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1

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

Massoudi M., Phuoc T. X.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 3

489-503

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.

2

A theoretical study of heat transfer to flowing granular materials

Massoudi M., Anand N. K.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 2

383-398

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.

3

Normal stress differences in Couette flow of granular materials

Kumar J., Lakshmana Rao C., Massoudi M.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 1

5-16

EN

Normal stress differences, a phenomenon which is exhibited by many non-Newtonian fluids or non-linear elastic materials, also arises in the Couette flow of granular materials. This problem is studied using a continuum model proposed by Rajagopal and Massoudi (1990). For a steady, fully developed condition, the governing equations were reduced to a system of coupled non-linear ordinary differential equations, and the resulting boundary value problem was solved numerically (Kumar et al., 2003). The expression for one of the normal stress differences is derived in this paper and from the values of volume fraction obtained in (Kumar et al., 2003), the normal stress difference is calculated. The effect of material parameters, i.e., dimensionless numbers on the normal stress difference is studied. It is observed that the distribution parameter, "B2" and the density parameter "P" affect the normal stress differences most.

4

Averaged equations for developing flow of a fluid-solid mixture

Massoudi M.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 2

1025-1049

EN

A mathematical description of a mixture of a Newtonian fluid infused with particulate solids is presented within the context of Mixture Theory. In the absence of any thermal effects, the balance of mass and balance of linear momentum equations for each component are averaged over the cross section of the flow to obtain ordinary differential equations describing developing flow between parallel plates. The resulting coupled equations describe the variation of the average velocities and volume fraction in the direction of flow, and represent a simplified approximate set of equations which are used in engineering applications.

5

A non-linear constitutive relation for flowing granular materials

Massoudi M., Rao C. L.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 2

457-471

EN

We study the flow of granular materials down an inclined plane. We assume steady fully developed conditions. The constitutive relation is that of Rajagopal and Massoudi (1990), where the material parameters are given by the theory of Boyle and Massoudi (1990). We do not consider the effects of ?granular temperature? (a measure of the fluctuating component of the velocity of the grains). The material parameters are given in this model as functions of volume fraction, particle diameter, restitution coefficient, and the excluded volume. The momentum equations are non-dimensionalized and the resulting coupled non-linear ordinary differential equations are solved numerically; the results are presented for the volume fraction and velocity profiles for different dimensionless numbers.