Open Access

ARTICLE

Analytical Solution of the Thermal Behavior of a Circulating Porous Heat Exchanger

R. Henda¹, W. Quesnel², Z. Saghir³

1 School of Engineering, Laurentian Univ., Sudbury, ONCanada
2 Xstrata Plc, Technology Center, Falconbridge, ONCanada
3 Dept. Mechanical Engineering, Ryerson Univ., Toronto, ON Canada

Fluid Dynamics & Materials Processing 2008, 4(4), 237-244. https://doi.org/10.3970/fdmp.2008.004.237

Abstract

The transient thermal behavior of a two-dimensional circulating porous bed is analytically investigated. A one-energy equation model, representing both the gas and solid phases via a unified temperature, is employed to describe the thermal behavior of the circulating bed. The latter is essentially a tube and shell heat exchanger commonly used in technologically important applications. The model equation is transformed into a simpler set of partial differential equations using an analytical procedure. The analytical solution, based on the method of separation of variables and the principle of superposition, is formulated for the calculation of the temperature distribution in the radial and axial directions of the bed. The temperature distribution can be determined under different process parameters and conditions. Convergence criteria of the solution are derived for typical process conditions. The developed closed-form solution of the transient one-equation energy model provides a simple and convenient means for estimating the thermal behavior of the circulating bed.

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