Thermal creep

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 ... 

Other processes that have increased importance at small length scales such as thermal creep (transpiration) and electrokinetic effects are also being considered for use in microcombustors. For example, transpiration effects are currently being investigated by Ochoa el al. [117] to supply fuel to the combustion chamber creating an in-situ thermally driven reactant flow at the front end of the combustor. 

For thermal creep Maxwell (see Kennard, 1938) proposed the equation... 

For concrete at high temperature the most important is the effect of cracking and dehydration process on the material properties, e.g. porosity n=f(Thydr)> intrinsic permeability k=/(T/,(/,/r. /7. T), and its deformations. Irreversible part of strains and so called thermal creep are expressed as functions of thermochemical damage parameter V, [8],... 

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. 

The first theory of the thermal force acting on a particle which took thermal creep into account was developed by Epstein (1929), using the slip formula proposed by Maxwell (1880). Epstein s equation was of the form... 

Beskok, A. and Karniadakis, G.E., Simulation of Heat and Momentum Transfer in Complex Micro Geometries, J. Thermophysics and Heat Transfer, 1994, 8(4), 647-655. Beskok, A., Karniadakis, G.E. and Trimmer, W., Rarefaction, Compressibility and Thermal Creep Effects in Micro-Elows, Proceedings of the ASME Dynamic Systems and Control Division, 1995, DSC-57-2, 877-892. 

A study on a dilute hard-sphere gas in the transition regime using the DSMC was conducted by [44]. The simulation is for 0.02 < Kn < 2 and unity Em and Fj. They found a weak dependence of the Nusselt number on the Peclet number, which explains the weak dependence on the axial heat conduction. In the case of constant wall heat flux, a positive thermal creep, which occurs when the exit temperature is higher than the inlet temperature, tends to increase the Nusselt number while negative thermal creep tends to decrease the Nusselt number. 

The laminar gaseous flow heat convection problem in the slip flow region was solved both analytically and numerically for various geometries [3-6], The compressibility effects were included in [7],[8-11] and the results were compared with the experimental results of [12], Thermal creep effects were studied by [13], Exact solutions for flows in circular, rectangular, and parallel plate microchannels were given in [14-17],... 

Surface creep must be very low, both to restrict loss of lubricant from bearings, etc. and to avoid contamination of other components. Creep is a surface tension effect where oil surface tensions are typically in the range 18-30 mN/m. To mitigate surface creep, thermal gradients should be avoided or minimised and the surface finish of components should be optimised. Capillary creep occurs if Ra> 0.1 mm, thermal creep occurs if Ra < 0.6 mm. 

The results of thermal stress demonstrate that due to the setup of one temporary transverse joint and three longitudinal joints, the horizontal tensile stresses within the concrete are controlled so that the tensile stresses in the vertical direction are much higher than those in horizontal directions. Figs.5 illusu-ates the thermal creep stress evolutions at the interior centre points of the concrete blocks close to ground surface. 

Parrott [130] is considering that the polymerization of silicate anions, occurring with increasing temperature in C-S-H phase, plays an important role in the so-called thermal creep. Simultaneously, a coagulation of gel particles with a change of porosity, evidenced its rapid reduction, takes place. The creep is improved by rearrangement of anions. The other materials exhibit creep too, if they undergo the phase transformations under load [130]. 

The thermal creep coefficient Gt in both channel and tube is given by... 

The thermal creep coefficient Gj is also obtained from the Navier-Stokes equation, but applying the thermal slip botmdary condition (9). It is verified that this coefficient does not depend on the type of the cross section in... 

Gas Flow In Nanochannels, Fig. 3 Thermal creep coefficient versus rarefaction parameter 6 solid lines, kinetic equation solution [11] pointed line, free-molecular value based on Eqs. 12 and 15 dashed line, Navier-Stokes solution Eq. 19... 

Numerical results on the capillary flow of polyatomic gases can be found in [4]. Comparing these results with the data presented here, it is concluded that the Poiseuille coefficient Gp is slightly affected by the internal structure of molecules. The thermal creep coefficient Gp for polyatomic gases differs from that for monatomic gases. 

Loyalka SK (1989) Temperature jump and thermal creep slip rigid sphere gas. Phys Fluid A 1 403-408... 

Ohwada T, Sone Y, Aoki K (1989) Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall an the basis of the linearized Boltzmann equation for hard-sphca e molecules. Phys Fluid A 1(9) 1588-1599... 

Sharipov F (2003) Application of the Cercignani-Lampis scattering kernel to calculations of rarefied gas flows. III. Poiseuille flow and thermal creep through a long tube. Eur J Mech B/Fluid 22 145-154... 

Velocity Slip Boundary Conditions The commonly used slip boxmdary conditions are called Maxwellian boxmdary conditions [5]. The first-order approximation for the velocity slip within the Knudsen layer, which does not take into accoxmt thermal creep, is given by... 

Hadjicrnistantinou and Simek [35] investigated the case for fuUy developed flow with uniform wall temperature. They found that Eqs. 7 and 17 with both F = 1 and = 1 were adequate in determining the physics in this slip-flow problem. They compared their results with the direct simulation Monte Carlo method. They concluded that slip-flow models neglecting viscous dissipation, expansion cooling, and thermal creep were adequate in describing the heat transfer. However, when considering viscous dissipation, the Nu expression becomes [34]... 

Kamiadakis and Beskok [6] developed a code H Flow with implementation of spectral element methods. They employed both the Navier-Stokes (incompressible and compressible) and energy equations in order to compute the relative effects of compressibility and rarefaction in gas microflow simulations. In addition, they also considered the velocity slip, temperature jump, and thermal creeping boundary conditions in the code Flow. The spatial discretization of fi Flow was based on spectral element methods, which are similar to the hp version of finite-element methods. A typical mesh for simulation of flow in a rough micro-channel with different types of roughness is shown in Fig. 1. The two-dimensional domain is broken up into elements, similar to finite elements, but each element employs high-order interpolants based on... 

---