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Year 2018, Volume: 4 Issue: 6, 2496 - 2508, 29.09.2018
https://doi.org/10.18186/thermal.465731

Abstract

References

  • [1] Ostrach S. (1972). Natural convection in enclosures. Advances in heat transfer.,8,161-227.
  • [2] Khalifa A.J. (2001). Natural convective heat transfer coefficient–A review II, surfaces in two and three- dimensional enclosures. Energy conversion and management., 42,505-517.
  • [3] Jha B.K., Ajibade A.O. (2010). Transient natural convection flow between vertical parallel plates: one plate isothermally heated and the other thermally insulated. Journal of process mechanical engineering, 224(4)247-252.
  • [4] Noghrehabadi A., Behseresht A., Ghalambaz M. (2013). Natural convection of nanofluid over vertical plate embedded in porous medium: prescribed surface heat flux. Applied mathematics and mechanics.,1573-2754.
  • [5] Rashad, A. M., El-Hakiem, M. A., Abdou, M. M. M. (2011). Natural convection boundary layer of a non-Newtonian fluid about a permeable vertical cone embedded in a porous medium saturated with a nanofluid. Computers & Mathematics with Applications, 62(8), 3140-3151.
  • [6] Narahar M. (2009). Natural convection in unsteady Couette flow between two vertical parallel plates in the presence of constant heat flux and radiation. MACMESE'09 Proceedings of the 11th WSEAS international conference on mathematical and computational methods in science and engineering, 73-78.
  • [7] Ternik, P., Rudolf, R., Zunic, Z. (2012). Numerical study of heat transfer enhancement of homogeneous water-Au nanofluid under natural convection. Materials and Technology, 46(3), 257-261.
  • [8] Niu, J., Fu, C., & Tan, W. (2012). Slip-flow and heat transfer of a non-Newtonian nanofluid in a microtube. PLoS One, 7(5), e37274.
  • [9] Kargar, A., Akbarzade, M. (2012). Analytic solution of natural convection flow of a non-newtonian fluid between two vertical flat plates using homotopy perturbation method (HPM). World Applied Sciences Journal, 20(11), 1459-1465.
  • [10] Farooq, A. A., Siddiqui, A. M., Rana, M. A., Haroon, T. (2012). Application of He’s Method in Solving a System of Nonlinear Coupled Equations Arising in Non-Newtonian Fluid Mechanics. International Journal of Applied Mathematical Research, 1, 130-140.
  • [11] Rahmani, Y., Yousefi, R., Ghasemi, S. E., Ganji, D. D. (2013). Thermal and fluid effects of non-Newtonian water-based nanofluids on the free convection flow between two vertical planes. Phys. Rev. Res. Int, 3(4), 688-701.
  • [12] He, J. H., Wu, X. H. (2007). Variational iteration method: vew development and applications, Computers and Mathematics with applications, 54, 881-894.
  • [13] He, J. H. (2007). Variational iteration method-Some recent results and new interpretations, Journal of Computational and applied mathematics., 207, 3-17.
  • [14] Imani, A. A., Rostamian, Y., Ganji, D. D., & Rokni, H. B. (2012). Analytical Investigation of Jeffery-Hamel Flow with High Magnetic Field and Nano Particle by RVIM.
  • [15] Khidir, A. A. (2014). Spectral-Homotopy Perturbation Method for Solving Governing MHD Jeffery-Hamel Problem. Journal of Computational Methods in Physics, 2014.
  • [16] Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method, Dodrecht. Kluwer Academic Publishers.
  • [17] Song, L., Wang, W. (2013). A new improved Adomian decomposition method and its application to fractional differential equations. Applied Mathematical Modelling, 37(3), 1590-1598.
  • [18] Hasan, Y. Q., Zhu, L. M. (2008). Modified Adomian decomposition method for singular initial value problems in the second-order ordinary differential equations. Surveys in Mathematics and its Applications, 3, 183-193.
  • [19] Jiao, Y. C., Dang, C., Yamamoto, Y. (2008). An extension of the decomposition method for solving nonlinear equations and its convergence. Computers & Mathematics with Applications, 55(4), 760-775.
  • [20] Khanafer, K., Vafai, K., Lightstone, M. (2003). Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International journal of heat and mass transfer, 46(19), 3639-3653.
  • [21] Rajagopal, K. R., Na, T. Y. (1985). Natural convection flow of a non-Newtonian fluid between two vertical flat plates. Acta Mechanica, 54(3-4), 239-246.
  • [22] Hatami, M., Ganji, D. D. (2014). Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods. Case Studies in Thermal Engineering, 2, 14-22.
  • [23] Kundu, B. (2015). Semianalytical methods for heat and fluid flow between two parallel plates. Journal of Thermal Engineering, 1(3), 175-181.

