Journal of Nanoscience and Nanoengineering
Articles Information
Journal of Nanoscience and Nanoengineering, Vol.1, No.4, Dec. 2015, Pub. Date: Sep. 13, 2015
MHD Stagnation-Point Flow and Heat Transfer of Nanofluid over a Shrinking Surface
Pages: 183-192 Views: 1574 Downloads: 679
Authors
[01] Samir Kumar Nandy, Department of Mathematics, A.K.P.C Mahavidyalaya, Bengai, Hooghly, India.
[02] Rajib Kumar Mandal, Department of Physics, A.K.P.C Mahavidyalaya, Bengai, Hooghly, India.
Abstract
This paper analyzes the combined effects of magnetic field, Brownian motion, thermophoresis and thermal radiation on stagnation–point flow and heat transfer due to nanofluid towards a nonlinearly stretching/shrinking sheet. A variable magnetic field is applied normal to the sheet. Using a similarity transformation, the governing mathematical equations are transformed into coupled nonlinear ordinary differential equations which are then solved numerically using fourth order Runga–Kutta method with shooting technique. Different from a nonlinearly stretching sheet, it is found that the solutions for a nonlinearly shrinking sheet are non-unique. The numerical results pertaining to the present study indicate that the magnetic field parameter enhances the existence range of solution domain. The influences of various relevant parameters on flow, temperature and concentration as well as skin friction coefficient, local Nusselt number and local Sherwood number are investigated. A comparison with the previous study available in the literature is done and we found an excellent agreement with them.
Keywords
Stagnation-Point Flow, Heat Transfer, Nanofluid, Magnetic Field, Thermal Radiation
References
[01] S. Choi, Enhancing thermal conductivity of fluid with nanoparticles, developments and applications of non-Newtonian flow, ASMEFED, vol. 231(1995), p. 99-105.
[02] S. Das, Temperature depends on thermal conductivity enhancement for nanofluids. J. HeatTrans. 125(2003), 567-574.
[03] S. Kakac, A. Pramaumjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Trans. , 52(2009), 3187-3196.
[04] T.C. Chiam, Stagnation point flow towards a stretching plate, J. Phys Soc. Japan , 63(1994),2443-2444.
[05] T.R. Mahapatra, A.S. Gupta, Heat Transfer in Stagnation point flow towards a stretching sheet, Heat Mass Trans. 38(2002), 517-521.
[06] A. Ishak, R. Nazar, I. Pop, MHD boundary layer flow due to a moving extensible surface, J. Eng. Math, 62(2008), 23-33.
[07] A. Ishak. R. Nazan, I. Pop, Heat Transfer over a stretching surface with variable heat flux in micro polar fluids, Phys. Lett. A, 372(2008), 559-561.
[08] H. Rosali, A. Ishak, I. Pop, Stagnation point flow and heat transfer over a stretching/shrinking sheet in a porous medium, Int. Comm. Heat Mass Trans. 38(2011), 1029-1032.
[09] N.A. Yacob, A. Ishak, I. Pop, Melting Heat Transfer in boundary - layer stagnation point flow towards a stretching / shrinking sheet in a micropolar fluid, Computers and Fluids, 47(2011), 16-21.
[10] W. Ibrahim, B. Shanker, Unsteady MHD boundary layer flow and heat transfer due to a stretching sheet in the presence of heat source or sink, Computers and Fluids, 70(2012), 21-28.
[11] X.Q. Wang, A.S. Majumdar, Heat transfer Characteristics of nanofluids: a review, Int. J. Th.Sc., 46(2007), 1-9.
[12] J. Buongiorno, Convective transport in nanofluids, ASME Journal of Heat Transfer,128(2006), 240-250.
[13] D.A. Nield, A.V. Kuznetsov, The Cheng-Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a noanofluid, Int. J. Heat MassTrans., 52(2009), 5792-5795.
[14] A.V. Kuznetsov, D.A. Nield. Natural convective boundary layer flow of a nono fluid past avertical plate. Int. J. Ther. Sci., 49(2010), 243-247.
[15] N. Bachok, A. Ishak, I. Pop. Boundary layer flow of nanofluids over a moving surface in a flowing fluid. Int. J. Therm. Sci.,. 49(2010), 1663-1668.
[16] W.A. Khan, I. Pop. Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Trans., 53(2010), 2477-2483.
[17] N.A. Yacob, A. Ishak, R. Nazar, I. Pop, Falkner-Skan problem for a static and moving wedge with prescribed surface heat flux in a nanofluid, Int. Comm. Heat Mass Trans., 38(2011), 149-153.
[18] O.D. Makinde, A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, Int. J. Ther. Sci.,50(2011), 1326-1332.
[19] W. Ibrahim, B. Sankar, M.M. Nandeppanavar, MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet, Int. J. Heat Mass Trans., 56(2013), 1-9.
[20] M. Miklavčič, C.Y. Wang. Viscous flow due to a shrinking sheet. Quart. Appl. Math.,64(2006),283-290.
[21] C.Y. Wang. Stagnation flow towards a shrinking sheet. Int. J. Nonlinear Mech., 43(2008), 377-382.
[22] Y.Y. Lok, A. Ishak, I. Pop. MHD stagnation-point flow towards a shrinking sheet. Int. J. Numer. Methods Heat Fluid Flow. 21(1) (2011), 61–72.
[23] K. Bhattacharyya, S. Mukhopadhyay, G.C. Layek. Effects of suction/blowing on steady boundary layer stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation. Int. J. Heat Mass Transf. 54(2011), 302–307.
[24] K. Bhattacharyya. Dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet. Int. Commun. Heat Mass Transfer. 38(2011), 917–922.
[25] T.R. Mahapatra, S.K. Nandy, A.S. Gupta, Oblique stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation, Meccanica, 47(2012), 1325-1335.
[26] N.C. Rosca, T. Grason, I. Pop, Stagnation-point flow and mass transfer with chemical reaction past a permeable stretching/shrinking sheet in a nanofluid, Sains Malaysiana, 41(2012), 1271-1279.
[27] N. Bachok, A. Ishak, I. Pop. Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet. Int. J. Heat Mass Transfer, 55(2012), 2101-2109.
[28] A.M. Rohni, S. Ahmad, A.I. Ismail, I. Pop, Flow and heat transfer over an unsteady shrinking sheet with suction in a nanofluid using Buongiorno’s model, Int. Commun. Heat Mass Transfer. 43(2013), 75–80.
[29] S.K. Nandy, T.R. Mahapatra, Effects of slip and heat generation/absorption on MHD stagnation point flow of nanofluid past a stretching/shrinking surface, Int. J. Heat Mass Transfer, 64(2013), 1091-1100.
[30] J.A. Shercliff. A Textbook of Magnetohydrodynamics, Oxford, Pergamon Press, 1965.
[31] E.M. Sparrow, R.D. Cess, Radiation heat transfer. Hemisphere, Washington (Chaps. 7 &10), 1978.
[32] E. Magyari, A. Pantokratoras, Note on the effect of thermal radiation in the linearizedRosseland approximation on the heat transfer characteristics of various boundary layerflows. Int. Comm. HeatMass Transfer 38 (2011) 554–556.
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