Heat-Exchangers

A heat exchanger is a device which transfers heat from one fluid to another. A basic diagram of a heat exchanger is shown in Fig. 5.44, fluid on the hot side of the heat exchanger warms fluid on the cold side. Generally, there are three main designs of heat exchangers  

During design point calculation, pressure drop across the heat exchanger can be kept at a constant value and is defined by the following coefficient  

The heat exchanger outlet pressures can be calculated by the formula  

During ofif-design operation calculations, temperatures of fluids can be calculated based on Backman s equation for known mass flows at heat exchanger inlets. Cold stream temperature can be estimated at the heat exchanger outlet (Toutiet, cow) by the following equation  

The pressure drop coefficient (at both sides—cold and hot) during the off-design operation can be determined based on knowledge of its value at design point and reduced mass flows at both nominal and off-design conditions. 

A stack may generate as much heat as the electrical power. The heat must be dissipated in order to prevent the stack from overheating. The stack of a PEMFC is typically operated at a coolant outlet temperature of less than 75°C to achieve a longer lifetime. The excess heat is released by a heat exchanger. 

A heat exchanger is composed of heat radiation fins and a fan. The coolant flowing in the heat exchanger radiates heat out through the fins, and the radiated heat is sent out of the fuel cell system by the fan. The radiation fins are made with thin metal sheets with large surface areas in order to achieve high heat radiation efficiency. Without the fan, the air temperature around the fins will quickly get close to the coolant temperature after the fuel cell is running for a short time because the heat accumulates inside the fuel cell system s enclosure. Then, the heat that is able to radiate out of the fins will become smaller 

Let us have a look at an example. An electrical heater that generates 5000 W of heat is used as the heat source to simulate the stack. Water is the liquid coolant and its flow rate is 10 L mimL The density and the heat capacity of water are 0.98 g cm- and Cp = 4.18 J g Kr respectively, at around 60°C. The water flow rate is 

The amount of heat dissipated by the heat exchanger is given in Equation 4.21  

Corresponding to a given wall temperature 0, it is desired to attain a steady state temperature distribution Ts z) of the fluid in a specified time interval [0, t ]. For the control to be meaningful, t is less than the time spent by the fluid inside the heat exchanger. A simple heat transfer model of the heat 

The steady state temperature Ts z) is the temperature defined by Equation (1.13) with the time derivative set to zero and T t) replaced with 6. Thus, 

Subject to the satisfaction of Equations (1.13)-(1.15), the optimal control problem is to And the control function T t) that brings in time the final unsteady state fluid temperature closest to the steady state wall temperature. Hence it is desired to minimize the objective functional 

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Of course, some processes do not require a reactor, e.g., some oil refinery processes. Here, the design starts with the sepauration system and moves outward to the heat exchanger network and utilities. However, the basic hierarchy prevails. 

The reactor products are so hot or corrosive that if passed directly to a heat exchanger, special materials-of-construction or an expensive mechanical design would be required. 

One disadvantage of fluidized heds is that attrition of the catalyst can cause the generation of catalyst flnes, which are then carried over from the hed and lost from the system. This carryover of catalyst flnes sometimes necessitates cooling the reactor effluent through direct-contact heat transfer hy mixing with a cold fluid, since the fines tend to foul conventional heat exchangers. 

When recycling material to the reactor for whatever reason, the pressure drop through the reactor, phase separator (if there is one), and the heat exchangers upstream and downstream of the reactor must be overcome. This means increasing the pressure of any material to be recycled. 

Having found the best nonintegrated sequence, most designers would then heat integrate. In other words, the total problem is not solved simultaneously but in two steps. Moving outward from the center of the onion (see Fig. 1.6), the separation layer is addressed first, followed by the heat exchanger network layer. 

Heat Exchanger Network and Utilities Energy Targets... 

The analysis of the heat exchanger network first identifies sources of heat (termed hot streams) and sinks (termed cold streams) from the material and energy balance. Consider first a very simple problem with just one hot stream (heat source) and one cold stream (heat sink). The initial temperature (termed supply temperature), final temperature (termed target temperature), and enthalpy change of both streams are given in Table 6.1. 

TABLE 6.2 Heat Exchange Stream Data for the Flowsheet in Fig. 6.2... 

These rules are both necessary and sufficient to ensure that the target is achieved, providing the initialization rule is adhered to that no individual heat exchanger should have a temperature difference smaller than... 

After maximizing heat recovery in the heat exchanger network, those heating duties and cooling duties not serviced by heat recovery must be provided by external utilities. The outer-most layer of the onion model is now being addressed, but still dealing with targets. 

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