Thermal equilibrium, simple fluid

A simple fluid in thermal equilibrium, at its most primitive level of description, is characterized by a particle density n(r) controlled by an applied external potential u(r). In the grand ensemble, it is only the combination... 

Statistical physics considers the task of predicting the (often macroscopic) observables of a physical system from the knowledge of interactions between the (microscopic) constituents (such as atoms or molecules, or suitably defined subunits of a polymer chain, for instance). Consider, for example, a simple fluid of N particles in a box of volume V held at a temperature T in thermal equilibrium. In the framework of classical statistical mechanics (i.e., neglecting the quantum-mechanical effects), the average of any observable A (e.g., the total potential energy 7(X ) in the system or the pair distribution function of particles) is given by... 

The original Reynolds analogy involves a number of simplifying assumptions which are justifiable only in a limited range of conditions. Thus it was assumed that fluid was transferred from outside the boundary layer to the surface without mixing with the intervening fluid, that it was brought to rest at the surface, and that thermal equilibrium was established. Various modifications have been made to this simple theory to take account of the existence of the laminar sub-layer and the buffer layer close to the surface. 

In the two-medium treatment of the single-phase flow and heat transfer through porous media, no local thermal equilibrium is assumed between the fluid and solid phases, but it is assumed that each phase is continuous and represented with an appropriate effective total thermal conductivity. Then the thermal coupling between the phases is approached either by the examination of the microstructure (for simple geometries) or by empiricism. When empiricism is applied, simple two-equation (or two-medium) models that contain a modeling parameter hsf (called the interfacial convective heat transfer coefficient) are used. As is shown in the following sections, only those empirical treatments that contain not only As/but also the appropriate effective thermal conductivity tensors (for both phases) and the dispersion tensor (in the fluid-phase equation) are expected to give reasonably accurate predictions. 

In this section, the phenomena of thermal creep and its influence on the slip flow boundary condition is discussed. Let us explain the thermal creep phenomena using a simple experiment. Figure 3.10 shows the schematic of thermal creep experimental setup. The two tanks are connected with each other through an array of microchannel. The pressure relief valves are kept open, and both the tanks are initially at equilibrium with the atmosphere. Then the tanks are dipped to the fluid bath. If the continuum hypothesis is valid, the pressure will remain unchanged. If thermal creep effects are present, then pressure in the cold reservoir will decrease and hot reservoir will increase indicating the pumping action from the cold reservoir to the hot reservoir. It is possible to increase the thermal creep effects by performing the... 

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