Heat exchangers simplified cases

Heat exchanger cost laws often can be adjusted with little loss of accuracy such that the coefficient c is constant for different specifications, i.e.. Cl = Ca = c. In this case, Eq. (7.23) simplifies to ... 

The contact region is simplified as a cylindrical heated volume with only lateral heat exchange, and it is an optimized case that the heat flow towards the interfaces is neglected. The heat flow Q at a steady state can be given by [82]... 

Several simplified cases may be encountered in heat exchanger design. 

This preheating can be achieved by indirect heat exchange between hot product gases. This is practised in the manufacture of cement clinker. The clinker is cooled in process air, which is thus preheated for the precalcination step. The next calculation example treats a simplified case of this type. 

For a tube with no inner chaimels the boimdary conditions for conversion and temperature simplifies to the gradients being zero at the centre. In the general case with heat exchange to inside and outside channels, this feature is not valid, and the following dimensionless variable is introduced ... 

An important extreme case is the so-called adiabatic reactor. In an adiabatic reactor, no heat exchange takes place with the surroundings, that is, 1/ = 0. In this case. Equation 3.179 is simplified to the form... 

Tubular flow reactors are characterized by a continuous and decreasing concen-tiadon of reactants in the direction of flow. This is in contrast to the discontinuous characteristic of the CSTR reactor. Most of these units consist of one or several pipes or tubes in parallel. Either horizontal or vertical orientation is common. The reactants are charged continuously at one end, and the products are removed continuously at the other end. The unit almost always operates in a steady-state mode. This greatly simplifies design and predictive calculations. It is a unit that is amendable to automatic control and to experimental work. When heat transfer is required, a jacketed tube or a construction similar to that of a shell-and-tube heat exchanger is employed. In the latter case the reactants may be on either the tube or shell side. 

The entire system weighs in the neighborhood of 17 lbs. and is designed in such a way that the heat exchanger case which fits within the impermeable suit, acts as a pack for the liquid air container located outside the suit. The liquid air container is vacuum insulated, self-pressurizing, with simplified plumbing. 

The heat flux boundary condition at the wall of the catalyst bed is used when heat is exchanged with an external charmel, where the heat transfer is described using a flux profile. This is the case for an adiabatic catalyst bed as in a prereformer or an autothermal reformer where the heat flux is zero so that the heat transfer equations simplify to a onedimensional model. The heat flux boundary condition is also used when the tubular reformer is coupled with a furnace type model (refer to Section 3.3.6). 

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