Steady-state temperature fields

In the simplest case of one-dimensional steady flow in the x direction, there is a parallel between Eourier s law for heat flowrate and Ohm s law for charge flowrate (i.e., electrical current). Eor three-dimensional steady-state, potential and temperature distributions are both governed by Laplace s equation. The right-hand terms in Poisson s equation are (.Qy/e) = (volumetric charge density/permittivity) and (Qp // ) = (volumetric heat generation rate/thermal conductivity). The respective units of these terms are (V m ) and (K m ). Representations of isopotential and isothermal surfaces are known respectively as potential or temperature fields. Lines of constant potential gradient ( electric field lines ) normal to isopotential surfaces are similar to lines of constant temperature gradient ( lines of flow ) normal to... 

CFD is appropriate in cases where the detailed flow field is of interest in a configuration with mostly known or at least steady-state boundary conditions (surface temperatures). Combined thermal and ventilation modeling is more suited to cases where the dynamic behavior of the building masses and the changing driving forces for the natural ventilation are of importance. 

If kinetic processes on catalytic surfaces in S02 oxidation are assumed to be at steady state, temperature and concentration fields in a radially symmetrical, adiabatic catalyst bed are described by the equations collected in Table IX for the reactor space 0 and time I > 0 (Matros, 1989 ... 

Following the steps for formulation of a CFD model introduced earlier, we begin by determining the set of state variables needed to describe the flow. Because the density is constant and we are only interested in the mixing properties of the flow, we can replace the chemical species and temperature by a single inert scalar field (x, t), known as the mixture fraction (Fox, 2003). If we take = 0 everywhere in the reactor at time t — 0 and set / = 1 in the first inlet stream, then the value of (x, t) tells us what fraction of the fluid located at point x at time t originated at the first inlet stream. If we denote the inlet volumetric flow rates by qi and q2, respectively, for the two inlets, at steady state the volume-average mixture fraction in the reactor will be... 

Spodumen is a monoclinic pyroxene, space group C C2 c), with two not equivalent metal cation sites Ml and M2. The aluminum occupies the smaller Ml site, which is approximately octahedral (actual symmetry C2) with an average metal-oxygen distance of 1.92 A. The M2 site, occupied by Li, is also six-fold coordinated with an average metal-oxygen distance of 2.23 A. Both A1 and Li sites may be substitutionally replaced by ions of the transitional metals in various proportions. Both Mn " " and Cr " centers have been identified in luminescence spectra by steady-state spectroscopy (Tarashchan 1978 Walker et al. 1997). At room and lower temperatures only one emission band of Mn + occurs and the excitation spectra taken for the different wavelengths of the luminescence bands are always the same. So it is very probable that Mn + ions in the spodumen matrix present only in one site. The calculated values of 10D,j and B are consistent with the occupation of larger M2(Li) weak-field site. Mn + is mainly in Li-sites rather than Al-sites. 

Photoinduced spin-related phenomena are a particularly important field of the solid-state photophysics, because fast spin switching is a prospective basis for applications in the field of spintronics. An illustrative example is the production of the metastable state of the iron propyltetrazole (ptz) complex [Fe(ptz)6](BF4)2 by laser light-induced excited spin-state trapping (LIESST) and the determination of the resulting structure by steady-state X-ray photodiffraction [68]. In another example, steady-state X-ray photodiffraction at cryogenic temperatures was successfully utilized to study photoinduced phase transition due to spin crossover in the tris(a-picolylamine)iron(II) complex [69]. The phase transition is accompanied by... 

Experiments with the field emission microscope show in a striking manner that the adsorption properties of a metal vary considerably from one crystallographic plane to another. The sticking probability, which determines the rate of adsorption, may be about 100 times smaller on one plane than on another as a result, at a fixed low pressure one plane may build up to only one layer while another builds up to two layers at a higher pressure, both planes may build up to two layers before a steady state is reached. If the surface is exposed to a high pressure until the whole surface is covered, and if the pressure is then reduced to a very low value, the rate of evaporation at a particular temperature from one plane may be hundreds of times greater than from a second plane. From such experimental facts one may safely conclude that the catalytic activity too will be found to vary for different crystallographic planes. 

Connection between Transport Processes and Solid Microstructure. The formation of cellular and dendritic patterns in the microstructure of binary crystals grown by directional solidification results from interactions of the temperature and concentration fields with the shape of the melt-crystal interface. Tiller et al. (21) first described the mechanism for constitutional supercooling or the microscale instability of a planar melt-crystal interface toward the formation of cells and dendrites. They described a simple system with a constant-temperature gradient G (in Kelvins per centimeter) and a melt that moves only to account for the solidification rate Vg. If the bulk composition of solute is c0 and the solidification is at steady state, then the exponential diffusion layer forms in front of the interface. The elevated concentration (assuming k < 1) in this layer corresponds to the melt that solidifies at a lower temperature, which is given by the phase diagram (Figure 5) as... 

Results from a quasi steady-state model (QSSM) valid for long crystals and a constant melt level (if some form of automatic replenishment of melt to the crucible exists) verified the correlation (equation 39) for the dependence of the radius on the growth rate (144) and predicted changes in the radius, the shape of the melt-crystal interface (which is a measure of radial temperature gradients in the crystal), and the axial temperature field with important control parameters like the heater temperature and the level of melt in the crucible. Processing strategies for holding the radius and solid-... 

---