Contents 1. Introduction . 2. Microscopic specification of a simple fluid 2.1. Three states of matter . 2.2. Empirical determination . 2.3. The radial distribution and total correlation functions 2.4. Certain physical associations . 3. Formulae from statistical mechanics . 3.1. The energy function . . 3.2. Correlation functions . 3.3. Formal link with thermodynamic functions . 3.4. Thermodynamics and the pair correlation . 3.5. The use of the equations . 3.6. The virial coefficients . 4. Equations for the pair correlation , 4.1. Method of approach . 4.2. First-order equations.4.3. The superposition approximation . 4.4. Fisher's application of the approximation 4.5. A second-order equation . 4.6. Dependence on density and temperature . 5. Attempts to improve the closure procedure . 5.1. Comments on functional differentiation . 5.2. Rederivation of established equations . 5.3. The triplet indirect correlation . 5.4. Alternative closure approximations . . 6.1. The interparticle force potential . . 6.2. The virial coefficients . 6.3. Liquid densities . 6.4. Further deductions from the theory 6.5. The use of laboratory models..
Convective heat transfer measurements are reported for staggered arrays of round turbulent air jets impinging upon a heated flat surface. Spent air was constrained by skirts to exit at one end of the test section, thus establishing a crossflow. Geometric variables included the jet hole diameter d, the streamwise spacing X and spanwise spacing Y between jet holes, and the standoff distance Z between the orifice plate and the target plate. Three patterns of holes, all having d = 3.5 mm, were tested. Their (X, Y) were (4d, 4d), (4d, 8d), and (8d, 4d). Values of the standoff were Z = d, 2d, and 3d; and tests were run for 4, 6, and 8 rows of holes. The airflow was varied to achieve a range of mean jet Reynolds number from 2500 to 25,000. Microfoil heat flux sensors were used to determine streamwise variations in (spanwise-averaged) heat transfer. Excellent resolution was obtained by employing a sensor whose streamwise dimension is considerably less than one hole diameter d. Heat transfer profiles were periodic, with a peak corresponding to each spanwise row of holes. Such peaks were displaced in the steamwise direction by the crossflow, and those nearest the exhaust end of the channel exhibited the largest deflections. Array-averaged heat transfer coefficients were obtained by numerically averaging the local measurements; values agree well with the results of other experiments on similar impingement-with-crossflow systems.
The theory of Prigogine is applied to the deduction of the molecular structure of a simple dense fluid not in equilibrium, described in terms of the phase singlet distribution. The intermolecular interaction is assumed to have the form of the sum of constituent pair forces, and the pair force itself is supposed to be composed of a hard core and an extended weak interaction. It is shown how the Rice-Allnatt equation can be derived in this way, but that the natural development of the theory of the time evolution of the singlet distribution is such as to lead as a first approximation to the equation recently given independently by Popielowski, Rice and Hurt. An improved equation for the singlet distribution is derived, in w 8, and some comments are made about the present standing of the theory in its application to dense fluids.
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