The fluid velocity across the tube bundle in the shell of a heat exchanger with segmental baffles is mostly dictated from hydrodynamic considerations. This determines the distance between two adjacent baffles for a given shell-side flow rate and given geometry and tube bundle dimensions. While keeping the distance between the baffles effectively constant, the designer chooses the length of the tube bundle and the corresponding number of baffles to fulfil the given thermal load. A heat exchanger with a constant baffle spacing and a variable bundle length has effectively a constant cell effectiveness. The influence of a stepwise increase in the number of the segmental baffles, coupled with a stepwise increase in the number of the shell-side passes, on the exchanger effectiveness can be easily determined for a heat exchanger with two tube-side passes by means of the procedure described in Section 113. The heat exchanger effectiveness can be successively determined after each shell-pass addition from the previously calculated heat exchanger effectiveness and the effectivenesses of the additional two cells. Table 1 shows the dependence of the effectiveness of a shell-and-tube heat exchanger with two tube-side passes on the number of the shell-side passes for four different numerical values of the cell effectiveness and equal heat capacity rates of the two streams. In each of the four examined cases, it was assumed that the cell effectiveness remains constant in all cells, while the number of the shell-side passes is increased. The starting case of one shell-side pass corresponds to the case of no baffles; a counter flow between the two coupled cells was assumed in this case (geometry G.2 and geometry G.4 are identical). Furthermore, it was assumed that each additional shell-side pass is always added at the side of the inlet and outlet nozzles of the tube-side stream. A new calculation for the whole heat exchanger after adding a shell-side pass is thus not necessary. Each additional shell-side pass changes the geometry of the heat exchanger either to the geometry G.1 or to the geometry G.2. The results in Table 1 are shown graphically in Figure 1, Figure 2, Figure 3, and Figure 4. The following remarks can be made:

• At the lowest cell effectiveness examined (E_c = 0.1), the heat exchanger effectiveness increases smoothly with increasing number of shell-side passes. The fluctuations in the effectiveness with the variation of the number of the shell-side passes are negligible.
•   With increasing cell effectiveness the heat exchanger effectiveness fluctuates with the change of the number of the shell-side passes. Odd numbers of shell-side passes (geometry G.2) yield higher effectiveness than even numbers (geometry G.1).
•   The fluctuations in the cell effectiveness with varying the number of the shell-side passes become very noticeable at the highest cell effectiveness examined (E_c = 0.4). After already three shell-side passes, the higher and the lower heat exchanger effectiveness values become virtually constant (0.63 and 0.54 respectively). The difference between the two values amounts to about 16%.

Figure 1 Dependence of the heat exchanger effectiveness on the number of shell-side passes for a cell effectiveness of 0.1