MHD Non-Newtonian Nanofluid Flow over a Permeable Stretching Sheet with Heat Generation and Velocity Slip

Authors: Rama Bhargava, Mania Goyal

Abstract:

The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.

Keywords: Viscoelastic nanofluid, partial slip, stretching sheet, heat generation/absorption, MHD flow, FEM.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1093128

References:

[1] S.U.S. Choi, "Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of Non-Newtonian flows”, FED-vol. 231/MD-vol. 66, 1995, pp. 99-105.
[2] S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, and E.A. Grulke, "Anomalously thermal conductivity enhancement in nanotube suspensions”, Appl. Phys. Lett. , vol. 79, 2001, pp. 2252-2254.
[3] H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, "Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles”, Netsu Bussei, vol. 7, 1993, pp. 227-33.
[4] J. Buongiorno, "Convective transport in nanofluids”, ASME J. Heat Transfer, vol. 128, 2006, pp. 240-250.
[5] W.A. Khan, and I. Pop, "Boundary-layer flow of a nanofluid past a stretching sheet”, Int. J. Heat Mass Transfer, vol. 53, 2010, pp. 2477-2483.
[6] A.V. Kuznetsov, and D.A. Nield, "Natural convective boundary-layer flow of a nanofluid past a vertical plate”, Int. J. Therm. Sci., vol. 49, 2010, pp. 243-247.
[7] O. Makinde , and A. Aziz, "Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition”, Int. J. Therm. Sci., vol. 50, 2011, pp. 1326-1332.
[8] P.D. McCormack, and L.J. Crane, Physical Fluid Dynamics, Academic Press, New York, 1973.
[9] P.S. Gupta, and A.S. Gupta, "Heat and mass transfer on a stretching sheet with suction or blowing”, Can. J. Chem. Eng., vol. 55, 1977, pp. 744-746.
[10] B.K. Dutta, P. Roy, and A.S. Gupta, "Temperature field in the flow over a stretching sheet with uniform heat flux”, Int. Commun. Heat Mass Transf., vol. 12, 1985, pp. 89-94.
[11] C.K. Chen, and M.I. Char, "Heat transfer of a continuous stretching surface with suction or blowing”, J. Math Anal. Appl., vol. 135, 1988, pp. 568-580.
[12] K.R. Rajagopal, T.Y. Na, and A.S. Gupta, "Flow of a viscoelastic fluid over a stretching sheet”, Rheol. Acta, vol. 23, 1984, pp. 213-221.
[13] W.D. Chang, "The non-uniqueness of the flow of a viscoelastic fluid over a stretching sheet”, Q. Appl. Math., vol. 47, 1989, pp. 365-366.
[14] C.Y. Wang, "Flow due to a stretching boundary with partial slip-an exact solution of the Navier Stokes equations”, Chem. Eng. Sci., vol. 57, 2002, pp. 3745-3747.
[15] A. Noghrehabadi, R. Pourrajab, and M. Ghalambaz, "Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature”, Int. J. Therm. Sci., vol. 54, 2012, pp. 253-261.
[16] E.M. Sparrow, and R.D. Cess, "Temperature dependent heat sources or sinks in a stagnation point flow”, Appl. Sci. Res., vol. 10, 1961, pp. 185-197.
[17] M.A. Azim, A.A. Mamun, and M.M. Rahman, "Viscous joule heating MHD-conjugate heat transfer for a vertical flat plate in the presence of heat generation”, Int. Commun. Heat Mass Transfer, vol. 37, 2010, pp. 666-74.
[18] P. Rana, and R. Bhargava, "Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids”, Commun. Nonlinear Sci. Numer. Simulat., vol. 16, 2011, pp. 4318-4334.
[19] C.Y. Wang, "Free convection on a vertical stretching surface”, J. Appl. Math. Mech., vol. 69, 1989, pp. 418-420.
[20] R.S.R. Gorla, and I. Sidawi, "Free convection on a vertical stretching surface with suction and blowing”, Appl. Sci. Res., vol. 52, 1994, pp. 247-257.