A theoretical study of heat transfer to flowing granular materials

• Autorzy: Massoudi M. , Anand N. K.
• Języki publikacji: EN

Abstrakty

EN

The mechanics of flowing granular materials such as coal, sand, agricultural products, fertilizers, dry chemicals, metal ores, etc., and their flow characteristics have received considerable attention in recent years. In a number of instances these materials are also heated prior to processing or cooled after processing. In this paper, the governing equations for the flow of granular materials, taking into account the heat transfer mechanism are derived using a continuum model proposed by Rajagopal and Massoudi (1990). For a fully developed flow down a heated inclined plane, the governing equations reduce to a system of non-linear ordinary differential equations for the case where the material properties are assumed to be constants. The boundary value problem is solved numerically and the results are presented for the volume fraction, velocity, and temperature profiles.

Słowa kluczowe

EN

granular materials; convective heat transfer; inclined fully developed flow; continuum mechanics

PL

mechanika; materiały ziarniste; transfer ciepła; przepływ

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2004
• Tom: Vol. 9, no 2
• Strony: 383--398
• Opis fizyczny: Bibliogr. 66 poz., wykr.

Twórcy

autor

Massoudi M.

• U.S. Department of Energy, National Energy Technology Laboratory P.O. Box 10940, Pittsburgh, PA 15236, USA

autor

Anand N. K.

• Department of Mechanical Engineering, Texas A&M University College Station, Texas 77843, USA

