Thermal Creep Phenomena

For thin channel, that is, A h, free molecular flow condition can be assumed. Here, the intermolecular collisions are negligible in comparison to the interaction of molecules with the surface. Let us assume the molecule wall interaction to be specular (o- = 0) and explain the thermal creep phenomena observed experimentally. 

We can assume the density (p) to be directly proportional to the number of molecules per unit volume ( ) as 

Similarly, the average molecular speed can be assumed to be proportional to the temperature 

The mass flux at the hot and cold sides of the channel are, respectively, equal to m Cj and 

Using P = pRT and = 1, the ratio of mass flux between the hot and cold sides is given by 2 

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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... 

Graphite will creep imder neutron irradiation and stress at temperatures where thermal creep is normally negligible. The phenomenon of irradiation creep has been widely studied because of its significance to the operation of graphite moderated fission reactors. Indeed, if irradiation induced stresses in graphite moderators could not relax via radiation creep, rapid core disintegration would result. The observed creep strain has traditionally been separated into a primary reversible component ( ,) and a secondary irreversible component (Ej), both proportional to stress and to the appropriate unirradiated elastic compliance (inverse modulus) [69]. The total irradiation-induced creep strain (ej is thus ... 

Even with an adequate description of molecular velocities near the particle surface, it is not possible to completely establish all variables influencing thermal force. This is because there also exists a so-called thermal slip flow or creep flow at the particle surface. Reynolds (see Niven, 1965) and others have pointed out that as a consequence of kinetic theory, a gas must slide along the surface of a solid from the colder to the hotter portions. However, if there is a flow of gas at the surface of the particle up the temperature gradient, then the force causing this flow must be countered by an opposite force acting on the particle, so that the particle itself moves in an opposite direction down the temperature gradient. This is indeed the case, known as thermal creep. Since the velocity appears to go from zero to some finite value right at the particle surface, this phenomenon is often described as a velocity jump. A temperature jump also exists at the particle surface. 

Another mechanism that may affect the velocity profile in a microchannel is thermal creep. It is a molecular transport phenomenon that occurs when two isopressure containers at different temperatures are connected by a channel whose diameter is close to the gaseous mean free path. Under this condition, gaseous molecules start to flow from the cooler... 

When there is no primary stress, voids grow by absorption of vacancies, dislocations climb in aU directions and the material simply increases in volume with an isotropic volume expansion this is the swelling phenomenon. But in the presence of a stress and independently of thermal creep, a plastic creep strain is also observed under irradiation in the direction of the applied stress [29]. Several, but mainly two, irradiation creep mechanisms caused by dislocation motion are invoked depending on whether they involve pure dislocation climb, or slip controlled by climb... 

Thermal creep is the phenomenon in which we are able to start rarefied gasfiows because of tangential temperature gradients along the channel walls, where the fluid starts creeping in the direction from cold toward hot (see Figure 3.11). Equilibrium condition requires no flow in the channel for thick channel (A h). If channel thickness /i A (mean free path), rarefied gas effects have to be taken into account. Here, the local equilibrium mechanism is very complex, and interaction of gas molecules with the walls must be considered. 

The extent of molecular motion depends on the free volume. In the glassy state, the free volume depends on the thermal history of the polymer. When a sample is cooled from the melt to some temperature below Tg and held at constant temperature, its volume will decrease (see Rgure 8.18). Because of the lower free volume, the rate of stress relaxation, creep, and related properties will decrease (29-33). This phenomenon is sometimes called physical aging (29,32), although the sample ages in the sense not of degradation or oxidation but rather of an approach to the equilibrium state in the glass. 

These last numerical results show that the plastic strain is obviously greatly influenced by the presence of the creep/relaxation phenomenon. In fact, the level of the plastic strain was considerably reduced from 0.004 to 0.0018, i.e a reduction ratio of 2.2 based on the reference case (Figure 6), which does not take into accormt creep behaviour of the ramming paste. Also, the anelastic strain level at the end of the simulation (i = 40 hours) is almost negligible compared to the other strains (e.g., plastic, thermal, etc.). This result directly ensues from the assumption that the baked ( = 1) ramming p>aste creep/relaxation behaviour is similar to that of the carbon cathode block (Richard et al., 2006). This case study thus shows the importance of taking all the relevant phenomena including creep behaviour into account in similar problems. A similar analysis could be done for all other deformations (chemical, thermal, plastic, etc.). 

The benefits may arise indirectly through enhanced thermal conductivity and creep resistance or through a subtle modification of the wear mechanism. It is the latter that are of particular interest in the context of interfacial wear phenomenon. 

If a constant strain is imposed on a metal or alloy, the stress relaxes with time as the system reduces its free energy. Dislocations are annihilated and the remaining dislocations move to lower-energy configurations. This is the nature of the recovery process. At higher temperatures, diffusional processes equivalent to creep occur. This phenomenon is very important for solder joints in electronic devices because the device spends much time at the strain extremes when it is turned on and off or put into a sleep mode and returned to active duty. Stress at constant strain vs. time curves for Sn-3.5Ag solder at 25 °C and 80 ° C, and at 0.3 % strain maximum are given in Fig. 6(a,b). The stress as a result of the coefficient of thermal expansion mismatches initially decreases very rapidly with time to a more or less steady state value. At 25 °C, the steady state value is about 15 MPa and is rather independent of the initial stress value however, at 80°C, the stress relaxes to zero. Thus when an electronic device is turned on, the thermal stress will relax to a low value possibly zero during use. 

Table 9-24 below, presents several wall thickness values for varying bend radii and pipe operating parameters (temperature and pressure) which would have been experienced in the piping assembly for a mission lifetime of 15 yrs ( 132,000 hrs). It should be noted that these values are minimum wall thicknesses and additional phenomenon may occur which would could have required the wall thicknesses to increase, such as creep-fatigue interactions, irradiation, and thermal ratcheting. 

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