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Exact analytical solution for suction and injection flow with thermal enhancement of five nanofluids over an isothermal stretching sheet with effect of the slip model: a comparative study. (English) Zbl 1470.76031

Summary: We introduced a direct and effective approach to obtain the exact analytical solution for the nanoparticles-water flow over an isothermal stretching sheet with the effect of the slip model. In particular, we examined and compared the effect of the existence of five metallic and nonmetallic nanoparticles, namely, Silver, Copper, Alumina, Titania, and Silicon Dioxide, in a base of water. The most interesting physical parameters were then discussed in the presence of no-slip model, first order slip, and second order slip parameters. It is found that, with no-slip effect, the present exact solutions are in a very good agreement with the previous published results. On the other hand, with the effect of the slip model, increase in the nanoparticle volume friction decreases the velocity for the high density of nanoparticles, increases it for the low density of them, and increases the temperature for all investigated nanoparticles. Further, increase in the wall mass decreases the velocity and temperature; however, it increases the local skin friction. Furthermore, increase in the slips slows down the velocity, increases the temperature with an impressive effect in the injection case, and decreases the local skin friction and the reduced Nusselt number. It was also demonstrated that, as the nanoparticle becomes heavier, this results in increase and decrease in reduced skin friction coefficient and reduced Nusselt number, respectively, with significant effect in the presence of the second slip. Finally, Silver is the suitable nanoparticle if slowing down the velocity and increasing the temperature are needed; Silicon Dioxide is the appropriate nanoparticle if different behavior is to be considered.

MSC:

