Design Formulae for Mingled Shell-side stream P M V Subbarao Professor Mechanical Engineering Department I I T Delhi A Confluence Model for A Circuitous Flow ……

Multiplicative Participation Model: A Multiplicative Relation is always an Exact Function, also called as Pffafian Function. A Best way to represent Characteristics of A Thermodynamic System. Vlid Model for Mingled Flow

Flow Fractions The fractions of the total flow represented by these five streams is a strong function of baffle geometry and shell side flow conditions. Sophisticated thermal design software packages for STHE are required to predict the flow fractions. The five streams are acting like parallel network and flow along paths of varying hydraulic resistances. The flow fractions will be such that the pressure drop of each stream is identical, since all the streams begin and end at the inlet and outlet nozzles. Subsequently, based upon the thermal efficiency of each of these streams, the overall shell side stream efficiency and thus the shell side heat-transfer coefficient are established.

The Role of Fluid Viscosity The shell side fluid viscosity also affects stream analysis profoundly. In addition to influencing the shell side heat transfer and pressure drop performance, the stream analysis also affects the mean temperature difference (MTD) of the exchanger. It is important to realize that the LMTD and F factor concept assumes that there is no significant variation in the overall heat-transfer coefficient along the length of the shell. In the case of cooling of a viscous liquid — as the liquid is cooled, its viscosity increases, and this results in a progressive reduction in the shellside heat-transfer coefficient. In this case, the simplistic overall MTD approach will be inaccurate, and the exchanger must be broken into several sections and the calculations performed zone-wise.

The Performance of Non B Streams All the streams other than B affect the performance of the essential B stream. The first effect of the various streams is that they reduce the B stream and therefore the local heat transfer coefficient. Secondly, they change the shell-side temperature profile. The Delaware method lumps these two effects together into a single correction.

Bell’s Development Bell (1963) developed therefore Delaware method in which correction factors were introduced for the following elements: Leakage through the gaps between the tubes and the baffles and the baffles and the shell, respectively. Effect of the baffle configuration (i.e., a recognition of the fact that only a fraction of the tubes are in pure cross flow). Bypassing of the flow around the gap between the tube bundle and the shell. Effect of adverse temperature gradient on heat transfer in laminar flow.

The Rating Method Delaware method is a rating analysis. In a rating problem, the process specifications are given: The flow rates, outlet temperatures, inlet temperatures, physical properties, fouling characteristics, and geometrical parameters of the heat exchanger which are the shell inside diameter, the outer tube limit, the tube diameter, the tube layout, the baffle spacing and the baffle cut are all given. The shell inside diameter value found before in Kern method (or other methods) is used as the input data The length & Pressure drop are calculated.

Tube length definitions

Basic geometrical Features D otl : Diameter of circle touching the outer surface of outermost tubes. D ctl : Diameter of circle passing through the centers of of outermost tubes.

Angles of The sectors  ctl : The angle intersecting D ctl due to baffle cut.  ds : The angle intersecting D s due to extended baffle cut.

Shell-side heat transfer coefficient Where h i is heat transfer coefficient for ideal cross flow past a tube bank. J c : Segmental baffle window correction factor J l : Correction factor for baffle leakage effects for heat transfer J b : Correction factor for bundle bypass effects for heat transfer J s : Heat transfer correction for unequal baffle spacing at inlet and/or outlet. J r : Correction factor for adverse temperature gradient in laminar flow

Heat transfer coefficient for Ideal Cross Flow

Area for Ideal Cross Flow

Selection of Shell Diameter A simple but reasonably accurate correlation was developed by Bell’s Group for single pass. CL is tube layout constant, CL =0.87 for 30º and 60º layouts or CL=1.0 for 45º and 90º layouts. For multipass arrangement, a correction factor ψ n must be used to account for the decrease of tube count due to tube pass

Where Shell-Side Reynolds Number

Coefficients of Correlations