Session: 12-08-02: Computational Heat Transfer and Applications II

Paper Number: 164172

Prediction Model of Heat Transfer Coefficients of Flowing Granular Media In Smooth Tubes 

This investigation presents an effective method for determining the heat transfer rate in granular media flowing through smooth tubes under a uniform wall heat flux boundary condition. Central to this approach is the application of accurate equations to evaluate the thermophysical properties of the medium in the critical region near the heat transfer surface—specifically, thermal conductivity, density, specific heat, and voidage.
An efficient numerical finite element technique is employed to solve the energy equation within this boundary layer framework, accounting for the influence of the surface on the local packing of the granular bed. The behavior of particles in the core of the flow is treated as homogeneous. Local time-averaged and surface-mean heat transfer coefficients are predicted for various granular materials with different interstitial gases. The results are compared with predictions from other theoretical methods and available experimental data.
For predictions of heat transfer coefficients of surfaces immersed in moving packed beds, there are two distinct general approaches: the homogeneous approach and the discrete particle model. Many investigators have proposed modifications to these basic models to achieve better agreement with experimental data. The homogeneous model has recently been modified to account for the presence of the surface and its effect on the thermophysical properties of the bulk material near the wall.
In the present model, the packet theory of heat transfer is adapted to account for the surface's presence and its effect on local voidage. This is achieved by introducing a property boundary layer concept, which has been found to be physically justified. The bed is considered to consist of a region of higher voidage within one particle diameter of the cylindrical heat transfer surface, and a core region representing the bulk of the bed. The model is based on the following assumptions: (1) Transient heat transfer occurs in a disk of the granular media that contacts the hot surface. (2) The region adjacent to the wall has higher voidage, which alters the local effective thermophysical properties, such as density, specific heat, and thermal conductivity. (3) The variation in voidage is confined to within one particle diameter from the wall in any plane perpendicular to the channel’s longitudinal axis. (4) The core of the bed has a constant voidage, and the temperature difference between the gas and solid particles at any point in the bed is negligible due to the large exposed particle surface area. (5) Interparticle heat transfer due to thermal radiation is negligible, as the maximum temperature of the flowing media in the experiment was about 100°C and radiation considered above 400°C. (6) A constant heat flux is maintained on the tube surface.
The present analysis yields predictions for local time-averaged and surface mean heat transfer coefficients for flows of copper/air, sand/air, sand/helium, glass/carbon dioxide, and glass/helium. Notably, the predictions align well with experimental data for local Nusselt number measurements across a broad range of Fourier numbers. This agreement extends to data on controlled residence times found in the literature. Importantly, the developed model does not rely on assumed film properties or empirical approximations. The numerical solutions derived from this framework are straightforward and user-friendly, facilitating practical application.

Presenting Author: Mohamed Alsharif Consolidated Nuclear Security

Presenting Author Biography: He has over 50 years of experience and PhD in Mechanical Engineering from the University of Tennessee. He has had a long career including supporting work for NASA and the Department of Energy.

Authors:

Mohamed Alsharif Consolidated Nuclear Security