Transient Combustion Analysis for Iron Micro-Particles in a Gaseous Oxidizing Medium Using Adomian Decomposition Method

Document Type : Original Article


Department of Mechanical Engineering, University of Lagos, Nigeria


The present study presents analytical solution to transient combustion analysis for iron micro-particles in a gaseous oxidizing medium using Adomian decomposition method. The analytical solutions obtained by the Adomian decomposition method are verified with those of the fourth order Runge–Kutta numerical method. Also, parametric studies are carried out to properly understand the chemistry of the process and the associated burning time. Thermal radiation effect from the external surface of burning particle and variations of density of iron particle with temperature are considered. Furthermore, the results show that by increasing the heat realized parameter, combustion temperature increased until a steady state is reached. This work will be useful in solving to a great extent one of the challenges facing industries on combustion of metallic particles such as iron particles as well as in the determination of different particles burning time.


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[1] J.H. Sun, R. Dobashi, T. Hirano, Combustion behavior of iron particles suspended in air. Combust. Sci. Technol. 150 (2000) 99e114
[2] Haghiri A, Bidabadi M. Dynamic behavior of particles across flame propagation through micro-iron dust cloud with thermal radiation effect. Fuel 2011;90:2413–21.
[3] Liu Y, Sun J, Chen D. Flame propagation in hybrid mixture of coal dust and methane. J Loss Prev Process Ind 2007;20:691–7.
[4] Bidabadi M, Haghiri A, Rahbari A. Mathematical modeling of velocity and number density profiles of particles across the flame propagation through a micro-iron dust cloud. J Hazard Mater 2010;176:146–53.
[5] Haghiri A, Bidabadi M. Modeling of laminar flame propagation through organic dust cloud with thermal radiation effect. Int J Therm Sci 2010;49: 1446–56.
[6] Hatami M, Ganji DD, Boubaker K. Temperature variations analysis for condensed matter micro- and nanoparticles combustion burning in gaseous oxidizing media by DTM and BPES. ISRN Condensed Matter Phys 2013;2013:8, (Article ID 129571).
[7] Bidabadi M, Mafi M. Time variation of combustion temperature and burning time of a single iron particle. Int J Therm Sci 2013;65:136–47.
[8] Stern RH, Rasmussen H. Left ventricular ejection: Model solution by collocation, an approximate analytical method. Comput Boil Med 1996;26:255–61.
[9] Vaferi B, Salimi V, Dehghan Baniani D, Jahanmiri A, Khedri S. Prediction of transient pressure response in the petroleum reservoirs using orthogonal collocation. J Petrol Sci and Eng 2012;.
[10] Hatami M, Hasanpour A, Ganji DD. Heat transfer study through porous fins (Si3N4 and AL) with temperature-dependent heat generation. Energy Convers Manage 2013;74:9–16.
[11] Bouaziz MN, Aziz A. Simple and accurate solution for convective–radiative fin with temperature dependent thermal conductivity using double optimal linearization. Energy Convers Manage 2010;51:76–82.
[12] Aziz A, Bouaziz MN. A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity. Energy Convers Manage 2011;52:2876–82.
[13] Shaoqin G, Huoyuan D. negative norm least-squares methods for the incompressible magneto-hydrodynamic equations. Act Math Sci 2008;28B(3): 675–84.
[14] Hatami M, Nouri R, Ganji DD. Forced convection analysis for MHD Al2O3–water nanofluid flow over a horizontal plate. J Mol Liq 2013;187:294–301.
[15] Hatami M, Sheikholeslami M, Ganji DD. Laminar flow and heat transfer of nanofluid between contracting and rotating disks by least square method. Powder Technol 2014;253:769–79.
