Abstract
The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a nanofluid under the effect of heat generation and partial slip is simulated using numeric symbolic approach. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDEs are transformed into a set of ODEs with the help of transformations. The differential equations are solved by variational finite element method as well as hybrid approach. The results obtained by the two approaches match well. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The comparison confirms excellent agreement. The efficiency of the hybrid approach is demonstrated through a table. 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.
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References
Kaminski, M.: On semi-analytical probabilistic finite element method for homogenization of the periodic fiber-reinforced composites. Int. J. Numer. Meth. Eng. 86, 1144–1162 (2011)
Alns, M.S., Mardal, K.: On the efficiency of symbolic computations combined with code generation for finite element methods. ACM Trans. Math. Softw. 37, 1–26 (2010)
Griffiths, D., Huang, J., Schiermeyer, R.P.: Elastic stiffness of straight-sided triangular finite elements by analytical and numerical integration. Commun. Numer. Meth. Eng. 25, 247–262 (2009)
Videla, L., Baloa, T., Griffiths, D., Cerrolaza, M.: Exact integration of an 8-node plane elastic finite element by symbolic computation. Numer. Meth. Part. Diff. Eqns. 24, 249–261 (2008)
Eyhermandy, D., Saad, R.: A dynamic approach for automating finite element code development. In: 11th World Congress on Computational Mechanics (WCCM XI), July 20–25, 2014. Spain, Barcelona (2014)
Choi, S.: Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of Non-Newtonian flows. ASME FED 231/MD 66, 99–105 (1995)
Choi, S., Zhang, Z., Yu, W., Lockwood, F., Grulke, E.: Anomalously thermal conductivity enhancement in nanotube suspensions. Appl. Phys. Lett. 79, 2252–2254 (2001)
Masuda, H., Ebata, A., Teramae, K., Hishinuma, N.: Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7, 227–33 (1993)
Buongiorno, J.: Convective transport in nanofluids. ASME J. Heat Transf. 128, 240–250 (2006)
Khan, W., Pop, I.: Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transf. 53, 2477–2483 (2010)
Kuznetsov, A., Nield, D.: Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int. J. Therm. Sci. 49, 243–247 (2010)
Makinde, O., Aziz, A.: Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int. J. Therm. Sci. 50, 1326–1332 (2011)
McCormack, P., Crane, L.: Physical Fluid Dynamics. Academic Press, New York (1973)
Gupta, P., Gupta, A.: Heat and mass transfer on a stretching sheet with suction or blowing. Can. J. Chem. Eng. 55, 744–746 (1977)
Dutta, B., Roy, P., Gupta, A.: Temperature field in the flow over a stretching sheet with uniform heat flux. Int. Commun. Heat Mass Transf. 12, 89–94 (1985)
Chen, C., Char, M.: Heat transfer of a continuous stretching surface with suction or blowing. J. Math Anal. Appl. 135, 568–580 (1988)
Rajagopal, K., Na, T., Gupta, A.: Flow of a viscoelastic fluid over a stretching sheet. Rheol. Acta 23, 213–221 (1984)
Chang, W.: The non-uniqueness of the flow of a viscoelastic fluid over a stretching sheet. Q. Appl. Math. 47, 365–366 (1989)
Wang, C.: Flow due to a stretching boundary with partial slip-an exact solution of the Navier Stokes equations. Chem. Eng. Sci. 57, 3745–3747 (2002)
Sparrow, E., Cess, R.: Temperature dependent heat sources or sinks in a stagnation point flow. Appl. Sci. Res. 10, 185–197 (1961)
Azim, M., Mamun, A., Rahman, M.: Viscous joule heating MHD-conjugate heat transfer for a vertical flat plate in the presence of heat generation. Int. Commun. Heat Mass Transfer 37, 666–74 (2010)
Rana, P., Bhargava, R.: 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. 16, 4318–4334 (2011)
Noghrehabadi, A., Pourrajab, R., Ghalambaz, M.: 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. 54, 253–261 (2012)
Wang, C.: Free convection on a vertical stretching surface. J. Appl. Math. Mech. 69, 418–4334 (1989)
Gorla, R., Sidawi, I.: Free convection on a vertical stretching surface with suction and blowing. Appl. Sci. Res. 52, 247–257 (1994)
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Authors 1 and 3 are thankful to SERB, DST for providing financial support for completing this paper under the project sponsored by them.
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Bhargava, R., Goyal, M., Pratibha (2015). An Efficient Hybrid Approach for Simulating MHD Nanofluid Flow over a Permeable Stretching Sheet. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_56
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DOI: https://doi.org/10.1007/978-81-322-2485-3_56
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