Steady period

The primary nucleation process is divided into two periods in CNT one is the so called induction period and the other is the steady (or stationary) nucleation period (Fig. 2) [16,17]. It has been proposed by CNT that small (nanometer scale) nuclei will be formed spontaneously by thermal fluctuation after quenching into the supercooled melt, some of the nuclei could grow into a critical nucleus , and some of the critical nuclei will finally survive into macroscopic crystals. The induction period is defined as the period where the nucleation rate (I) increases with time f, whereas the steady period is that where I nearly saturates to a constant rate (fst). It should be noted that I is a function of N and t,I = I(N, t). In Fig. 2, N and N mean the size of a nucleus and that of the critical nucleus, respectively. The size N is defined... 

The purpose of this section is to present direct evidence of nucleation during the induction period by means of synchrotron small angle X-ray scattering (SAXS). In the classical nucleation theory (CNT), the number density distribution function of nuclei of size N at time t, f(N, t), is expected to increase with an increase of t during the induction period and saturates to a steady f(N, t),fst(N) in the steady period. The change off(N, t) should correspond to that of the scattering intensity of SAXS. 

Figure 14. Simple model demonstrating how adsorption and surface diffusion can co-Urnit overall reaction kinetics, as explained in the text, (a) A semi-infinite surface establishes a uniform surface coverage Cao of adsorbate A via equilibrium of surface diffusion and adsorption/desorption of A from/to the surrounding gas. (b) Concentration profile of adsorbed species following a step (drop) in surface coverage at the origin, (c) Surface flux of species at the origin (A 4i(t)) as a function of time. Points marked with a solid circle ( ) correspond to the concentration profiles in b. (d) Surface flux of species at the origin (A 4i(ft>)) resulting from a steady periodic sinusoidal oscillation at frequency 0) of the concentration at the origin.

Seeking a steady periodic solution, the right hand side suggest that the solution should be [6],... 

A. Barletta and E. Zanchini, Hyperbolic heat conduction and thermal resonances in a cylindrical solid carrying a steady-periodic electric field, Int. J. Heat Mass Transf. 39, 1307-1315 (1996). 

That is, in the specific case of electrochemical impedance spectroscopy (EIS), the steady, periodic linear response of a cell to a sinusoidal current or voltage perturbation is measured and analyzed in terms of gain and phase shift as a function of frequency, to, where the results are expressed in terms of the impedance, Z. In this regard, the impedance response of an electrode or a battery is given by... 

For example, supported TiCl4/MgCl2 catalysts show a short period of acceleration, followed by a prolonged steady period 92,93). However, in the presence of electron donors, they may show the typical decay rate kinetics observed during propylene polymerization 93). Bulk catalysts prepared by interaction of TiCU with Mg(OR)2 show either a stationary rate, or a non-stationary rate, according to the titanium content 88,94). Bulk catalysts prepared by reduction of TiCl4 with organomagnesium compounds show a decay type rate 92-95>. 

The catalyst showed high rate of deactivation (9°F/month WABT ) during first 2 months or so followed by a relatively steady period of 5-6 months (4°F/month WABT). The EOR was characterized by steep temperature rise. 

SO that we have N = N. Nt measurements in total. In the present steady state estimation procedure, the sensors are assumed to be distributed along the channel wall length and the measurements are taken as an average in a time interval within the steady period (A) = 1). 

The imaginary part of Eq. 3.64 is the starting periodic solution of the complementary problem.) As t - oo, the last term in parentheses approaches zero, and Eq. (3.65) reduces to the steady periodic solution,... 

For linear problems, the input and response have the same harmonic variation. A steady periodic solution must then have the form... 

In Section 3.2 we focused on the unsteady solution and its steady part for periodic lumped problems. We learned then the practical importance of steady periodic solutions and, in terms of the method of complex temperature, an easy way of obtaining only the steady part of periodic solutions. In this section we apply the method of complex... 

Consider a semi-infinite solid whose surface temperature is oscillating as So cos a>t relative to an ambient at temperature rw. We wish to determine the steady periodic temperature of this solid. 

Consider a flat plate steadily oscillating with velocity V0 sin cat on top of another flat plate (Fig. 3P-4). The pressure and dry friction coefficient between the plate are p and pc, respectively. Find the steady periodic temperature fluctuations in the system. 

In this equation T is the mean fluid temperature at any time, T is the wall temperature, 7] is the mean temperature of the quiescent fluid before the transient is initiated, and L is the length of the cylinder. All physical properties are evaluated at T . The length scales L and D were not sufficiently different to affect the correlation much, and L was arbitrarily chosen. The heat transfer coefficient q"l(T - T) remained constant throughout the quasi-steady period. Hiddink et al. [138] found that Eq. 4.137 also correlated data for heating only the bottom and side walls of vertical cylinders provided the cylinder diameter replaced L, and a coefficient of 0.52 rather than 0.55 was used. Their experiments were performed for length-to-diameter ratios of 0.25 to 2.0 and for 5 < Pr < 83,000. 

THERMAL ATTENUATION THROUGH HOMOGENEOUS AND MULTILAYER SLABS IN STEADY PERIODIC CONDITIONS-THEORY AND EXPERIMENTS. FROM PROCEEDINGS OF THE SEVENTH CONFERENCE ON THERMAL CONDUCTIVITY. GAITHERSBURa MARYLAND. NOV. 13-16,1967. 

The insolation data provided in Table XI of the Regulations are uniform heat fluxes. They are to be applied at the levels stated for 12 h (daylight) followed by 12 h of no insolation (night). The cyclic step functions representing insolation should be applied until the temperatmes of interest reach conditions of steady periodic behaviour. 

For a more precise model, a time dependent sinusoidal heat flux may be used to represent insolation during daylight hours for flat surfaces or for curved surfaces. The integrated (total) heat input to a surface between sunrise and sunset is required to be equal to the appropriate value of total heat for the table values over 12 h (i.e. multiply the table value by 12 h to get total heat input in W/m ). The period between sunset and sunrise gives zero heat flux for this model. The cyclic insolation model should be applied until the temperatures of interest reach conditions of steady periodic behaviour. 

Evaluation of the package temperature for transport of radioactive material may be done by analysis or test. Tests, if used, should be performed on full scale models. If the radiation source is not sunlight, differences between solar wavelength and the source wavelength should be taken into account. The test should continue until thermal equilibrium is achieved (either constant steady state or steady periodic state, depending on the source). Corrections should be made for ambient temperatures and internal heat, where necessary. 

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