Analysis of heat transfer in the pyrolysis of differently shaped biomass particles subjected to different boundary conditions: integral transform methods

Document Type: Full Lenght Research Article


University of Lagos


The conversion and utilization of biomass as an alternative source of energy have been subjects of interest in various countries, but technical barriers to the technology and design of conversion plants have considerably impeded the development and use of alternative power sources. Theoretical studies on the conversion process enhance our understanding of the thermochemical conversion of solid fuels. Carrying out such research necessitates the development of thermal and kinetic models of pyrolysis, on which the conversion process integrally depends. Another requirement is to analytically solve the aforementioned models to derive valuable insight into the actual process of biomass conversion. Accordingly, this study used Laplace and Hankel transforms to obtain analytical solutions to heat transfer models of rectangular, cylindrical, and spherical biomass particles. Pyrolysis kinetic models were also analytically solved using the Laplace transform. The study then investigated the effects of particle shape, particle size, isothermal and non-isothermal heating conditions, and convective and radiative heat transfer (calculated using a modified Biot number) on the pyrolysis of a biomass particle. This work is expected to substantially contribute to the design of pyrolysis reactors/units and the optimal design of biomass gasifiers.


Main Subjects

D. L. Pyle, C. A. Zaror. Heat transfer and kinetics in the low temperature pyrolysis of solids. Chemical Engineering Science 39(1984.), 147–158.

[2] C. H. Bamford, J. Crank, D. H. Malan. The combustion of wood. Part I. Proceedings of the Cambridge Philosophical Society 42(1946)., 166–182.

[3] A. F. Roberts, G. Clough. Thermal degradation of wood in an inert atmosphere. In: Proceedings of the ninth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh,. 1963.  158–167.

[4] W. D. Weatherford and D. M. Sheppard, 10th int. Symposium on Combustion, the Combustion Institute, Pitts., (1965), 897

[5] E. R. Tinney, The combustion of wood dowels in heated air. In: Proceedings of the 10th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, .1965.  925–930

[6] T. Matsumoto, T. Fujiwara and J. Kondo, 12th int. Symposium on combustion, the combustion institute, pitts., (1969),.515.

[7] A. F. Roberts. 13th Int. Symposium on Combustion, The Combustion Institute, Pitts. , (1971). 893.

[8] H. C. Kung. A mathematical model of wood pyrolysis. Combustion and Flame 18(1972)., 185–195.

[9] P. S. Maa, and R. C. Bailie. Combustion Science and Technology, 7(1973), 257.

[10] E. J. Kansa, H. E. Perlee and R. F. Chaiken, R. Mathematical model of wood pyrolysis including internal forced convection. Combustion and Flame 29(1977), 311–324.

[11] W. R. Chan, M. Kelbon and B. B. Krieger, Modeling and experimental verification of physical and chemical processes during pyrolysis of large biomass particle. Fuel 64(1985.), 1505–1513.

[12] C. A. Koufopanos, N. Papayannakos, G. Maschio and A. Lucchesi. Modelling of the pyrolysis of biomass particles. Studies on kinetics, thermal andheat transfer e4ects. The Canadian Journal of Chemical Engineering 69(1991.), 907–915.

[13] C. K. Lee, R. F. Chaiken, J. M. Singer. Charring pyrolysis of wood in 0res by laser simulation. In: Proceedings of the 16th Symposium (International) on Combustion. The Combustion Institute: Pittsburgh,. 1976, 1459–1470.

[14] K. Miyanami, L. S. Fan,L. T. Fan and W. P. Walawender. A mathematical model for pyrolysis of a solid particle—effects of the heat of reaction. The Canadian Journal of Chemical Engineering 55(1977)., 317–325.

[15] L. T. Fan, L. S. Fan,K. Miyanami,, T. Y. Chen, and W. P. Walawender. A mathematical model for pyrolysis of a solid particle—effects of the Lewis number. The Canadian Journal of Chemical Engineering 55(1977)., 47–53.


[16] G. M. Simmons and M. Gentry. Particle size limitations due to heat transfer in determining pyrolysis kinetics of biomass. J. Anal. and Appl. Pyrolysis, 10(1986),117-127.

[17] J. Villermaux,B. Antoine., J. Lede, F. Soulignac. A new model for thermal volatilization of solid particles undergoing fast pyrolysis. Chemical Engineering Science 41(1986),, 151–157.

[18] C. Di Blasi. Analysis of convection and secondary reaction effects within porous solid fuels undergoing pyrolysis. Combustion Science and Technology 90(1993),, 315–340.

[19] M. C. Melaaen. and M. G. Gronli.. Modeling and simulation of moist wood drying and pyrolysis. In: Bridgwater, A.V., Boocock, D.B.G. (Eds.), Developments in Thermochemical Biomass Conversion. Blackie, London,  1997, 132–146.

