Analytical investigation of temperature of a single micron sized iron particle during combustion

Abstract

The present study deals with analytical investigation of temperature of a single burning iron particle. Three mathematical methods including AGM (Akbari-Ganji’s method), CM (Collocation method) and GM (Galerkin Method) are applied to solving non-linear differential governing equation and effectiveness of these methods is examined as well. For further investigation, forth order Runge-Kutta approach, a numerical method, is used to validate the obtained analytical results. In the present study, the developed mathematical model takes into account the effects of thermal radiation, convective heat transfer and particle density variations during combustion process. Due to particles’ small size and high thermal conductivity, the system is assumed to be lumped in which the particle temperature does not change within the body and all of its regions are at the same temperature. The temperature distributions obtained by analytical methods have satisfactory agreement with numerical outputs. Finally, the results indicate that AGM is a more appropriate method than GM and CM due to its lower mean relative error and less run time.

References

[1] EckhoffrKDust explosions in the process industries [M], 2003, New York, Elsevier Publisher

[2] EckhoffR K. Current status and expected future trends in dust explosion research [J]. Journal of Loss Prevention in the Process Industries, 2005, 18(4-6): 225-237

[3] SapkoM J, WeissE S, CashdollarK L, ZlochowerI A. Experimental mine and laboratory dust explosion research at NIOSH [J]. Journal of Loss Prevention in the Process Industries, 2000, 13(3-5): 229-242

[4] van der VoortM M, KleinA J J, de MaaijerM, van den BergA C, van DeursenJ R, VerslootN H A. A quantitative risk assessment tool for the external safety of industrial plants with A dust explosion hazard [J]. Journal of Loss Prevention in the Process Industries, 2007, 20(4-6): 375-386

[5] AbbasiT, AbbasiS A. Dust explosions-Cases, causes, consequences, and control [J]. Journal of Hazardous Mterials, 2007, 140(12): 7-44

[6] KleinerK. Powdered metal: The fuel of the future [J]. New Scientist, 2005, 2522: 34-37

[7] HaghiriA, BidabadiM. Dynamic behavior of particles across flame propagation through micro-iron dust cloud with thermal radiation effect [J]. Fuel, 2011, 90(7): 2413-2421

[8] PopokE V, LevashovaA I, BurlutskiyN P, KhudyakovD V, ZhuravkovS P. Ultradispersed electro-explosive iron powders as catalysts for synthesis of liquid hydrocarbons of CO and H2 [J]. Procedia Chemistry, 2015, 15: 225-230

[9] LissianskiV V, MalyP M, ZamanskyV M, GardinerW C. Utilization of iron additives for advanced control of NO_x emissions from stationary combustion sources [J]. Industrial & Engineering Chemistry Research, 2001, 40(15): 3287-3293

[10] BergthorsonJ M, GoroshinS, SooM J, JulienP, PaleckaJ, FrostD L, JarvisD J. Direct combustion of recyclable metal fuels for zero-carbon heat and power [J]. Applied Energy, 2015, 160: 368-382

[11] TangF D, GoroshinS, HigginsA, LeeJ. Flame propagation and quenching in iron dust clouds [J]. Proceedings of the Combustion Institute, 2009, 32(2): 1905-1912

[12] TangF D, GoroshinS, HigginsA J. Modes of particle combustion in iron dust flames [J]. Proceedings of the Combustion Institute, 2011, 33(2): 1975-1982

[13] SunJ H, DobashiR, HiranoT. Combustion behavior of iron particles suspended in air [J]. Combustion Science and Technology, 1990, 150(1-6): 99-114

[14] SunJ H, RitsuD, ToshisukeH. Velocity and number density profiles of particles across upward and downward flame propagating through iron particle clouds [J]. Journal of Loss Prevention in the Process Industries, 2006, 19(23): 135-141

[15] SunJ, DobashiR, HiranoT. Concentration profile of particles across A flame propagating through an iron particle cloud [J]. Combustion and Flame, 2003, 134(4): 381-387

[16] SunJ H, DobashiR, HiranoT. Temperature profile across the combustion zone propagating through an iron particle cloud [J]. Journal of Loss Prevention in the Process Industries, 2001, 14(6): 463-467

[17] BroumandM, BidabadiM. Modeling combustion of micron-sized iron dust particles during flame propagation in A vertical duct [J]. Fire Safety Journal, 2013, 59: 88-93

[18] BarariA, OmidvarM, GhotbiA R, GanjiD D. Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations [J]. Acta Applicandae Mathematicae, 2008, 104(2): 161-171

[19] GanjiD D. The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer [J]. Physics Letters A, 2006, 355(45): 337-341

[20] NaveO, Gol’dshteinV. A combination of two semi-analytical method called “singular perturbed homotopy analysis method, (SPHAM)” applied to combustion of spray fuel droplets [J]. Cogent Mathematics & Statistics, 2016, 3(1): 1256467

[21] DomairryG, NadimN. Assessment of homotopy analysis method and homotopy perturbation method in non-linear heat transfer equation [J]. International Communications in Heat and Mass Transfer, 2008, 35193-102

[22] DomairryG, HatamiM. Squeezing Cu-water nanofluid flow analysis between parallel plates by DTM-Padé method [J]. Journal of Molecular Liquids, 2014, 193: 37-44

[23] ArslanturkC. Performance analysis and optimization of radiating fins with A step change in thickness and variable thermal conductivity by homotopy perturbation method [J]. Heat and Mass Transfer, 2011, 47(2): 131-138

[24] JalaalM, GanjiD D. An analytical study on motion of A sphere rolling down an inclined plane submerged in A Newtonian fluid [J]. Powder Technology, 2010, 198(1): 82-92

