Page 137 - Modelling in Transport Phenomena A Conceptual Approach

4.6. FLOW IN PACKED BEDS 117

= (0.799 - m) = - 0.644
1’3
Hence the average porosity of the bed is

0.476
E = 1.231 - 0.644 + - 0.746
=
3
b) Equation (3) is rearranged as
F(E) = e3 - 0.476 e2 + 2.455 E - 1.979 = 0 (4)

From Eq. (A.7-18) the iteration scheme is

The derivative of the function F is given by

dF
- 3 c2 - 0.952 E + 2.455
=
de
Assuming a starting value of 0.7, the calculation scheme is
0.151
€2 = 0.7 + - 0.746
=
3.259
0.003
€3 = 0.746 - - 0.745
=
3.414
Since €2 M €3, the value of porosity is 0.746.
4.6.2 Heat Transfer Correlation

Whitaker (1972) proposed the following correlation for heat transfer in packed beds:

(4.6-6)

The Nusselt number in Eq. (4.66) is defined by

(4.6-7)

Equation (4.66) is valid when