A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM)

Year 2018, Volume: 4 Issue: 6, 2496 - 2508, 29.09.2018
https://doi.org/10.18186/thermal.465731

Abstract

In this work, natural convection
in a non-Newtonian fluid/nanofluid between two vertical plates is investigated.
The study was carried out on three types of nanofluids, namely Silver/Water,
Oxide Copper-Water and  Titanium oxide/Water.
The mathematical formulation gives a set of strongly coupled nonlinear ordinary
differential equations of the second order. These equations, characterizing velocity
and temperature distributions, were solved numerically by the Runge-Kutta fourth
order method, and analytically by a new Adomian of decomposition approach named
the Adomian generalized method (GDM). The results show clearly the
effectiveness, accuracy and applicability of the used technique (GDM).
Using nanoparticles (Ag, CuO
and




















)
in water as a base fluid substantially increases the coefficient of friction
and characteristics of heat transfer. Compared to other works, the generalized
Adomian decomposition technique (GDM) offers the advantages of precision and velocity
of convergence.

References

  • [1] Ostrach S. (1972). Natural convection in enclosures. Advances in heat transfer.,8,161-227.
  • [2] Khalifa A.J. (2001). Natural convective heat transfer coefficient–A review II, surfaces in two and three- dimensional enclosures. Energy conversion and management., 42,505-517.
  • [3] Jha B.K., Ajibade A.O. (2010). Transient natural convection flow between vertical parallel plates: one plate isothermally heated and the other thermally insulated. Journal of process mechanical engineering, 224(4)247-252.
  • [4] Noghrehabadi A., Behseresht A., Ghalambaz M. (2013). Natural convection of nanofluid over vertical plate embedded in porous medium: prescribed surface heat flux. Applied mathematics and mechanics.,1573-2754.
  • [5] Rashad, A. M., El-Hakiem, M. A., Abdou, M. M. M. (2011). Natural convection boundary layer of a non-Newtonian fluid about a permeable vertical cone embedded in a porous medium saturated with a nanofluid. Computers & Mathematics with Applications, 62(8), 3140-3151.
  • [6] Narahar M. (2009). Natural convection in unsteady Couette flow between two vertical parallel plates in the presence of constant heat flux and radiation. MACMESE'09 Proceedings of the 11th WSEAS international conference on mathematical and computational methods in science and engineering, 73-78.
  • [7] Ternik, P., Rudolf, R., Zunic, Z. (2012). Numerical study of heat transfer enhancement of homogeneous water-Au nanofluid under natural convection. Materials and Technology, 46(3), 257-261.
  • [8] Niu, J., Fu, C., & Tan, W. (2012). Slip-flow and heat transfer of a non-Newtonian nanofluid in a microtube. PLoS One, 7(5), e37274.
  • [9] Kargar, A., Akbarzade, M. (2012). Analytic solution of natural convection flow of a non-newtonian fluid between two vertical flat plates using homotopy perturbation method (HPM). World Applied Sciences Journal, 20(11), 1459-1465.
  • [10] Farooq, A. A., Siddiqui, A. M., Rana, M. A., Haroon, T. (2012). Application of He’s Method in Solving a System of Nonlinear Coupled Equations Arising in Non-Newtonian Fluid Mechanics. International Journal of Applied Mathematical Research, 1, 130-140.
  • [11] Rahmani, Y., Yousefi, R., Ghasemi, S. E., Ganji, D. D. (2013). Thermal and fluid effects of non-Newtonian water-based nanofluids on the free convection flow between two vertical planes. Phys. Rev. Res. Int, 3(4), 688-701.
  • [12] He, J. H., Wu, X. H. (2007). Variational iteration method: vew development and applications, Computers and Mathematics with applications, 54, 881-894.
