Flow and heat transfer of nanofluids at a stagnation point flow over a stretching/shrinking surface in a porous medium with thermal radiation. (English) Zbl 1334.76155
Summary: The effects of thermal radiation and viscous dissipation on a stagnation point flow and heat transfer over a flat stretching/shrinking surface in nanofluids are analyzed. The effects of suction/injection are also considered. Using a similarity transformation, the governing equations are transformed into a system of nonlinear ordinary differential equations. The resulting system is then solved numerically by Runge-Kutta-Fehlberg method with shooting technique. It is observed that the local Nusselt number increases with increment in the suction/injection parameter for stretching sheet whereas reverse effect is observed for shrinking sheet. It is found that skin-friction coefficient increases for both stretching/shrinking sheet with increase in volume fraction of the nanoparticles.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 82D80 | Statistical mechanics of nanostructures and nanoparticles |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
References:
| [1] | Choi, U. S., Enhancing thermal conductivity of fluids with nanoparticle, (Siginer, D. A.; Wang, H. P., Developments and Applications of Non- Newtonian Flows, FED-vol. 231/MD-vol. 66 (1995), ASME: ASME New York), 99-105 |
| [2] | Xuan, Y.; Li, Q., Investigation on convective heat transfer and flow features of nanofluids, J. Heat Transfer, 125, 151-155 (2003) |
| [3] | Buongiorno, J., Convective transport in nanofluids, J. Heat Transfer, 128, 240-250 (2006) |
| [4] | Pantzali, M. N.; Mouza, A. A.; Paras, S. V., Investigating the efficacy of nanofluids as coolants in plate heat exchangers (PHE), Chem. Eng. Sci., 64, 3290-3300 (2009) |
| [5] | Duangthongsuk, W.; Wongwises, S., Heat transfer enhancement and pressure drop characteristics of \(\text{TiO}_2\)-water nanofluid in a double-tube counter flow heat exchanger, Int. J. Heat Mass Transfer, 52, 2059-2067 (2009) |
| [6] | Vajravelu, K.; Prasad, K. V.; Lee, Jinho; Lee, Changhoon; Pop, I.; Van Gorder, Robert A., Convective heat transfer in the flow of viscous Ag-water and Cu-water nanofluids over a stretching surface, Int. J. Therm. Sci., 50, 843-851 (2011) |
| [7] | Bachok, N.; Ishak, A.; Nazar, R.; Pop, I., Flow and heat transfer at a general three-dimensional stagnation point flow in a nanofluid, Physica B, 405, 4914-4918 (2010) |
| [8] | Vajravelu, K., Convection heat transfer at a stretching sheet with suction or blowing, J. Math. Anal. Appl., 188, 1002-1011 (1994) · Zbl 0816.76086 |
| [9] | Gorla, R. S.R.; Sidawi, I., Free convection on a vertical stretching surface with suction and blowing, Appl. Sci. Res., 52, 247-257 (1994) · Zbl 0800.76421 |
| [10] | Watanabe, T., Forced and free mixed convection boundary layer flow with uniform suction or injection on a vertical flat plate, Acta Mech., 89, 123-132 (1991) · Zbl 0753.76161 |
| [11] | Murthy, P. V.S. N.; Singh, P., Effect of viscous dissipation on a non-Darcy natural convection regime, Int. J. Heat Mass Transfer, 40, 1251-1260 (1997) · Zbl 0925.76649 |
| [12] | Al-Hadhrami, A. K.; Elliott, L.; Ingham, D. B.A., New model for viscous dissipation in a porous medium across a range of permeability values, Trans. Porous Media, 53, 117-122 (2003) |
| [13] | Sparrow, E. M.; Cess, R. D., Temperature-dependent heat sources or sinks in a stagnation point flow, Appl. Sci. Res., A10, 185-197 (1961) · Zbl 0102.41201 |
| [14] | Chamkha, A. J., Non-Darcy fully developed mixed convection in a porous medium channel with heat generation/absorption and hydromagnetic effects, Numer. Heat Transfer, 32, 853-875 (1997) |
| [15] | Fang, T., Boundary layer flow over a shrinking sheet with power-law velocity, Int. J. Heat Mass Transfer, 51, 5838-5843 (2008) · Zbl 1157.76010 |
| [16] | Fang, T.; Yao, S.; Zhang, J.; Aziz, A., Viscous flow over a shrinking sheet with a second order slip flow model, Commun. Nonlinear Sci. Numer. Simul., 15, 1831-1842 (2010) · Zbl 1222.76028 |
| [17] | Akbar, N. S.; Nadeem, S.; Ul Haq, R.; Khan, Z. H., Radiation effects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition, Chin. J. Aeronaut., 26, 6, 1389-1397 (2013) |
| [18] | Abdul Hakeem, A. K.; Vishnu Ganesh, N.; Ganga, B., Effect of heat radiation in a Walter’s liquid B fluid over a stretching sheet with non-uniform heat source/sink and elastic deformation, J. King Saud Univ. Eng. Sci. (2013) · Zbl 1336.35292 |
| [19] | Nadeem, S.; Ul Haq, R.; Khan, Z. H., Heat transfer analysis of water-based nanofluid over an exponentially stretching sheet, Alexandria Eng. J., 53, 219-224 (2014) |
| [20] | Elbashbeshy, E. M.A., Radiation effect on heat transfer over a stretching surface, Can. J. Phys., 78, 12, 1107-1112 (2000) |
| [21] | Mukhopadhyay, S., Heat transfer in a moving fluid over a moving non-isothermal flat surface, Chin. Phys. Lett., 28, 12, 124706 (2011) |
| [22] | Gururaj, A. D.M.; Anjali Devi, S. P., MHD boundary layer flow with forced convection past a nonlinearly stretching surface with variable temperature and nonlinear radiation effects, Int. J. Dev. Res., 4, 1, 75-80 (2014) |
| [23] | Pal, D.; Mondal, H., Effects of temperature-dependent viscosity and variable thermal conductivity on MHD non-Darcy mixed convective diffusion of species over a stretching sheet, J. Egypt. Math. Soc., 22, 123-133 (2014) · Zbl 1291.65230 |
| [24] | Tiwari, R. K.; Das, M. K., Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer, 50, 2002-2018 (2007) · Zbl 1124.80371 |
| [25] | Pal, D.; Mondal, H., Infuence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge, Appl. Math. Comput., 212, 194-208 (2009) · Zbl 1200.76172 |
| [26] | Hamad, M. A.A.; Pop, I., Scaling transformations for boundary layer flow near the stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects, Trans. Porous Medium, 87, 25-39 (2010) |
| [28] | Mahapatra, T. R.; Gupta, A. S., Heat transfer in stagnation-point flow towards a stretching sheet, Heat Mass Transfer, 38, 517-521 (2002) |
| [29] | Layek, G. C.; Mukhopadhyay, S.; Samad, Sk. A., Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing, Int. Commun. Heat Mass Transfer, 34, 347-356 (2007) |
| [30] | Wang, C. Y., Free convection on a vertical stretching surface, J. Appl. Math. Mech. (ZAMM), 69, 418-420 (1989) · Zbl 0698.76092 |
| [31] | Khan, W. A.; Pop, I., Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat Mass Transfer, 53, 2477-2483 (2010) · Zbl 1190.80017 |
| [32] | Hamad, M. A.A.; Ferdows, M., Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: a lie group analysis, Commun. Nonlinear Sci. Numer. Simul., 17, 132-140 (2012) · Zbl 1242.76192 |
| [33] | Oztop, H. F.; Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow, 29, 1326-1336 (2008) |
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