Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling
Applied and Computational Mathematics
Volume 3, Issue 3, June 2014, Pages: 75-84
Received: May 13, 2014; Accepted: May 27, 2014; Published: May 30, 2014
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Sara Khamis, Nelson Mandela African Institution of Science and Technology (NM-AIST), P. O. Box 447, Arusha, Tanzania
Oluwole Daniel Makinde, Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa
Yaw Nkansah-Gyekye, Nelson Mandela African Institution of Science and Technology (NM-AIST), P. O. Box 447, Arusha, Tanzania
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In this paper, the combined effects of variable viscosity, Brownian motion, thermophoresis and convective cooling on unsteady flow of nanofluids in a pipe with permeable wall are investigated. It is assumed that the pipe surface exchange heat with the ambient following the Newton’s law of cooling. Using a semi discretization finite difference method coupled with Runge-Kutta Fehlberg integration scheme, the nonlinear governing equations of momentum and energy balance, and the equation for nanoparticles concentration are tackled numerically. Useful results for the velocity, temperature, nanoparticles concentration profiles, skin friction and Nusselt number are obtained graphically and discussed quantitatively.
Porous Pipe Flow, Variable Viscosity, Nanofluids, Heat Transfer, Convective Cooling
To cite this article
Sara Khamis, Oluwole Daniel Makinde, Yaw Nkansah-Gyekye, Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling, Applied and Computational Mathematics. Vol. 3, No. 3, 2014, pp. 75-84. doi: 10.11648/j.acm.20140303.12
Karode, S. K., (2001), Laminar flow in channels with porous walls, J. Membr. Sci., 191, pp. 237–241.
Oxarango, L., Schmitz,. P., Quintard, M., (2004), Laminar flow in channels with wall suction or injection: a new model to study multi-channel filtration systems, Chem. Eng. Sci., 59, pp. 1039–1051.
Moussy, Y., Snider, A. D., (2009), Laminar flow over pipes with injec-tion and suction through the porous wall at low Reynolds number, J. Membr. Sci., 327, pp. 104–107.
Erdoğan , M. E., Imrak, C. E.,(2008), On the flow in a uniformly porous pipe, Int. J. Non-Linear Mech., 43, pp. 292–301.
Tsangaris, S. Kondaxakis, D., Vlachakis, N.W., (2007), Exact solution for flow in a porous pipe with unsteady wall suction and/or injection, Comm. Nonlinear Sci. Num. Simul., 12, pp. 1181–1189.
Mutuku-Njane, W. N., Makinde, O. D., (2014), Hydromagnetic bioconvection of nanofluid over a permeable vertical plate due to gy-rotactic microorganisms, Comp. Fluids, 95, pp. 88–97.
Theuri, D., Makinde, O. D., (2014), Thermodynamic analysis of variable viscosity MHD unsteady generalized Couette flow with per-meable walls, Appl. Computational Math., 3, 1-8.
Kaufui, V. W., Omar, D. L.(2003), Appli-cations of nanofluids: current and future, Adv. Mech. Eng. , 11 pp.
Xuan, Y. Li, Q., (2003), Investigation on convective heat transfer and flow features of nanofluids, J. Heat Transf., 125, pp. 151–155.
Buongiorno, J., (2006), Convective transport in nanofluids, J. Heat Transfer., 128, pp. 240-250.
Mutuku-Njane, W. N., Makinde, O. D., (2014), MHD nanofluid flow over a permeable vertical plate with convective heating, J. Compl Theor. Nanoscience, 3, pp. 667-675.
Olanrewaju, M., Makinde,. O. D., (2013) On boundary layer stagnation point flow of a nanofluid over a permeable flat surface with Newtonian heating, Chem. Eng. Comm., pp. 200 836-852.
Makinde, O. D., (2013), Effects of viscous dissipation and New-tonian heating on boundary layer flow of nanofluids over a flat plate, Int. J. Num. Meth. Heat and Fluid flow 23, pp. 1291-1303.
Makinde, O. D., Khamis, S. A., Tshehla, M. S., Franks, O. (2014), Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipa-tion, and Convective Cooling, Adv. Math. Phys., 2014, 13 pages.
Makinde, O. D., (2013), Computational modelling of nanofluids flow over a convectively heated unsteady stretching sheet, Curr. Nanoscience, 9, pp. 673-678.
Oztop, H. F., Abu-Nada, E., (2008), Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow. 29, pp. 1326–1336.
Kakac¸ S., Pramuanjaroenkij, A., (2009), Review of convec-tive heat transfer enhancement with nanofluids, Int. J. Heat Mass Transf., 52, pp. 3187–3196.
Makinde, O. D., (2009), Hermite–Pade approach to thermal radiation effect on inherent irreversibility in a variable viscosity channel flow, Comp. Math. Appl., 58, pp. 2330-2338.
Kuppalapalle, V., Kerehalli, P. V., Chiu-on, NG., (2013), The effect of variable viscosity on the flow and heat transfer of a viscous Ag-water and Cu-water nanofluids, J. Hydro., 25, 8 pages.
Makinde, O. D., (2012), Effects of variable viscosity on thermal boundary layer over a permeable flat plate with radiation and convective surface boundary condition. J. Mech. Science Tech., 26, pp. 1615-1622.
Na, T. Y. (1979), Computational methods in en-gineering boundary value problems, Academic press, New York.
Klemp K., Herwig H., Selmann M.,(1990), Entrance flow in channel with temperature dependent viscosity including viscous dissipation effects. Proc. Third Int. Cong. Fluid Mech., Proc. Third Int. Cong. Fluid Mech., Cairo, Egypt, 3, p. 1257.
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