  • [13] He, J. H. (2007). Variational iteration method-Some recent results and new interpretations, Journal of Computational and applied mathematics., 207, 3-17.
  • [14] Imani, A. A., Rostamian, Y., Ganji, D. D., & Rokni, H. B. (2012). Analytical Investigation of Jeffery-Hamel Flow with High Magnetic Field and Nano Particle by RVIM.
  • [15] Khidir, A. A. (2014). Spectral-Homotopy Perturbation Method for Solving Governing MHD Jeffery-Hamel Problem. Journal of Computational Methods in Physics, 2014.
  • [16] Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method, Dodrecht. Kluwer Academic Publishers.
  • [17] Song, L., Wang, W. (2013). A new improved Adomian decomposition method and its application to fractional differential equations. Applied Mathematical Modelling, 37(3), 1590-1598.
  • [18] Hasan, Y. Q., Zhu, L. M. (2008). Modified Adomian decomposition method for singular initial value problems in the second-order ordinary differential equations. Surveys in Mathematics and its Applications, 3, 183-193.
  • [19] Jiao, Y. C., Dang, C., Yamamoto, Y. (2008). An extension of the decomposition method for solving nonlinear equations and its convergence. Computers & Mathematics with Applications, 55(4), 760-775.
  • [20] Khanafer, K., Vafai, K., Lightstone, M. (2003). Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International journal of heat and mass transfer, 46(19), 3639-3653.
  • [21] Rajagopal, K. R., Na, T. Y. (1985). Natural convection flow of a non-Newtonian fluid between two vertical flat plates. Acta Mechanica, 54(3-4), 239-246.
  • [22] Hatami, M., Ganji, D. D. (2014). Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods. Case Studies in Thermal Engineering, 2, 14-22.
  • [23] Kundu, B. (2015). Semianalytical methods for heat and fluid flow between two parallel plates. Journal of Thermal Engineering, 1(3), 175-181.
There are 23 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Tabet Ismail

Publication Date September 29, 2018
Submission Date February 4, 2017
Published in Issue Year 2018 Volume: 4 Issue: 6

Cite

APA Ismail, T. (2018). A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM). Journal of Thermal Engineering, 4(6), 2496-2508. https://doi.org/10.18186/thermal.465731
AMA Ismail T. A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM). Journal of Thermal Engineering. September 2018;4(6):2496-2508. doi:10.18186/thermal.465731
Chicago Ismail, Tabet. “A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM)”. Journal of Thermal Engineering 4, no. 6 (September 2018): 2496-2508. https://doi.org/10.18186/thermal.465731.
EndNote Ismail T (September 1, 2018) A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM). Journal of Thermal Engineering 4 6 2496–2508.
IEEE T. Ismail, “A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM)”, Journal of Thermal Engineering, vol. 4, no. 6, pp. 2496–2508, 2018, doi: 10.18186/thermal.465731.
ISNAD Ismail, Tabet. “A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM)”. Journal of Thermal Engineering 4/6 (September 2018), 2496-2508. https://doi.org/10.18186/thermal.465731.
JAMA Ismail T. A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM). Journal of Thermal Engineering. 2018;4:2496–2508.
MLA Ismail, Tabet. “A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM)”. Journal of Thermal Engineering, vol. 4, no. 6, 2018, pp. 2496-08, doi:10.18186/thermal.465731.
Vancouver Ismail T. A NEW ANALYTICAL INVESTIGATION OF NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUIDS FLOW BETWEEN TWO VERTICAL FLAT PLATES BY THE GENERALIZED DECOMPOSITION METHOD (GDM). Journal of Thermal Engineering. 2018;4(6):2496-508.

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