[25] HatamiM, HosseinzadehK, DomairryG, BehnamfarM T. Numerical study of MHD two-phase Couette flow analysis for fluid-particle suspension between moving parallel plates [J]. Journal of the Taiwan Institute of Chemical Engineers, 2014, 45(5): 2238-2245

[26] ZiabakhshZ, DomairryG. Solution of the laminar viscous flow in A semi-porous channel in the presence of A uniform magnetic field by using the homotopy analysis method [J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(4): 1284-1294

[27] SheikholeslamiM, GanjiD D, AshorynejadH R, RokniH B. Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method [J]. Applied Mathematics and Mechanics, 2012, 33(1): 25-36

[28] GanjiD D, AfrouziG A, TalarposhtiR A. Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations [J]. Physics Letters A, 2007, 368(6): 450-457

[29] AkbariM R, GanjiD D, NimafarM, AhmadiA R. Significant progress in solution of nonlinear equations at displacement of structure and heat transfer extended surface by new AGM approach [J]. Frontiers of Mechanical Engineering, 2014, 9(4): 390-401

[30] MirgolbabaeeH, LedariS T, GanjiD D. Semi-analytical investigation on micropolar fluid flow and heat transfer in A permeable channel using AGM [J]. Journal of the Association of Arab Universities for Basic and Applied Sciences, 2017, 24(1): 213-222

[31] HatamiM, MosayebidorchehS, JingD. Two-phase nanofluid condensation and heat transfer modeling using least square method (LSM) for industrial applications [J]. Heat and Mass Transfer, 2017, 53(6): 2061-2072

[32] Al MersA, MimetA. Numerical study of heat and mass transfer in adsorption porous medium heated by solar energy: Boubnov-Galerkin method [J]. Heat and Mass Transfer, 2005, 41(8): 717-723

[33] PetroudiI R, GanjiD D, NejadM K, RahimiJ, RahimiE, RahimifarA. Transverse magnetic field on Jeffery-Hamel problem with Cu-water nanofluid between two non parallel plane walls by using collocation method [J]. Case Studies in Thermal Engineering, 2014, 4: 193-201

[34] GhadikolaeiS S, HosseinzadehK, GanjiD D. Analysis of unsteady MHD Eyring-Powell squeezing flow in stretching channel with considering thermal radiation and Joule heating effect using AGM [J]. Case Studies in Thermal Engineering, 2017, 10: 579-594

[35] RahimiJ, GanjiD D, KhakiM, HosseinzadehK. Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fluid over A linear stretching sheet by collocation method [J]. Alexandria Engineering Journal, 2017, 56(4): 621-627

[36] ArdahaieS S, AmiriA J, AmoueiA, HosseinzadehK, GanjiD D. Investigating the effect of adding nanoparticles to the blood flow in presence of magnetic field in A porous blood arterial [J]. Informatics in Medicine Unlocked, 2018, 10: 71-81

[37] HosseinzadehK, AmiriA J, ArdahaieS S, GanjiD D. Effect of variable Lorentz forces on nanofluid flow in movable parallel plates utilizing analytical method [J]. Case Studies in Thermal Engineering, 2017, 10: 595-610

[38] AtoueiS A, HosseinzadehK, HatamiM, GhasemiS E, SahebiS, GanjiD D. Heat transfer study on convective-radiative semi-spherical fins with temperature-dependent properties and heat generation using efficient computational methods [J]. Applied Thermal Engineering, 2015, 89: 299-305

[39] AfzalabadiA, PoorfarA K, BidabadiM, MoghadasiH, HochgrebS, RahbariA, DuboisC. Study on hybrid combustion of aero-suspensions of boron-aluminum powders in A quiescent reaction medium [J]. Journal of Loss Prevention in the Process Industries, 2017, 49: 645-651

[40] BidabadiM, BioukiS A, AfzalabadiA, DehghanA A, PoorfarA K, RouboaA. Modeling propagation and extinction of aluminum dust particles in A reaction medium with spatially uniform distribution of particles [J]. Journal of Thermal Analysis and Calorimetry, 2017, 129(3): 1855-1864

[41] SonntagR E, BorgnakkeC, van WylenG J, van WykSFundamentals of thermodynamics [M], 1998, New York, Wiley

[42] BergmanT L, IncroperaF P, DewittD P, LavineA SFundamentals of heat and mass transfer [M], 2011, New York, John Wiley & Sons

[43] WilsonD B, SteinbergT A, StoltzfusJ M. Thermodynamics and kinetics of burning iron [M]. Flammability and Sensitivity of Materials in Oxygen-Enriched Atmospheres: Eighth Volume. ASTM International, 1997

[44] PapanastasiouT, GeorgiouG, AlexandrouA NViscous fluid flow [M], 1999

[45] YarinL P, HetsroniG, MosyakACombustion of two-phase reactive media [M], 2013

[46] GlassmanIMetal combustion processes [M], 1959, New Jersey, Princeton University Publisher

[47] HoffmannK A, ChiangS TComputational fluid dynamics volume I [M], 2000

[48] IedariS T, MirgolbabaeeH, GanjiD D. An assessment of A semi analytical AG method for solving two-dimension nonlinear viscous flow [J]. International Journal of Nonlinear Analysis and Applications, 2015, 6(2): 47-64

[49] PerryR H, ChiltonC HChemical Engineers Handbook [M], 1963, New York, McGrawHill

[50] MillsA F. Basic heat and mass transfer [M]. Pearson College Div, 1999

[51] FukuyamaH, WasedaY. High-temperature measurements of materials (Vol. 11) [M]. Springer Science & Business Media, 2008