Thermal force

To protect terminal equipment or other (weaker) portions of the system, restraints (such as anchors and guides) shall be provided where necessary to control movement or to direct expansion into those portions of the system that are adequate to absorb them. The design, arrangement, and location of restraints shall ensure that expansion-joint movements occur in the directions for which the joint is designed. In addition to the other thermal forces and moments, the effects of friction in other supports of the system shall be considered in the design of such anchors and guides. 

As part of a Process Hazards Analysis (PHA). I was required to check a naturally ventilated building containing electrical equipment and a fuel gas supply, for adequate air flow due to thermal forces (stack effect). API RP 500 has a method that they recommend for buildings of l,000fP or less. The building in question was much larger, because ... 

Convection The mechanism of heat transfer due to different temperatures, and hence different densities in fluids. It may be natural, dependent only on thermal forces, or forced, when use is made of a rotodynamic device to improve the rate of heat exchange. 

Dry The interception and retention by surfaces of gases or particulate matter by diffusion, gravitational settling, or thermal forces. 

Gauge pressure of a space The positive or negative pressure in a space with respect to its surroundings, due to wind or thermal forces or the relationship of supply air to extract air. 

Natural ventilation system Ventilation of a space by the influence of thermal forces and wind forces over and around a building. Under certain conditions only one of these applies, however, in the majority of cases it is assumed that both apply. 

Smoke generator A device that electri cally heats oil-producing smoke. The smoke is liberated from a nozzle by either thermal forces or by means of a fan and used to observe airflow patterns within a space or to observe leakage from ductwork, etc. 

Ventilation, natural Air movement created by wind forces, thermal forces, or a combination of both. 

Wind Air motion relative to the earth s surface caused by thermal forces and the earth s rotation. 

Note that the so-called thermal forces, N, are true thermal forces only when the total strains and curvatures are perfectly restrained, that is, zero. 

Actually, only in the restricted case of perfect constraint are the and thermal forces and moments, respectively. However, the force and moment resultants can be rearranged to read... 

Consider a constant temperature of the laminate different from, and relative to, its stress-free curing temperature. Then, the thermal forces are, from Equation (4.105),... 

For two- and three-layered cross-ply and angle-ply laminates of E-glass-epoxy, Tsai [4-10] tabulates all the stiffnesses, inverse stiffnesses, thermal forces and moments, etc. Results are obtained for various cross-ply ratios and lamination angles, as appropriate, from a short computer program that could be used for other materials. 

Verify that the thermal forces n][, Ny, and for a three-layered cross-ply laminate with M =. 2 are given by Equation (4.117). 

Temperature swings following frontal passages are common in North America and Eurasia, but are rare in the tropics, where differences in cloudiness and precipitation arise from seasonal variability in thermal forcing. Poleward from the tropical regions, extratropical cyclones transform latitudinal temperature gradients into kinetic energy. 

The region from the Helmholz plane into the solution, across which the potential varies exponentially attaining a value of zero at some distance in this region the ions are subjected to both ordering electrical forces and disordering thermal forces. 

The modeling of complex solids has greatly advanced since the advent, around 1960, of the finite element method [196], Here the material is divided into a number of subdomains, termed elements, with associated nodes. The elements are considered to consist of materials, the constitutive equations of which are well known, and, upon change of the system, the nodes suffer nodal displacements and concomitant generalized nodal forces. The method involves construction of a global stiffness matrix that comprises the contributions from all elements, the relevant boundary conditions and body and thermal forces a typical problem is then to compute the nodal displacements (i. e., the local strains) by solving the system K u = F, where K is the stiffness matrix, u the... 

The control of sedimentation is required to ensure a sufficient and uniform dosage. Sedimentation behavior of a disperse system depends largely on the motion of the particles which may be thermally or gravitationally induced. If a suspended particle is sufficiently small in size, the thermal forces will dominate the gravitational forces and the particle will follow a random motion owing to molecular bombardment, called Brownian motion. The distance moved or displacement, Dt, is given by ... 

