Three-layer analogy

Some simple methods of determining heat transfer rates to turbulent flows in a duct have been considered in this chapter. Fully developed flow in a pipe was first considered. Analogy solutions for this situation were discussed. In such solutions, the heat transfer rate is predicted from a knowledge of the wall shear stress. In fully developed pipe flow, the wall shear stress is conventionally expressed in terms of the friction factor and methods of finding the friction factor were discussed. The Reynolds analogy was first discussed. This solution really only applies to fluids with a Prandtl number of 1. A three-layer analogy solution which applies for all Prandtl numbers was then discussed. 

Consider the flow of water through a 65-mm diameter smooth pipe at a mean velocity of 4 m/s. The walls of the pipe are kept at a uniform temperature of 40°C and at a certain section of the pipe the mean water temperature is 30°C. Find the heat transfer coefficient for this situation using both the Reynolds analogy and the three-layer analogy solution. 

The explicit three-layer scheme. We now turn to the simplest explicit three-layer scheme known as the Richardson scheme and being an analog of scheme (59) from Section 1 ... 

Drawing an analogy with the case of heat flow by conduction through a three-layered wall discussed earlier, one can write... 

A method for solving three-dimensional problems on the diffusion boundary layer based on a three-dimensional analog of the stream function, was proposed in [348, 350]. In [27, 166, 353], this method was used for studying mass exchange between spherical particles, drops, and bubbles and three-dimensional shear flow. 

The latest development in the subfield of surface-modified semiconductor nanocrystals is the synthesis of three-layered colloidal particles [55-58]. The novel structures consist of a size-quantized semiconductor particle acting as the core spherically covered by several monolayers of another semiconductor material, which by themselves are surrounded by several monolayers of, again, the core material acting as the outermost shell. These particles are called quantum dot quantum wells (QDQWs) or, metaphorically, nano-onions. The more scientific naming is motivated by the analogy to real quantum wells, which are semiconductor structures with alternating layers of two semiconductor materials exhibiting quantum confinement in one dimension in at least one of the materials. 

The three transition-metal molybdate layers defining the unit cell are stacked at a separation of c/3, analogous to the rhombohedral LDH precursor. In these layers, the position of the ordered vacancy capped by the molybdate groups follows the sequence A-B-C-A (where A, B, and C are the three threefold axes at x,y = 0,0 2/3,l/3 and l/3,2/3). This three layer arrangement is shown in Figure 5. Between each layer, in the space defined by the apical oxygens of six tetrahedral molybdates, lie ammonium ions. The positions of the nitrogen atoms follow the sequence C-A-B-C. The ammonium ions do not serve to connect the array of layers in the [00/] direction, the distance between the... 

A three layer teehnique to combine immiscible material combinations was provided by the Billion Corporation of France. Their solution to polymer incompatibility for sandwich injection moulding used the third intermediate polymer layer as a binder adhesive, this is analogous to methods used in extrusion blow moulding. However, there are obvious machine cost disadvantages here, because the runner system is complex and a third injection unit is required. 

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