Bibliografia

• [1] Ahmadi G. (1982): A generalized continuum theory for granular materials. - Int. J. Non-Linear Mech., vol. 17, pp.21-33.
• [2] Ahn H., Brennen C.E. and Sabersky R.H. (1991): Measurements of velocity fluctuation, density, and stresses in chute flows of granular materials. - J. Appl. Mech.,Transactions of ASME, vol.58, pp.792-803.
• [3] Ahn H., Brennen C.E. and Sabersky R.H. (1992): Analysis of the fully developed chute flows of granular materials. - J. Appl. Mech., Transactions of ASME, vol.59, pp.109-119.
• [4] Ascher U., Christianson J. and Russel R.D. (1981): Collocation software for boundary value ODE’s. - ACM Transactions on Mathematical Software, vol.7, No.2, pp.209-222.
• [5] Bagnold R.A. (1954): Experiments on a gravity free dispersion of large solid spheres in a Newtonian fluid under shear. - Proc. Roy. Soc. London, vol.225, pp.49-63.
• [6] Bagnold R.A. (1956): The flow of cohesionless grains in fluids. - Phil. Trans. Roy. Soc. London, Series A, vol.249, pp.219-232.
• [7] Boyle E.J. and Massoudi M. (1990): A theory for granular materials exhibiting normal stress effects based on Enskog’s dense gas theory. - Int. J. Engng. Sei., vol.28, No. 1261-1275.
• [8] Brown R.L. and Richards J.C. (1970): Principles of Powder Mechanics. - London: Pergamon Press.
• [9] Campbell C. (1990): Rapid granular flows. - Annual Rev. Fluid Mech., vol.22, pp.57-92.
• [10] Cowin S.C. (1974a): A theory for the flow of granular material. - Powder Tech., vol.9, pp.61-69.
• [11] Cowin, S.C. (1974b): Constitutive relations that imply a generalized Mohr-Coulomb criterion. - Acta Mechanica, vol.20, pp.41-46.
• [12] de Gennes P.G. (1998): Reflections on the mechanics of granular matter. - Physica A, vol.261, pp.267-293.
• [13] Drucker D.C. and Prager W. (1952): Soil mechanics and plastic analysis or limit design. - Quart. Appl. Math., vol. 10, pp.157-165.
• [14] Elaskar S. A. and Godoy L.A. (1998): Constitutive relations for compressible granular materials using non-Newtonian fluid mechanics. - Int. J. Mech. Sci., vol.40, pp. 1001-1018.
• [15] Goddard J.D. (1999): Granular dilatancy and the plasticity of glassy lubricants. - Ind. Eng. Chem. Res., vol.38, pp.820-822.
• [16] Goldhirsch I. and Sela N. (1996): Origin of normal stress differences in rapid granular flows. - Physical Rev. E, vol.54, pp.4458-4461.
• [17] Goodman M.A. and Cowin S.C. (1971): Two problems in the gravity flow of granular materials. - J. Fluid Mech., vol.45, pp.321-339.
• [18] Goodman M.A. and Cowin S.C. (1972): A continuum theory for granular materials. - Arch. Rat. Mech. and Anal., vol.44, pp.249-266.
• [19] Gudhe R., Yalamanchili R.C. and Massoudi M. (1994a): Flow of granular materials down a vertical pipe. - Int. J. Non- Linear Mech., vol.29, pp.1-12.
• [20] Gudhe R., Rajagopal K.R. and Massoudi M. (1994b): Heat transfer and flow of granular materials down an inclined plane, Acta Mechanica, vol. 103, pp.63-78.
• [21] Hagen G. (1852): Berlin Monaster Akad. Wiss., pp.35-42.
• [22] Hui K., Haff P.K., Ungar J.E. and Jackson R. (1984): Boundary conditions for high-shear grain flows. - J. Fluid Mech,, vol. 145, pp.223-233.
• [23] Hutter K., Szidarovszky F. and Yakowitz S. (1986a): Plane steady shear flow of a cohesionless granular material down an inclined plane: A model for flow avalanches part-1: Theory. - Acta Mechanica, vol.63, pp.87-112.
• [24] Hutter K., Szidarovszky F. and Yakowitz S. (1986b): Plane steady shear flow of a cohesionless granular material down an inclined plane: A model for flow avalanches part-11: Numerical results. - Acta Mechanica, Vol.65, pp.239-261.
• [25] Hutter K. and Rajagopal K.R. (1994): On the flows of granular materials. - Continuum Mech. Thermodyn., vol.6, pp.81-139.
• [26] Jenkins J.T. and Savage S.B. (1983): A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles, J. Fluid Mech., vol.130, pp.187-202.
• [27] Jenike A.W. (1964): Steady gravity flow of frictional-cohesive solids in converging channels. - J. Appl. Mech., vol.31, pp.5-11.
• [28] Johnson P.C. and Jackson R. (1987): Frictional-collisional constitutive relations for granular materials with application to plane shearing. - J. Fluid Mech., vol. 176, pp.67-93.
• [29] Johnson G., Massoudi M. and Rajagopal K.R. (1991a): Flow of a fluid-solid mixture between flat plates. - Chemical Engng Science, vol.46, pp.1713-1723.
• [30] Johnson G., Massoudi M. and Rajagopal K.R. (1991b): Flow of a fluid infused with solid particles through a pipe. – lnt. J. Engng. Science, vol.29, pp.649-661.
• [31] Jyotsna R. and K. Kesava Rao (1997): A frictional-kinetic model for the flow of granular materials through a wedge-s hopper. - J. Fluid Mech., vol.346, pp.239-270.
• [32] Marcus R.D., Leung L.S., Klinzing G.E. and Rizk F. (1990): Pneumatic Conveying of Solids. - London: Chapman and Hall.