[20] R. K. Jalan and V. K. Srivastava.. Studies on pyrolysis of a single biomass cylindrical pellet–kinetic and heat transfer effects. Energy Conversion and Management 40 (1999),, 467–494.

[21] M. R. Ravi, A.  Jhalani., S. Sinha andA. Ray. “Development of a semi-empirical model for pyrolysis of an annular sawdust bed”. Journal of Analytical and Applied Pyrolysis, 71(2004): 353-374.

[22] B. V. Babu and A. S. Chaurasia. Modeling for pyrolysis of solid particle: kinetics and heat transfer effects. Energy Conversion and Management 44(2003), 2251–2275.

[23] P. N. Sheth and  B. V. Babu.   Kinetic Modeling of the Pyrolysis of Biomass National Conference on Environmental Conservation, Pilani, India; 2006, 453-458.

[24] Y. B. Yang, A. N.  Phan, C.  Ryu, V. Sharifi. andJ. Swithenbank, Mathematical modelling of slow pyrolysis of segregated solid wastes in a packed-bed pyrolyser Elsevier Journal of fuel.2006.

[25] C. Mandl, I. Obernberger and F. Biedermann.Updraft fixed-bed gasification of softwood pellets: mathematical modelling and comparison with experimental data  In: proceedings of the 17, European Biomass Conference & Exhibition Hamburg, Italy,  2009.

[26] P. Weerachanchai, C. Tangsathitkulchai and M. Tangsathitkulchai. Comparison of Pyrolysis Kinetic Model for Thermogravimetric analysis of Biomass. Suranree Journal of Tecnologies 17(4) (2010), 387-400.

[27] K. Slopiecka, P. Bartocci and F. Fantozzi. Thermogravimetric analysis and Kinetic study of poplar wood pyrolysis, 3rd International Conference on Applied Energy, Perugia, Italy; 2011, 1687-1698.

[28] C. A. Zaror “Studies of the pyrolysis of wood at low temperatures”. Ph.D Dissertation, University of Lordon, 1982

[29] S. J. Ojolo, C. A. Osheku  and M. G. Sobamow.  Analytical Investigations of Kinetic and Heat Transfer in Slow Pyrolysis of a Biomass Particle.  Int. Journal of Renewable Energy Development 2 (2) 2013: 105-115

[30] M. Bidabadi, S. A. Mostafavi, F. F. Dizaji, B. H. Dizaji. An analytical model for flame propagation through moist lycopodium particles with non-unity Lewis number [J]. International Journal of Engineering, 27(5), 2014, 793−802.

[31] B. H. Dizaji, M. Bidabadi. Analytical study about the kinetics of different processes in pyrolysis of lycopodium dust [J]. Journal of Fuel and Combustion, 2014, 6(2): 13−20. (in Persian)

[32] J. Lédé, and O. Authier.  Temperature and heating rate of solid particles undergoing a thermal decomposition. Which criteria for characterizing fast pyrolysisJournal of Analytical and Applied Pyrolysis, 113 (2015)1–14

[33] R. Font., A. Marcilla., E. Verdu and J. Devesa,, Kinetics of the pyrolysis of almond shells and almond shells impregnated with COCl2 in a Fluidized bed reactor and in a Pyroprobe 100. Industrial and Engineering Chemistry Research 29 (1990)., 1846–1855.

[34] F. Shafizadeh and P. P. S.Chin. Thermal deterioration of wood. ACS Symposium Series 43(1977), 57–81.

[35] F. Thurner andU. Mann. Kinetic investigation of wood pyrolysis. Industrial andEngineering Chemical Process Design and Development 20(1981), 482–488.

[36] A. M. C. Janse, A. M. C Westerhout and W. Prins. “Modelling of flash pyrolysis of a single wood particle”. Chemical Engineering and Processing, 39(2000), 239-252.

[37] V. K. Srivastava, Sushil and R. K Jalan.  Prediction of Concentration in the Pyrolysis of Biomass Materials-II. Energy Conversion and Management 37(4) (1996), 473-483.

[38] C. K. Liden, F. Berruti., D. S. Scott. “A kinetic model for the production of liquids from the flash pyrolysis of biomass”. Chem. Eng.Commun. 65(1988), 207–221.

[39] N. Prakash and T. Karunanithi. “Kinetic Modelling in Biomass pyrolysis – a review”. Journal of applied sciences research, 4(12) (2008), 1627-1636.

[40] C. Branca and C. Di Blasi . Kinetics of the isothermal degradation of wood in the temperature range, 528-708 K. Journal of Analytical and Applied Pyrolysis, 67(2003),  207-219.

[41] J. P. Holman. “Heat transfer” Sixth Edition, McGraw-Hill Book Company, (1986)