ARTICLE:

• DERIVATION AND VALIDATION OF TRANSPORT EQUATION FOR DISPERSION HEAT FLUX IN POROUS MEDIA  download article

Akira Nakayama
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432-8561, Japan

F. Kuwahara
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432 Japan

T. Nakayama
Shizuoka University, Japan

ABSTRACT

In this study, the gradient diffusion hypothesis for the thermal dispersion heat flux in porous media has been examined in terms of its transport equation derived from the Navier-Stokes and energy equations. It has been shown that the differential transport equation reduces to an algebraic transport equation as we drop the spatial transport terms. The gradient diffusion expression usually adopted for the thermal dispersion heat flux can naturally be generated from this algebraic transport equation. Taylor-Aris diffusion problem, namely, a macroscopically unidirectional flow through a tube, has been considered to determine the unknown model constants. It has been found that Taylor's expression for the axial dispersion is obtainable as we assume adiabatic tube walls. Both laminar and turbulent flow cases are investigated to obtain two distinct limiting expressions for low and high Peclet number regimes. The results obtained for the tube flow are translated into the case of flow in a packed bed using an equivalent tube diameter concept, supported by our LES study on a periodic porous structure. The resulting expression for the high Peclet number case agrees well with the empirical formula.

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