[16] Hatami M, Hatami J, Ganji DD. Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel. Comput Methods Programs Biomed 2014;113:632–41.
[17] Hatami M, Ganji DD. Thermal performance of circular convective–radiative porous fins with different section shapes and materials. Energy Convers Manage 2013;76:185–93.
[18] Hatami M, Ganji DD. Heat transfer and nanofluid flow in suction and blowing process between parallel disks in presence of variable magnetic field. J Mol Liq 2014;190:159–68.
[19] Hatami M, Ganji DD. Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods. Case Studies Therm Eng 2014;2:14–22.
[20] Hatami M, Domairry G. Transient vertically motion of a soluble particle in a Newtonian fluid media. Powder Technol 2014;253:481–5.
[21] Domairry G, Hatami M. Squeezing Cu–water nanofluid flow analysis between parallel plates by DTM-Padé Method. J Mol Liq 2014;193:37–44.
[22] Ahmadi AR, Zahmtkesh A, Hatami M, Ganji DD. A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate. Powder Technol 2014;258:125–33
[23] Saedodin, S. and Shahbabaei, M. Thermal analysis of natural convection in porous fins with homotopy perturbation method (HPM). Arabian Journal for Science and Engineering, 38, (2013), 2227{2231.
[24] Darvishi, M. T., Gorla, R. S. R., Gorla, R. and Aziz, A. Thermal performance of a porous radial fin with natural convection and radiative heat losses. Thermal Science, 19(2), (2015), 669-678.
[25] Moradi, A., Hayat, T. and Alsaedi, A. Convective-radiative thermal analysis of triangular fins with temperature-dependent thermal conductivity by DTM. Energy Conversion and Management, 77, (2014), 70{77.
[26] Ha, H. Ganji, D. D. and Abbasi, M. Determination of temperature distribution for porous fin with temperature-dependent heat generation by homotopy analysis method. Journal of Applied Mechanical Engineering, 4(1), (2005), 1-5.
[27] G. Adomian, Solving Frontier Problems on Physics: The Decomposition Method, Kluwer Academic Publisher, Boston, 1994.
[28] G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135, 501–544, 1988.
[29] G. Adomian, Solution of the Thomas–Fermi equation, Appl. Math. Lett. 11 (3), 31–133, 1998.
[30] G. Adomian: Analytical solution of Navier-Stokes Flow of a viscous compressible Fuid" Foundations of Physics Letters, Vol. 8, No. 4, 1995.
[31]H. Arora H., F. Abdelwahid: Solution of non-integer order differential equations via the Adomian decomposition method". Applied Mathematics Letters, 6(1),  21-23, 1993.
[32] S. Momani : A Decomposition Method for Solving Unsteady Convection Diffusion Problems", Turk J Math 32 , pp. 51 – 60, 2008.
[33] D. D. Ganji, M. Sheikholeslami, H. R. Ashorynejad: Analytical Approximate Solution of Nonlinear Differential Equation Governing Jeffery-Hamel Flow with High Magnetic Field by Adomian Decomposition Method". ISRN Mathematical Analysis Volume 2011, Article ID 937830, 16 pages.
[34] K. Haldar: Application of Adomian's Approximation to Blood Flow through Arteries in the Presence of a Magnetic Field ". Applied Mathematics, 1, 17 – 28, 2009.
[35] O. D. Makinde, B. I. Olajuwon, A. W. Gbolagade: Adomian Decomposition Approach to a Boundary Layer Flow with Thermal Radiation past a Moving Vertical Porous Plate". Int. J. of Appl. Math and Mech.  3(3), 62–70, 2007.
[36] S. Somali, G. Gokmen: Adomian Decomposition Method for Nonlinear Sturm-Lioville Problems". ISSN 1842-6298, 2, 11 – 20, 2007.
[37] K. Haldar: Application of Adomian's Approximations to the Navier Stokes Equations in Cylindrical Coordinates". Appl. Math. Lett., 9(4), 109 – 113, 1996.
[38] C. H. Chiu, C. K. Chen: A Decomposition Method for Solving the Convective Longitudinal Fins with Variable Thermal Conductivity". International Journal of Heat and Mass Transfer 45, 2067 – 2075, 2002.