This paper aims to study the problem of unsteady mixed convection in a stagnation flow on a heated vertical surface embedded in a nanofluid-saturated porous medium. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The presence of a solid matrix, which exerts first and second resistance parameters, is considered in this study. The self-similar solutions for the system of equations governing the problem are obtained. The resulting system of ordinary differential equations that govern the flow is solved numerically using fourth-fifth order Runge-Kutta with shooting method. Numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as skin friction, Nusselt number and Sherwood number are produced for different values of the influence parameters.
| Published in |
American Journal of Energy Engineering (Volume 3, Issue 4-1)
This article belongs to the Special Issue Fire, Energy and Thermal Real-Life Challenges |
| DOI | 10.11648/j.ajee.s.2015030401.13 |
| Page(s) | 42-51 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Unsteady Mixed Convection, Self-Similar Solution, Nanofluids, Stagnation, Porous Media
| [1] | Ramachandra N., Chen T. and Armaly B, 1988. Mixed convection in the stagnation flows adjacent to vertical surface, J. Heat Transfer Vol. 110, pp. 173-177. |
| [2] | Scshadri R., Srccshylan N. and Nath G., 2002. Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion, Int. J. Heat and Mass Transfer Vol. 45 pp. 1345-1352. |
| [3] | Hall M., 1969. The boundary layer over an impulsively started flat plate, Proc. R. Soc. Vol. 310A, pp. 401-414. |
| [4] | Dennis S., 1972. The motion of a viscous fluid past an impulsively started semi-infinite flat plate, J. Inst. Math. It's Appl. Vol. 10, pp. 105-117. |
| [5] | Watkins C., 1975. Heat transfer in the boundary layer over an impulsively started flat plate, J. Heat Transfer Vol. 97, pp. 492-484. |
| [6] | Smith S., 1967. The impulsive motion of a wedge in a viscous fluid, Z. Angew. Math. Phys. Vol. 18 , pp. 508-522. |
| [7] | Nanbu K., 1971. Unsteady Falkner Skan flow, Z. Angew. Math. Phys. Vol. 22, pp. 1167-1172. |
| [8] | Williams J. and Rhyne T.,1980. Boundary layer development on a wedge impulsively set into motion, SIAM J. Appl. Math. Vol. 38, pp. 215-224. |
| [9] | Kumari M., 1997. Development of flow and heat transfer on a wedge with a magnetic field, Arch. Mech. Vol. 49, pp. 977-990. |
| [10] | Ece M., 1992. An initial boundary layer flow past a translating and spinning rotational symmetric body, J. Eng. Math. Vol. 26, pp. 415-428. |
| [11] | Ozturk A. and Ece M., 1995. Unsteady forced convection heat transfer from a translating and spinning body, J. Energy Rcsour. Tcchnol. Vol. 117, pp. 318-323. |
| [12] | Brown S. and Riley N., 1973. Flow past a suddenly heated vertical plate, J. Fluid Mech. Vol. 59, pp. 225-237. |
| [13] | Ingham D., 1985. Flow past a suddenly heated vertical plate, Proc. R. soc. Vol. 402A, pp. 109-134. |
| [14] | Amin N. and Riley N., 1995. Mixed convection at a stagnation point, Quart. J. Mech. Vol. 48, pp. 111-121. |
| [15] | Hassanien I., Ibrahim, F. and Omer Gh.,2004. Unsteady free convection flow in the stagnation-point region of a rotating sphere embedded in a porous medium, Mech.Mech. Eng. Vol. 7, pp. 89-98. |
| [16] | Hassanien, I., Ibrahim, F. and Omer Gh.,2006. Unsteady flow and heat transfer of a viscous fluid in the stagnation region of a three-dimensional body embedded in a porous medium, J.Porous Media, Vol. 9, pp. 357-372. |
| [17] | Hassanien, I. and Al-Arabi, T.,2008. Thermal Radiation and variable viscosity effects on unsteady mixed convection flow in the stagnation region on a vertical surface embedded in a porous medium with surface heat flux Vol. 29, pp. 187 – 207. |
| [18] | Yacob N., Ishak A. and Pop I., 2011. Falkner–Skan problem for a static or moving wedge in nanofluids. Int J Thermal Sci. Vol 50, pp. 133–139. |
| [19] | Congedo P., Collura S. and Congedo P., 2009.Modeling and analysis of natural convection heat transfer in nanofluids. In: Proc ASME Summer Heat TransferConf. Vol. 3,pp. 569–579. |
| [20] | Hamad M., Pop I. and Ismail A. 2011. Magnetic field effects on free convection flow of a nanofluid past a semi-infinite vertical flat plate. Nonlinear Analysis:Real World Appl. Vol. 12, pp. 1338–1346. |
| [21] | Buongiorno J., 2006. Convective transport in nanofluids. ASME J Heat Transfer.Vol. 128, pp. 240–250. |
| [22] | Hamad M., 2011. Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. Int. Commun. Heat Mass Transfer. Vol. 38, pp. 487–492. |
| [23] | Khan W and Pop I.,2010. Boundary-layer flow of a nanofluid past a stretching sheet. Int. J Heat Mass Transfer. Vol. 53, pp. 2477–2483. |
| [24] | Abu-Nada E. and Chamkha A., 2010. Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–water nanofluid. Int. J. Thermal Sci. Vol. 49, pp. 2339–2352. |
