Vertical heat transfer

General Characteristics. Energy addition or extraction from fast fluidized beds are commonly accomplished through vertical heat transfer surfaces in the form of membrane walls or submerged vertical tubes. Horizontal tubes or tube bundles are almost never used due to concern with... 

Experiments for verifying the efficiency of heat transfer in the dilute phase were carried out in the equipment shown in Fig. 11 (Kwauk and Tai, 1964). It consisted of two vertical heat transfer columns, i.d. = 300 mm for... 

Another approach is the modify the MILP transshipment model P2 so as to have preferences among multiple global solutions of model P2 according to their potential of vertical heat transfer between the composite curves. Such an approach was proposed by Gundersen and Grossmann (1990) as a good heuristic and will be discussed in section 8.3.3. 

Minimum Number of Matches for Vertical Heat Transfer... 

As we discussed on Section 8.3.2.2, the MILP transshipment model may have several global solutions which all exhibit the same number of matches. To establish which solution is more preferable, Gundersen and Grossmann (1990) proposed as criterion the vertical heat transfer from the hot composite to the cold composite curve with key objective the minimization of the total heat transfer area. 

The vertical heat transfer between the hot and cold composite curves utilizes as a means of representation the partitioning of enthalpy (Q) into enthalpy intervals El). The partitioning into enthalpy intervals has a number of similarities with the partitioning of temperature intervals presented in section 8.3.1.3, but it has at the same time a number of key differences outlined next. 

The modified MILP transshipment model that favors vertical heat transfer is of the following form ... 

Remark 1 Note that the weight factor e has been selected to be the inverse of the total heat exchanged. As a result, the penalty term that corresponds to the nonvertical heat transfer (also called criss-cross heat transfer) is divided by the total heat exchanged, and hence it cannot be more than one. This implies that such an objective function will identify the minimum number of matches and at the same time select the combination of heat loads of the matches that correspond to the most vertical heat transfer. 

Remark 3 Model P4 will provide good results only when the heat transfer coefficients are equal or close in values, since in this case the vertical heat transfer results in minimum heat transfer area. If however, the heat transfer coefficients are different, then nonvertical heat transfer can result in less heat transfer area. Therefore, for such cases the vertical MILP model P4 is not applicable since it will discriminate among multiple global solutions of P2 with the wrong criterion. 

Another implicit assumption in model P4, in addition to favoring vertical heat transfer, is that the minimum total heat transfer area goes hand in hand with the minimum total investment cost solution. It should be emphasized that there exist cases where this is not true. 

Remark 4 Model P4 is applied to each subnetwork, that is after decomposition based on the location of the pinch point(s). If, however, we apply model P4 to overall networks without decomposing them into subnetworks, then the quality of lower bound on the nonvertical heat transfer becomes worse. This is due to the fact that the additional variables and constraints have been applied for the overall heat transfer in each match (ij). As a result they do not provide any direction/penalty for local differences, that is, differences between heat exchange loads versus maximum vertical heat transfer loads at each temperature interval k TI. This deficiency can be remedied by introducing the variables Sik,k TI and the parameters Q k corresponding to each temperature interval k, along with the constraints ... 

With the above data, we can now calculate the maximum vertical heat transfer of each match (ij). 

The same type of information is also provided by the vertical MILP transshipment model discussed in section 8.3.3.3 which discriminates among equivalent number of matches using the assumption of vertical heat transfer. 

The difficulty that arises in the selection of matches task is due to having multiple feasible combinations of matches which satisfy the minimum number of matches target. Discrimination among them can be achieved only via the vertical MILP model which however assumes the vertical heat transfer criterion. 

Minimum Number of Matches for Vertical Heat Transfer, 294 8.4. Decomposition-based HEN Synthesis Approaches, 304... 

During the R D of the upflow type catalyst cooler, using catalyst CRC-1 (pp = 1,700 kg/m), the influence of vertical heat transfer tubes on bed density was investigated by LPEC in a dt 0.36 m cold test model, with 0.04 m o.d. tubes and 0.08-0.2 m shell side equivalent diameters. The gas velocities and solid mass velocities were 1.0—1.6 m/s and 70-180 t/(m2 h), respectively. Average bed density was correlated by the equation... 

Figure 14. Apparent contact angle for rivulet evaporation on vertical heat transfer surface depending on wall superheat.

Heat exchange area can be estimated from the balanced composite curves. The simplest is adopting the hypothesis of counter-current, as well as vertical heat transfer driving force. The total area A. is obtained by summing the differential heat-exchange area in different temperature intervals, as expressed by the relation ... 

The bed-to-surface heat transfer coefficient (about 85 280 W/m °C) by solids convection and radiation is lower in circulating bed AFBC than in bubbling bed AFBC due to the lower bed density and vertical heat transfer surface orientation, and the heat transfer coefficient decreases with increased height. The dilute zone of the furnace is water-walled, with the heat transfer surfaces placed at the perimeter of the rectangular vessel enclosure. Additional vertical heat transfer surface walls or wing walls may be hung within the vessel to increase its heat removal capacity. Another means to increase the heat transfer surface is to place an exter-... 

Emulsion Models To simulate the core-annulus strueture, the cross section in emulsion models is divided into an inner dilute core region where particles are transported upwards, and a denser annular region where partieles descend along the wall, as in Fig. 26, but without the clusters. The thickness of the solid layer along the vertical heat transfer surfaces is often approximated as uniform. However, for membrane wall heat transfer surfaces, the annulus layer tends to be thicker at the fin than at the tube crest (Grace, 1990 Golriz 1992). 

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