Three-dimensional character

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

Chemists use a variation on the ball-and-stick model to depict more clearly the three-dimensional character of molecules, as shown for methane in Figure 9-1 Icf. The central carbon atom is placed in the plane of the paper, hi these models, solid lines represent bonds lying in the plane of the paper, solid wedges represent bonds that protmde outward from the plane of the paper, and dashed wedges represent bonds extending backward, behind the plane. 

Each protein has a unique three-dimensional shape called its tertiary structure. The tertiary structure is the result of the bends and folds that a polypeptide chain adopts to achieve the most stable structure for the protein. As an analogy, consider the cord in Figure 13-39 that connects a computer to its keyboard. The cord can be pulled out so that it is long and straight this corresponds to its primary structure. The cord has a helical region in its center this is its secondary structure. In addition, the helix may be twisted and folded on top of itself This three-dimensional character of the cord is its tertiary structure. 

Most of the conducting or magnetic materials investigated in the homoleptic series are salts while many of the radical heteroleptic complexes described above are in their neutral state, potentially allowing for a stronger three-dimensional character. 

Note 1 Originally, these mesophases were designated as smectic, but further investigations have demonstrated their three-dimensional character. 

In most cases, linear prepolymers are used for the production of elastomers. Gas evolution via dry polyols or diamines is therefore not encouraged. When a foam is required, however, a slight adjustment is made in the construction of the prepolymer. We referred to it earlier when we discussed polyfunctional polyols. By including a trifunctional alcohol in the prepolymer recipe or by using a polyol from a trifunctional initiator (e.g., trimethylol propane), a three-dimensional character is introduced into the prepolymer. 

In designing a prepolymer for a specific use, this technique provides for more control of the chemistry. For elastomers, for instance, including some three-dimensional character changes the physical properties of the polymer. More cross-linking lowers elongation and increases strength. Cross-linking is not necessary for elastomers, but it is required for foams. 

The three-dimensional character of molecules is expressed by its stereochemistry. By looking at the stereochemistry of a molecule, the spatial relationships between atoms on one carbon and the atoms on an adjacent carbon can be examined. Since rotation can occur around carbon-carbon single bonds in open chain molecules, the atoms on adjacent carbons can assume different spatial relationships with respect to each other. The different arrangements that atoms can assume as a result of a rotation about a single bond are called conformations. A specific conformation is called a conformer. While individual isomers can be isolated, conformers cannot since interconversion, by rotation, is too rapid. 

To explore the three-dimensional character of organic molecules. 

In four dendrimers terminated by 12 electroactive tetrathiafulvalenyl substituents (160), the three dimensional character of the inter- and intra-den-drimeric charge and eleetron transfer, and hence of the eleetroconductivity, has been assessed by examination of the electronic spectra of their corresponding neutral state and nation, radieal, dication, and mixed-valence salts, including a closed - shell anion (Figure 24). ... 

Since the latter is found to be the case for ionic polymers, only the derivation predicting a narrowing of the giectrum will be presented here. The conclusion that the spectrum would narrow upon an increase in the three-dimensional character of the pol5nner is based by Tobolsky (55) on the following considerations ... 

As can be seen from Fig. 16, the distribution of relaxation times narrows appreciably with increasing Ca " " content in the Na -Ca " copolymers and also with increasing Na in the Na -K system (not shown) in other words, with increasing qja or an increasing three-dimensional character of the material the distribution narrows. This tends to confirm the theoretical prediction of Tobolsky (55). However, there... 

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