P., Final steady flow near a stagnation point on a vertical surface in a porous medium, Int. J. Heat Mass Transfer, 49, 4681-4686 (2006) · Zbl 1121.76411 |
| [43] | Harris, S. D.; Ingham, D. B.; Pop, I., Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip, Transp. Porous Media, 77, 267-285 (2009) |
| [44] | Postelnicu, A.; Pop, I., Falkner-Skan boundary layer flow of a power-law fluid past a stretching wedge, Appl. Math. Comput., 217, 4359-4368 (2011) · Zbl 1416.76011 |
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