| [25] | Das S., S Choi SU, Yu W. and Pradeep T., 2007. Nanofluids: Science and Technology. New Jersey: Wiley. |
| [26] | Kakaç S. and Pramuanjaroenkij A., 2009. Review of convective heat transfer enhancement with nanofluids. Int. J Heat Mass Transfer. Vol. 52, pp. 3187–3196. |
| [27] | Muthtamilselvan M., Kandaswamy P. and Lee J., 2010. Heat transfer enhancement of copper–water nanofluids in a lid-driven enclosure. Commun Nonlinear Sci. Numer. Simulat. Vol. 15, pp. 1501–1510. |
| [28] | Pereyra V.,1978. PASVA3, an adaptive finite difference FORTRAN program for first order non-linear boundary value problems, in: Lecture Note in Computer Science, Vol. 76, Springer, Berlin. |
| [29] | Scshadri R., Srccshylan N. and Nath G., 2002. Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion, Int. J. Heat and Mass Transfer Vol. 45 pp. 1345-1352. |
APA Style
A. A. Abdullah, F. S. Ibrahim, A. F. Abdel Gawad, A. Batyyb. (2015). Investigation of Unsteady Mixed Convection Flow near the Stagnation Point of a Heated Vertical Plate embedded in a Nanofluid-Saturated Porous Medium by Self-Similar Technique. American Journal of Energy Engineering, 3(4-1), 42-51. https://doi.org/10.11648/j.ajee.s.2015030401.13
ACS Style
A. A. Abdullah; F. S. Ibrahim; A. F. Abdel Gawad; A. Batyyb. Investigation of Unsteady Mixed Convection Flow near the Stagnation Point of a Heated Vertical Plate embedded in a Nanofluid-Saturated Porous Medium by Self-Similar Technique. Am. J. Energy Eng. 2015, 3(4-1), 42-51. doi: 10.11648/j.ajee.s.2015030401.13
AMA Style
A. A. Abdullah, F. S. Ibrahim, A. F. Abdel Gawad, A. Batyyb. Investigation of Unsteady Mixed Convection Flow near the Stagnation Point of a Heated Vertical Plate embedded in a Nanofluid-Saturated Porous Medium by Self-Similar Technique. Am J Energy Eng. 2015;3(4-1):42-51. doi: 10.11648/j.ajee.s.2015030401.13
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Download@article{10.11648/j.ajee.s.2015030401.13,
author = {A. A. Abdullah and F. S. Ibrahim and A. F. Abdel Gawad and A. Batyyb},
title = {Investigation of Unsteady Mixed Convection Flow near the Stagnation Point of a Heated Vertical Plate embedded in a Nanofluid-Saturated Porous Medium by Self-Similar Technique},
journal = {American Journal of Energy Engineering},
volume = {3},
number = {4-1},
pages = {42-51},
doi = {10.11648/j.ajee.s.2015030401.13},
url = {https://doi.org/10.11648/j.ajee.s.2015030401.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajee.s.2015030401.13},
abstract = {This paper aims to study the problem of unsteady mixed convection in a stagnation flow on a heated vertical surface embedded in a nanofluid-saturated porous medium. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The presence of a solid matrix, which exerts first and second resistance parameters, is considered in this study. The self-similar solutions for the system of equations governing the problem are obtained. The resulting system of ordinary differential equations that govern the flow is solved numerically using fourth-fifth order Runge-Kutta with shooting method. Numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as skin friction, Nusselt number and Sherwood number are produced for different values of the influence parameters.},
year = {2015}
}
TY - JOUR T1 - Investigation of Unsteady Mixed Convection Flow near the Stagnation Point of a Heated Vertical Plate embedded in a Nanofluid-Saturated Porous Medium by Self-Similar Technique AU - A. A. Abdullah AU - F. S. Ibrahim AU - A. F. Abdel Gawad AU - A. Batyyb Y1 - 2015/02/24 PY - 2015 N1 - https://doi.org/10.11648/j.ajee.s.2015030401.13 DO - 10.11648/j.ajee.s.2015030401.13 T2 - American Journal of Energy Engineering JF - American Journal of Energy Engineering JO - American Journal of Energy Engineering SP - 42 EP - 51 PB - Science Publishing Group SN - 2329-163X UR - https://doi.org/10.11648/j.ajee.s.2015030401.13 AB - This paper aims to study the problem of unsteady mixed convection in a stagnation flow on a heated vertical surface embedded in a nanofluid-saturated porous medium. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The presence of a solid matrix, which exerts first and second resistance parameters, is considered in this study. The self-similar solutions for the system of equations governing the problem are obtained. The resulting system of ordinary differential equations that govern the flow is solved numerically using fourth-fifth order Runge-Kutta with shooting method. Numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as skin friction, Nusselt number and Sherwood number are produced for different values of the influence parameters. VL - 3 IS - 4-1 ER -
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