Packed beds radiative conductivity

J. D. Lu, G. Flamant, and B. Variot, Theoretical Study of Combined Conductive, Convective and Radiative Heat Transfer Between Plates and Packed Beds, Int. J. Heat Mass Transfer (37/5) 727, 1994. 

Here the numerical constants employed are consistent with in BTU/h —°R, T is in °R, h is the solid-gas heat transfer coelScient [c.f. equation (7-83)], Kg the thermal conductivity of the solid phase, Npe the mass Peclet number, G the mass velocity, Cp the heat capacity, dp the particle diameter, and e is the bed porosity. The second term in brackets represents the radiative heat transfer contribution to the apparent thermal conductivity this is normally negligible for operation at less than 300-350 °C. The quantity / is a surface emissivity factor that normally can be estimated as 0 < / <0.1 (see Argo and Smith). Keep in mind that equation (7-153) is for gas flow in packed beds with Npe < 40. Other situations are discussed by both Beck, and Argo and Smith. Note also that, with the possible exception of /, there are no adjustable parameters in equation (7-153). Since the radiative contribution is normally quite small except at very elevated temperatures, a typical working form of equation (7-153) is... 

The combined conduction and radiation heat transfer through a packed bed of spheres is more often studied because of its practical importance. The quasi-homogeneous theories predict that ETC (fee) is the sum of the effective conductivity feg,c without radiation contributions and the radiative conductivity fer without conduction contributions (Vortmeyer, 1978). That is... 

The radiative heat factor has been calculated using a cubic array packing with a void fraction e = (0.5 — 0.35). The effective thermal conductivity involving the void fraction, which is frequently used in estimating the bed heat transfer, is expressed as (Schotte, 1960)... 

Notably, the approach has taken into account almost aU the known heat transfer mechanisms including particle-fluid convection, particle-particle conduction, and radiative heat transfer between solid particles and surrounding environment. It can be tested through various comparisons of the predicted and measured results. The approach has a good capability in describing heat transfer in packed and fluidized beds at a particle scale. 

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