Cooling transfer resistance

Heat-transfer resistance Across two-phase interface in fast reactions Gas side of tube wall in liquid-cooled gas-phase or G/S reactors Within solid particles in solid-fluid reactions... 

Silicate scales are particularly adherent and extremely difficult to remove, and they are among the most heat-transfer-resistant of all scales. Where scale-based deposits have been found in cooling systems, analyses show they almost always contain some silica or silicate. Fortunately, the silica found is typically less than 5 to 6% unless there is a specific silica problem (under these circumstances the deposit may contain more than 20 to 30% Si02). 

If the alloy resists the action of aqua regia, fuse it with sodium hydroxide pellets in a silver dish or crucible (CAUTION). When decomposition is complete, allow to cool, transfer the silver vessel to a beaker and extract the melt with water remove the silver vessel from the beaker. Strongly acidify the contents of the beaker with nitric acid, evaporate to dryness on a water bath, and proceed as above. 

A small Biot number means that the resistance to thermal conduction in the body, for example due to its high thermal conductivity, is significantly smaller than the heat transfer resistance at its boundary. With small Biot numbers the temperature difference in the body is small in comparison to the difference ( w — f) between the wall and fluid temperatures. The reverse is valid for large Biot numbers. Examples of these two scenarios are shown for a cooling process in Fig. 2.5. Very large Biot numbers lead to very small values of — J), and for Bi —> oo, according to (2.34) we get (it/y — i p) —> 0. The heat transfer condition (2.34) can be replaced by the simpler boundary condition = -dj. 

A simple calculation for the heating or cooling of a body of any shape is possible for the limiting case of small Biot numbers (Bi — 0). This condition is satisfied when the resistance to heat conduction in the body is much smaller then the heat transfer resistance at its surface, cf. section 2.1.5. At a fixed time, only small temperature differences appear inside the thermally conductive body, whilst... 

As a comparison with the exact solution of the Stefan problem shows, the quasisteady approximation discussed in the last section only holds for sufficiently large values of the phase transition number, around Ph > 7. There are no exact solutions for solidification problems with finite overall heat transfer resistances to the cooling liquid or for problems involving cylindrical or spherical geometry, and therefore we have to rely on the quasi-steady approximation. An improvement to this approach in which the heat stored in the solidified layer is at least approximately considered, is desired and was given in different investigations. 

The stirring and the resulting flow pattern inside the tank can be very important for the overall heat transfer resistance, because the performance of the reactor affects the heat transfer coefficient at the process side hg. The other resistances are determined by the materials used and the properties of the cooling/heating media and are thus not influenced by the reactor performance. 

Calculated temperature profiles are shown in Fig. 5.21. By comparison, the 2D model with a heat-transfer resistance at the wall gives slightly higher hot-spot temperatures than the A(r)-model. This implies a somewhat better cooling performance according to the A(r)-model, in spite of the pronounced bypass flow near the membrane and the resulting lower fluid velocity in the core of the bed. In addition to the radially averaged temperature profiles, the results from the one-dimensional model are also depicted in Fig. 5.21a. While the maximal difference between predictions of the two-dimensional models is less than 4K, the one-dimensional model overestimates those results by about... 

This cooling of fluid in a pipe with wall heat transfer resistance was solved by Michelsen (1979) using the method of orthogonal collocation. This problem without the wall resistance is a special case of the situation dealt with by Michelsen, and is often referred to as the Graetz problem (see Example 10.3 and Problem 3.4). 

The overall heat transfer coefficient consists of different contributions from heat transfer resistances, For simplicity, we do not consider different exchange areas of the various heat transfer resistances. The heat transfer coefficient in the reaction channel is correlated with the Nusselt number, whUe the thermal resistances in the wall and the cooling channel are lumped together and replaced with a coefficient [17]. 

If the transfer resistances in the reactor wall and the cooling channel are similar a coefficient of = 0.5 results. Typical values for are 0.1-0.5... 

As noted above, a second exchanger cooled with chilled water is often added to increase the removal of water. All the problems referred to above with increasing mass-transfer resistances occur in this second exchanger as well. Added to this problem is the fact that the gas entering the exchanger is much leaner in water. The net result is that unit heat fluxes in chlorine chillers are much lower than those in the coolers, perhaps by a factor of five or ten. 

Heat transfer between packed beds and the external column wall has been widely studied because of its relevance to the design and operation of wall-cooled catalytic reactors. In the one-dimensional model, which is the basis of Eq. (7.17), the overall heat transfer resistance may be represented as the sum of the internal, external, and wall resistances ... 

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