As we have seen, the electric state of a surface depends on the spatial distribution of free (electronic or ionic) charges in its neighborhood. The distribution is usually idealized as an electric double layer one layer is envisaged as a fixed charge or surface charge attached to the particle or solid surface while the other is distributed more or less diffusively in the liquid in contact (Gouy-Chapman diffuse model, Fig. 3.2). A balance between electrostatic and thermal forces is attained. 

In terms of beam delivery, the DLW method is based on optical microscopy, confocal microscopy [4,6,13] and laser tweezers [14] (for reviews on laser tweezers see [ 15,16]). These techniques allow for a high spatial 3D resolution of a tightly focused laser beam with optical exposure of micrometric-sized volumes via linear and nonlinear absorption. In addition, mechanical and thermal forces can be exerted upon objects as small as 10 nm molecular dipolar alignment can be controlled by polarization of light in volumes of with submicrometric cross-sections. This circumstance widens the field of applications for laser nano- and microfabrication in liquid and solid materials [17-22]. 

Stern Combination of Parallel-Plate and Diffuse-Charge Models 9m = -9S = "[9h + J t 1 1 C Qi Qi maV=waVhaV Pole r R 1 of ,ial. linear variation V, ions are under the combined influence of the ordering electrical and the disordering thermal forces. Agrees with the experiment only for ions nonspecificaHy adsorbed on the electrode (e g. NaF). 

What happens now at the other extreme case, i.e., at solutions with low concentrations Under this condition (1/CG) (1/CH) and therefore, C CG. This indicates that the electrified interface has become in effect Gouy-Chapman-like in structure, with the solution charge scattered under the simultaneous influence of electrical and thermal forces. 

Adsorption. In the simple theory of the space charge inside a semiconductor, it was assumed that all the electrons and holes are free to move up to the surface. Being susceptible to thermal motion, their concentrations from a- = 0 to x — °° were said to be given by the interplay of electrical and thermal forces only, as expressed by the Boltzmann distribution law and Poisson s equation. 

Biot and Daughaday (B6) have improved an earlier application by Citron (C5) of the variational formulation given originally by Biot for the heat conduction problem which is exactly analogous to the classical dynamical scheme. In particular, a thermal potential V, a dissipation function D, and generalized thermal force Qi are defined which satisfy the Lagrangian heat flow equation... 

In other words, it is assumed here that the particles are surrounded by a isotropic viscous (not viscoelastic) liquid, and is a friction coefficient of the particle in viscous liquid. The second term represents the elastic force due to the nearest Brownian particles along the chain, and the third term is the direct short-ranged interaction (excluded volume effects, see Section 1.5) between all the Brownian particles. The last term represents the random thermal force defined through multiple interparticle interactions. The hydrodynamic interaction and intramolecular friction forces (internal viscosity or kinetic stiffness), which arise when the macromolecular coil is deformed (see Sections 2.2 and 2.4), are omitted here. 

The fourth term on the right hand side of (3.4) represents the elastic forces on each Brownian particle due to its neighbours along the chain the forces ensure the integrity of the macromolecule. Note that this term in equation (3.4) can be taken to be identical to the similar term in equation for dynamic of a single macromolecule due to a remarkable phenomenon - screening of intramolecular interactions, which was already discussed in Section 1.6.2. The last term on the right hand side of (3.4) represents a stochastic thermal force. The correlation function of the stochastic forces is connected... 

In the basic model, put forward by Asakura and Oosawa (5), the hard spherical particles immersed in a solution of macromolecules are considered to be surrounded by depletion layers from which the polymer molecules are excluded. When two particles are far apart with no overlap of the depletion zones, the thermal force acting over the entire particle surface is uniform. However, when the particles come closer, such that their depletion zones begin to overlap, there is a region in which the polymer concentration is zero and the force exerted over the surfaces facing this region is smaller compared to that exerted over the rest of the surface. This gives rise to an attractive force between the two particles which is proportional to the osmotic pressure of the polymer solution. 

Thermophoretic forces can be used in sampling aerosols the particles are passed through the dark space surrounding a hot body and are collected with nearly 100 percent efficiency on a cold surface placed nearby. To date, however, there has been no successful utilization of thermal forces for large-scale air cleaning. 

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