Heat transfer in flowing granular materials: The effects of radiation boundary condition

• Autorzy: Massoudi M. , Phuoc T. X.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider the free surface flow of granular materials down an inclined plane. The surface of the inclined is heated and the effects of radation heat transfer at the free surface are studied. It is assumed that the material behaves like a continuum, similar to a compressible non-Newtonian fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations simplify to a system of three non-linear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, etc., are presented.

Słowa kluczowe

EN

granular materials; heat transfer; fully developed inclined flow; radiation boundary condition; viscous dissipation; continuum mechanics

PL

materiałoznawstwo; przenikanie ciepła; materiały sypkie

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2005
• Tom: Vol. 10, no. 3
• Strony: 489--503
• Opis fizyczny: Bibliogr. 36 poz., wykr.

Twórcy

autor

Massoudi M.

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

autor

Phuoc T. X.

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

Bibliografia

• [1] Antony S.J., Hoyle W. and Ding Y. (2004): Granular Materials: Fundamentals and Applications. - Cambridge: The Royal Society of Chemistry.
• [2] Bashir Y.H. and Goddard J.D. (1990): Experiments on the conductivity of suspensions of ionically-conductive spheres. - AIChE J., vol.36, pp.387-396.
• [3] Chamkha A.J. (2000): Effects of heat absorption and thermal radiation on heat transfer in a fluid-panicle flow past a surface in the presence of a gravity field. - Int. J. Therm. Sci., vol.39, pp.605-615.
• [4] Cowin S.C. (1974a): A theory for the flow of granular material. - Powder Tech., vol.9, pp.61-69.
• [5] Cowin S.C. (1974b): Constitutive relations that imply a generalized Mohr-Coulomb criterion. - Acta Mech., vol.20, pp.41-46.
• [6] de Gennes P.G. (1998): Reflections on the mechanics of granular matter. - Physica A, vol.26, pp.267-293.
• [7] Duran J. (2000): Sands, Powders and Grains. - New York: Springer-Verlag.
• [8] Fuchs H.U. (1996): The Dynamics of Heat. - New York: Springer-Verlag, Inc.
• [9] Goldhirsch I. and Sela N. (1996): Origin of normal stress differences in rapid granular flows. - Physical Rev. E, vol.54, pp.4458-4461.
• [10] 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.
• [11] Gudhe R, Rajagopal K.R. and Massoudi M. (1994b): Heat transfer and flow of granular materials down an inclined plane. - Acta Mech., vol.103, pp.63-78.
• [12] Hutter K. and Rajagopal K.R (1994): On the flows of granular materials. - Continuum Mech. Thermodyn., vol.6, pp.81-139.
• [13] Jeffrey DJ. (1973): Conduction through a random suspension of spheres. - Proc. R Soc. Land. A., vol.335, pp.355-367.
• [14] Kaviany M. (1991): Principles of Heat Transfer in Porous Media. - New York: Springer-Verlag.
• [15] Massoudi M. and Anand N.K. (2004): A theoretical study of heat transfer to flowing granular materials. - International Journal of Applied Mechanics and Engineering, vol.9, pp.383-398.
• [16] Massoudi M. and Boyle E.J. (2001): A continuum-kinetic theory approach to the flow of granular materials: The effects of volume fraction gradient. - Int. J. Non-Linear Mech., vol.36, pp.637-648.
• [17] Massoudi M. and Phuoc TX. (1999): Flow and heat transfer due to natural convection in granular materials. - Int. J. Non-Linear Mech., vol.34, pp.347-359.
• [18] Massoudi M. and Phuoc T'X, (2005): Conduction heat transfer and dissipation in the flow of granular materials due to shear. - In press, J. Energy Heat Mass Transfer.
• [19] Massoudi M., Rajagopal K.R. and Phuoc T.X., (1999): On the Jully developed flow of a dense particulate mixture in a pipe. - Powder Tech., vol.104, pp.258-268.
• [20] Mehta A. (Ed.) (1994): Granular matter. - New York: Springer-Verlag.
• [21] Miller J.R. and Weaver P.M. (2003): Temperature profiles in composite plates subject to time-dependent complex boundary conditions. - Composite Structures, vol.59, pp.267-278.
• [22] Na T.Y. (1979): Computational Methods in Engineering Boundary Value Problems. - New York: Academic Press.
• [23] Nedderman RM. (1992): Statics and Kinematics of Granular Materials. - Cambridge: Cambridge University Press.
• [24] Patton J.S., Sabersky RH. and Brennen C.E. (1986): Convective heat transfer to rapidly flowing granular materials. - Int. J. Heat Mass Transfer, vol.29, pp. 1263.
• [25] 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.
• [26] 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.
• [27] 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.
• [28] 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.
• [29] Saldanha da Gama R.M. (2004): On the conduction/radiation heat transfer problem in a body with wavelength- dependent properties. - Appl. Math. Modelling, vol.28, pp.795-816.
• [30] Savage S.B. (1984): The mechanics of rapid granular flows. - Adv. Applied Mech., vol.24, pp.289-366.
• [31] Szeri A.Z. (1998): Fluid Film Lubrication. - Cambridge: Cambridge University Press.
• [32] Szeri A.Z. and Rajagopal K.R. (1985): Flow of a non-Newtonian fluid between heated parallel plates. - Int. J. Non-Linear Mech., vol.20, p.91.
• [33] Truesdell C. (1976): The meaning of viscometry in fluid mechanics. - Annual Rev. Fluid Mech., vol.6, pp.111-146.
• [34] Truesdell C. and Noll W. (1992): The Non-Linear Field Theories of Mechanies. - New York: Springer- Verlag.
• [35] Walton O.R. and Braun R.L. (1986): Stress calculations for assemblies of inelastic spheres in uniform shear. - Acta Mech., vol.63, No.1-4, pp.73-86.
• [36] Wu J.W. and Chu H.S. (1999): Combined conduction and radiation heat transfer in plane-parallel packed beds with variable porosity. - J. Quant. Spectrosc. Radiat. Transfer, vol.61, pp.443-452.