First Key Problem

Consider the problem involving peripheral heat transfer to an ambient. Assume a radially lumped and axially differential control volume (Step 1) shown in Fig. 2.38(a). Thie first law13 for this control volume (Step 2), interpreted in terms of Fig. 2.39 and with the conservation of mass, 

13 The first law conserves the total energy, which, in the present case, involves the thermomechanical energy. The mechanical part of this energy leads under certain conditions, to the Bernoulli equation, which can directly be obtained from Newton s law. 

For an incompressible fluid, the conservation of mass for flow of this fluid through a tube of constant cross section implies V = Constant. Furthermore, if the tube is horizontal, then z = Constant. Thus 

for this fluid, neglecting the small and usually ignored difference between the specific heat at constant pressure, cp, and at constant volume, cv, 

U being the total heat transfer coefficient, Ri the inside convective resistance, Rk the conductive resistance of pipe walls, and R0 the outside convective resistance. This result may be rearranged in terms of the characteristic length 1/m = JkAjVP for fins [recall Eq. (2.113)], the thermal diffiisivity, 

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Reconsider the control volume used for the first key problem. Since the axial conduction is neglected and the peripheral flux is specified, there is no need for any particular law. We now have a thermodynamically determined problem. The first law applied to the control volume shown in Fig. 2.41 directly gives the governing equation subject to the inlet boundary condition. The formulation is then... 

We have already learned the solution of Eq. (2.173) in connection with the first key problem. From the development leading to Eq. (2.158), we have... 

Follow the five steps of the first key problem to obtain h. 

The thermal design of heat exchangers discussed in the preceding sections rests usually on the following first key problem ... 

The search for inhibitors of this pathway began with the first key regulatory enzyme, HMG CoA reductase. Several clinically useful inhibitors of HMG CoA reductase are now known. One of the most successful, Mevacor, produced by Merck, is one of the pharmaceutical industry s best selling products. However, the problem with inhibiting a branched biosynthetic pathway at an early point is that the biosynthesis of other crucial biomolecules may also be inhibited. Indeed, there is some evidence that levels of ubiquinone and the dolichols are affected by some HMG CoA reductase inhibitors. Consequently, efforts have recently been directed towards finding inhibitors of squalene synthase, the enzyme controlling the first step on the route to cholesterol after the FPP branch point. 

To tackle this problem, we first need to know how a given representation F is reduced to its irreducible representations T) in other words, to determine the coefficients a, in the equation F= Sat Fi. Although this is a key problem in group theory, here we only explain how to perform this reduction without entering into formal details, which can easily be found in specialized textbooks. 

The protein microarray represents an emerging technology. While we have described its potential utility, several key problems remain to be overcome before this tool is fully adopted by the research and biopharmaceutical commxmities. The most likely first embodiment will be an antibody "protein-detecting" microarray. This is understandable based upon the availability and suitability of antibody libraries originally developed for ELISA. We have discussed many demonstrahons of antibody arrays in this chapter but commercial introductions (Pierce, Beckman Coulter) have been limited. 

Thus, its structure has proven difficult to fully characterize. The key problem is to identify the location of the hydrogen and lithium positions and the N—H bond orientations. The electronic structure of U2NH was investigated by first-principles calculations [58-60], indicating that the highest occupied states are non-bonding, consisting of N p orbitals. 

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