Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

The problem of laminar fluid flow which results from
the shrinking of a permeable surface in a nanofluid has been
investigated numerically. The model used for the nanofluid
incorporates the effects of Brownian motion and thermophoresis. A
similarity solution is presented which depends on the mass suction
parameter S, Prandtl number Pr, Lewis number Le, Brownian motion
number Nb and thermophoresis number Nt. It was found that the
reduced Nusselt number is decreasing function of each dimensionless
number.





References:
[1] 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, pp. 1325-1335, 2012.
[2] C.Y. Wang, "Liquid film on an unsteady stretching sheet,” Quart. Appl.
Math., 48, pp. 601-610, 1990.
[3] M. Miklavčič, C.Y. Wang, "Viscous flow due to a shrinking sheet,”
Quart Appl Math, 64, pp. 283–290, 2006.
[4] C.Y. Wang, "Stagnation flow towards a shrinking sheet,” Int. J. of Non-
Lin. Mech., 43, pp. 377-382, 2008.
[5] T-G. Fang, J. Zhang, S-S. Yao, "Viscous flow over an unsteady
shrinking sheet with mass transfer,” Chin Phys Lett, 26, pp. 014703,
2009.
[6] K. Bhattacharyya, "Boundary Layer Flow and Heat Transfer over an
exponentially shrinking sheet,” Chin. Phys. Lett., 28, pp. 074701, 2011.
[7] S.U.S. Choi, "Enhancing thermal conductivity of fluids with
nanoparticle,” ASME FED, 66, pp. 99-10, 1995.
[8] R.K. Tiwari, M.K. Das, "Heat transfer augmentation in a two-sided liddriven
differentlially heated cavity utilizing nanofluids,” Int. J. Heat
Mass Transf., 50, pp. 2002-2018, 2007.
[9] J. Buongiorno, "Convective transport in nanofluids,” ASME J. Heat
Transf., 128, pp. 240-250, 2006.
[10] N.M.D. Arifin, R. Nazar, I. Pop, "Viscous flow due to a permeable
stretching/shrinking sheet in a nanofluid,” Sains Malaysia, 40, pp. 1359-
1367, 2011.
[11] N. Bachok, A. Ishak, I. Pop, Stagnation-point flow over a
stretching/shrinking sheet in a nanofluid, Nanoscale Research Letters, 6,
2011, pp. 623-632.
[12] N. Bachok, A. Ishak, I. Pop, "Stagnation-point flow over a permeable
stretching/shrinking sheet in a copper-water nanofluid,” Boundary Value
Prob, 39, pp. 1-10, 2013.
[13] N. Bachok, A. Ishak, I. Pop, "Boundary layer stagnation-point flow and
heat transfer over an exponentially stretching/shrinking sheet in a
nanofluid,” Int. J. Heat Mass Transf., 55, pp. 8122-8128, 2012.
[14] A.M. Rohni, S. Ahmad, A.I M.D. Ismail, I. Pop, "Flow over an unsteady
shrinking sheet with suction in a nanofluid,” Int. J. of Modern Phys., 9,
pp. 512-519, 2012.
[15] P.K Kameswaran, M. Narayana, P. Sibanda, P.V.S.N. Murthy,
"Hydromagnetic nanofluid flow due to a stretching or shrinking sheet
with viscous dissipation and chemical reaction effects,” Int. J. Heat
Mass Transf., 55, pp. 7587-7595, 2012.
[16] M.K. Das, "Nanofluid flow over a shrinking sheet with surface slip,”
Microfluid Nanofluid, 16, pp. 391-401, 2014.
[17] D.A. Nield and A.V. Kuznetsov, "The Cheng-Minkowycz problem for
natural convective boundary layer flow in a porous medium saturated by
a nanofluid,” Int. J. Heat Mass Transfer, 52, pp. 3187-3196, 2009.
[18] D.A. Nield and A.V. Kuznetsov, "The Cheng-Minkowycz problem for
the double-diffusive natural convective boundary layer flow in a porous
medium saturated by a nanofluid,” Int. J. Heat Mass Transfer, 54, pp.
374-378, 2011.
[19] A.V. Kuznetsov and D.A. Nield, "Natural convective boundary layer
flow of a nanofluid past a vertical plate,” Int. J. Thermal Sci., 49, pp.
243-247, 2010.
[20] A.V. Kuznetsov and D.A. Nield, "Dounle-diffusive natural convective
boundary layer flow of a nanofluid past a vertical plate,” Int. J. Thermal
Sci., 50, pp. 712-717, 2011.
[21] A.V. Khan, I. Pop, "Boundary layer flow of a nanofluid past a stretching
sheet,” Int. J. Heat Mass Transf., 53, pp. 2477-2483, 2010.
[22] N. Bachok, A. Ishak, I. Pop, "Boundary layer flow of nanofluid over a
moving surface in a flowing fluid,” Int J Therm Sci, 49, pp. 1663-1668,
2010.
[23] N. Bachok, A. Ishak, I. Pop, "Unsteady boundary layer flow of a
nanofluid over a permeable stretching/shrinking sheet,” Int. J. Heat
Mass Transf., 55, pp. 2102-2109, 2012.
[24] W.A. Khan and A. Aziz, "Natural convection flow of a nanofluid over a
vertical plate with uniform surface heat flux,” Int. J. Thermal Sci, 50, pp.
1207-1214, 2011.
[25] S. Nadeem, C. Lee, "Boundary layer flow of a nanofluid over an
exponentially stretching surface,” Boundary Value Prob, 7, pp. 94-99,
2012.