化学工学
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充填層の温度分布解式について
若尾 法昭矢木 栄
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ジャーナル フリー

1959 年 23 巻 3 号 p. 161-163

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In a cylindrical packed tube heated under the uniform wall temperature, the partial differential equation for the temperature in the steady state is given by Eq. (1).
However, when no chemical reaction takes place, Eq. (1)reduces to Eq. (1') with the assumption thatCp G is uniform over the cross section and ke, r and ke, z are uniform within the bed.
The solutions can be obtained by applying the finite Hankel transform with respect to. In case of semi-infinite cylinder, Eq. (2) representing the boundary condition at the bed inlet and Eq. (3) representing the boundary condition at the inside wall surface, are applied to Eq. (1'). The solution is given by Eqs. (6) and (7), where ξi is the root of Eq. (4). On the other hand, in case of finite cylinder, Eq. (10) which stands for the bed outlet condition should be employed together with Eqs. (2) and (3), in solving Eq. (1'). The solution is shown by Eqs. (6) and (11).
The temperature at the center axis of the packed tube tc and the mixed-mean temperature over the cross section tm are represented by Eqs. (8) and (9), respectively, which are modified forms of Eq. (6).
However the solution for the temperature distribution in the finite cylinder will be valid for any value of δ, Eq. (11) is nearly equal to Eq. (7) when δ is less than 30 or so.
The value of δ is smaller than 10 for the usual packed beds14), consequently, it may be concluded that Eqs. (6) and (7) are applicable enough, regarding the packed bed as the semi-infinite cylinder.
In case the flow-rate is relatively high, k becomes small, and then Eqs. (6) and (7) are nearly equal to Eq. (13) obtained by Maeda et al4) and Marshall et al1), in which equation the axial heat conduction is neglected. But it should be pointed that Eqs. (6) and (7) serve as a good solution for the low flow-rate range, because k is not so small in this range.
When chemical reaction approximated by q=q0·exp[-αl] takes place, the temperature distribution is reprerented by Eq. (14), assuming the packed bed as the semi-infinite cylinder.

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