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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[1] Metal, T.; Oh, S.; Gegel, H., Metal Forming Fundamentals and Applications, (1979), Metals Park, Ohio, USA: American Society of Metals, Metals Park, Ohio, USA
[2] Karwe, M. V.; Jaluria, Y., Numerical simulation of thermal transport associated with a continuously moving flat sheet in materials processing, Journal of Heat Transfer, 113, 3, 612-619, (1991)
[3] Sakiadis, B. C., Boundary layer behaviour on continuous solid surfaces—I. Boundary layer equations for two-dimensional and axisymmetric flow, AIChE Journal, 7, 26-28, (1961)
[4] Sakiadis, B. C., Boundary layer behaviour on continuous solid surfaces—II. The boundary layer on a continuous flat surface, AIChE Journal, 7, 221-225, (1961)
[5] Crane, L. J., Flow past a stretching plate, Zeitschrift für Angewandte Mathematik und Physik, 21, 4, 645-647, (1970)
[6] Yoshimura, A.; Prud’homme, R. K., Wall slip corrections for Couette and parallel disk viscometers, Journal of Rheology, 32, 1, 53-67, (1988)
[7] Gad-el-Hak, M., Fluid mechanics of microdevices-the freeman scholar lecture, Journal of Fluids Engineering, Transactions of the ASME, 121, 1, 5-33, (1999)
[8] Wang, X.-Q.; Mujumdar, A. S., Heat transfer characteristics of nanofluids: a review, International Journal of Thermal Sciences, 46, 1, 1-19, (2007)
[9] Wang, X.-Q.; Mujumdar, A. S., A review on nanofluids—part II: experiments and applications, Brazilian Journal of Chemical Engineering, 25, 4, 631-648, (2008)
[10] Saidur, R.; Leong, K. Y.; Mohammad, H. A., A review on applications and challenges of nanofluids, Renewable and Sustainable Energy Reviews, 15, 3, 1646-1668, (2011)
[11] Choi, S. U. S., Enhancing thermal conductivity of fluids with nanoparticles, Developments and Applications of Non-Newtonian Flows, 66, 99-105, (1995)
[12] Eastman, J. A.; Choi, S. U. S.; Li, S.; Yu, W.; Thompson, L. J., Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, Applied Physics Letters, 78, 6, 718-720, (2001)
[13] Xuan, Y.; Li, Q., Investigation on convective heat transfer and flow features of nanofluids, Journal of Heat Transfer, 125, 1, 151-155, (2003)
[14] Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. J., Nanoscale hydrodynamics: enhanced flow in carbon nanotubes, Nature, 438, 7064, article 44, (2005)
[15] 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, International Journal of Thermal Sciences, 54, 253-261, (2012)
[16] Khan, W. A.; Pop, I., Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer, 53, 11-12, 2477-2483, (2010) · Zbl 1190.80017
[17] Nandeppanavar, M. M.; Vajravelu, K.; Abel, M. S.; Siddalingappa, M. N., Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition, International Journal of Thermal Sciences, 58, 143-150, (2012)
[18] Fang, T.; Yao, S.; Zhang, J.; Aziz, A., Viscous flow over a shrinking sheet with a second order slip flow model, Communications in Nonlinear Science and Numerical Simulation, 15, 7, 1831-1842, (2010) · Zbl 1222.76028
[19] Turkyilmazoglu, M., Heat and mass transfer of MHD second order slip flow, Computers & Fluids, 71, 426-434, (2013) · Zbl 1365.76349
[20] Roşca, A. V.; Pop, I., Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip, International Journal of Heat and Mass Transfer, 60, 355-364, (2013)
[21] Yacob, N. A.; Ishak, A.; Pop, I.; Vajravelu, K., Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid, Nanoscale Research Letters, 6, 314-321, (2011)
[22] Hamad, M. A. A., Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field, International Communications in Heat and Mass Transfer, 38, 4, 487-492, (2011)
[23] Noghrehabadi, A.; Ghalambaz, M.; Ghalambaz, M.; Ghanbarzadeh, A., Comparing thermal enhancement of Ag-water and SiO_{2}-water nanofluids over an isothermal stretching sheet with suction or injection, Journal of Computational and Applied Research in Mechanical Engineering, 2, 35-47, (2012)
[24] Vajravelu, K.; Prasad, K. V.; Ng, C.-O., The effect of variable viscosity on the flow and heat transfer of a viscous Ag-water and Cu-water nanofluids, Journal of Hydrodynamics, 25, 1-9, (2013)
[25] Wang, C. Y., Free convection on a vertical stretching surface, Journal of Applied Mathematics and Mechanics, 69, 418-420, (1989) · Zbl 0698.76092
[26] Reddy Gorla, R. S.; Sidawi, I., Free convection on a vertical stretching surface with suction and blowing, Applied Scientific Research, 52, 3, 247-257, (1994) · Zbl 0800.76421
[27] Oztop, H. F.; Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29, 5, 1326-1336, (2008)
[28] Khanafer, K.; Vafai, K.; Lightstone, M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer, 46, 19, 3639-3653, (2003) · Zbl 1042.76586
[29] Khanafer, K.; Vafai, K., A critical synthesis of thermophysical characteristics of nanofluids, International Journal of Heat and Mass Transfer, 54, 19-20, 4410-4428, (2011) · Zbl 1227.80022
[30] Wu, L., A slip model for rarefied gas flows at arbitrary Knudsen number, Applied Physics Letters, 93, 25, (2008)
[31] Vajravelu, K.; Prasad, K. V.; Lee, J.; Lee, C.; Pop, I.; Van Gorder, R. A., Convective heat transfer in the flow of viscous Ag-water and Cu-water nanofluids over a stretching surface, International Journal of Thermal Sciences, 50, 5, 843-851, (2011)
[32] Wang, C. Y., Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear Analysis. Real World Applications, 10, 1, 375-380, (2009) · Zbl 1154.76330
[33] Aly, E. H.; Ebaid, A., On the exact analytical and numerical solutions of nano boundary-layer fluid flows, Abstract and Applied Analysis, 2012, (2012) · Zbl 1253.76089
[34] Aly, E. H.; Ebaid, A., New exact solutions for boundary-layer flow of a nanofluid past a stretching sheet, Journal of Computational and Theoretical Nanoscience, 10, 2591-2595, (2013)
[35] Van Gorder, R. A.; Sweet, E.; Vajravelu, K., Nano boundary layers over stretching surfaces, Communications in Nonlinear Science and Numerical Simulation, 15, 6, 1494-1500, (2010) · Zbl 1221.76024
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