A. General Method of Calculation

In the applications referred to in Section 201, the fluid flowing through the packed bed has, typically, to be processed, and the solids help to do this in an efficient way. In many cases, however, the solids themselves are the product to be treated thermally by contact with a heat exchanger surface. The heat transfer coefficient α can be expressed in general form as

\[\label{eq1} \frac{1}{\alpha}=\dfrac{1}{\alpha_{\rm ws}}+\dfrac{1}{\alpha_{\rm bed}}\tag{1}\,,\]

with

\[\label{eq2} \alpha_{\rm bed}=\dfrac{2}{\sqrt{\pi}}\dfrac{\sqrt{(\lambda\rho c)_{{\rm bed},i}}}{\sqrt{t_{j}}}f(\mbox{Ph})\tag{2}\]

for particles of aluminum silicate, , : emissivities of wall, respectively, bed, = ): radiation coefficient of the black body]. For the modified mean-free path of the gas molecules , can be applied.