• [33] Massoudi M. and Phuoc T.X. (1999): Flow and heat transfer due to natural convection in granular materials. - Int. J. Non-Linear Mech., vol.34, pp.347-359.
• [34] Massoudi M., Rajagopal K.R. and Phuoc T.X. (1999): On the fully developed flow of a dense particulate mixture in a pipe. Powder Tech., vol. 104, pp.258-268.
• [35] Massoudi M. (2001): On the flow of granular materials with variable material properties. - Int. J. Non-Linear Mech., vol.36, pp.25-37.
• [36] McTigue D.F. (1982): A non-linear constitutive model for granular materials: Applications to gravity flow. - J. Appl. Mech., vol.49, pp.291-296.
• [37] Mehta A. (Ed.) (1994): Granular Matter. - New York: Springer-Verlag.
• [38] Muller I. (1967): On the entropy inequality. - Arch. Rat. Mech. and Anal., vol.26, pp.l 18-141.
• [39] Nedderman R.M. (1992): Statics and Kinematics of Granular Materials. - Cambridge University Press.
• [40] Nunziato J.W., Passman S.L. and Thomas J.P. Jr. (1980): Gravitational flows of granular materials with incompressible grains. - J. Rheology, vol.24, pp.395-420.
• [41] Passman S.L., Nunziato J.W., Bailey P.B. and Thomas J.P. Jr. (1980): Shearing flows of granular materials. - J. Engrg. Mech. Div., ASCE, vol. 106, pp.773-783.
• [42] Passman S.L., Nunziato J.W., Bailey P.B. and Reed K.W. (1986): Shearing motion of a fluid-saturated granular material. J. Rheology, vol.30, pp.167-192.
• [43] Patton J.S., Sabersky R.H. and Brennen C.E. (1986): Convective heat transfer to rapidly flowing granular materials. - Int. J. Heat Mass Transfer, vol.29, pp. 1263-1269.
• [44] Plasynski S.L, Peters W.C. and Passman S.L. (1992): The Department of Energy Solids Transport, Multiphase Flow Program. - Proc. of the NSF-DOE Joint Workshop on Flow of Particulates and Fluids, Gaithersburg, September 16-18.
• [45] Rajagopal K.R. and Massoudi M. (1990): A Method for Measuring Material Moduli of Granular Materials: Flow in an Orthogonal Rheometer. - Topical Report, DOE/PETC/TR-90/3.
• [46] Rajagopal K.R., Troy W.C. and Massoudi M. (1992): Existence of solutions to the equations governing the flow of granular materials. - European J. Mech., B/Fluids, vol. 11, pp.265-276.
• [47] Rajagopal K.R., Massoudi M., and Wineman A.S. (1994): Flow of granular materials between rotating disks. - Mech. Research Comm., vol.21, pp.629-634.
• [48] Reynolds O. (1885): On the dilatancy of media composed of rigid particles in contact with experimental illustrations. - Phil. Mag., Series 5, vol.20, pp.469-481.
• [49] Reynolds O. (1886): Experiments showing dilatancy, a property of granular material, possibly connected with gravitation. Proc. Roy. Inst, of Gr. Britain, vol.11, pp.354-363.
• [50] Reiner M. (1945): A mathematical theory of dilatancy. - American J. Math., vol.67, pp.350-362.
• [51] Richman M.W. and Marciniec R.P. (1990): Gravity-driven granular flows of smooth, inelastic spheres down bumpy inclines. Transactions of ASME, J. Appl. Mech., vol.57, pp. 1036-1043.
• [52] Savage S.B. (1979): Gravity flow of cohesionless granular materials in chutes and channels. - J. Fluid Mech., vol.92, pp.53-96.
• [53] Savage S.B. (1984): The mechanics of rapid granular flows. - Adv. in Applied Mech., vol.24, pp.289-366.
• [54] Sayed M. and Savage S.B. (1983): Rapid gravity flow of cohesionless granular materials down inclined chutes. - ZAMP, vol.34, pp.84-100.
• [55] Soo S.L. (1967): Fluid Dynamics of Multiphase Systems. - Blaisdell.
• [56] Sokolovski V.V. (1965): Statics of Granular Media. - Oxford: Pergamon.
• [57] Spelt J.K., Brennen C.E. and Sabersky R.H. (1982): Heat transfer to flowing granular material. - Int. J. Heat Mass Transfer, vol.25, pp.791-796.
• [58] Spencer A.J.M. (1964): A theory of the kinematics of ideal solids under plane strain conditions. - J. Mech. Phys. Solids, vol. 12, pp.337-351.
• [59] Spencer, A.J.M. (1986): Instability of steady shear flow of granular materials. - Acta Mechanica, vol.64, pp.77-87.
• [60] Stepanoff A.J. (1969): Gravity Flow of Bulk Solids and Transportation of Solids in Suspension. - New York: John Wiley & Sons Inc.
• [61] Sullivan W.N. and Sabersky R.H. (1975): Heat transfer to flowing granular media. - Int. J. Heat Mass Transfer, vol.18, pp.97-107.
• [62] Thornton C. and Barnes D.J. (1986): Computer simulated deformation of compact granular assemblies. - Acta Mechanica, vol.64, pp.45-61.
• [63] Truesdell C. and Noll W. (1965): The non-linear field theories of mechanics, In: Handbuck Der Physik, III/I, (Flugge, Ed.). - Springer-Verlag.
• [64] Uhl V.W. and Root W.L. (1967): Chem. Engng. Prog., vol.63, p.81.
• [65] Walton O.R. and Braun R.L. (1986a) Stress calculations for assemblies of inelastic spheres in uniform shear. - Acta Mechanica, vol.63, No. 1-4, pp.73-86.
• [66] Walton O.R. and Braun R.L. (1986b): Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. - J. Rheology, vol.30, pp.949-980.