Surface temperature, step change

Ta here is the temperature of the cooling fluid. In the case of the cylindrical geometry the corresponding boundary and initial conditions for the constant surface temperature (step change in temperature) or the step change in surface temperature due to convection are written, respectively, as... 

The atoms on the outennost surface of a solid are not necessarily static, particularly as the surface temperature is raised. There has been much theoretical [12, 13] and experimental work (described below) undertaken to investigate surface self-diffiision. These studies have shown that surfaces actually have dynamic, changing stmetures. For example, atoms can diflfiise along a terrace to or from step edges. When atoms diflfiise across a surface, they may move by hopping from one surface site to the next, or by exchanging places with second layer atoms. 

Fig. 18-8 Characteristic temperature-depth distributions at an ice divide. For a climatic temperature history as shown in (a) the temperature-depth distribution changes as shown in (b). Following the step increase in surface temperature, the initial steady temperature profile (fi in (b)) is altered by a warming wave (e.g., at time fa) but eventually reaches a new steady profile by time t. (c) Temperature data from Greenland measured by Gary Clow of the US Geological Survey, showing wiggles due to climate variations (Cuffey et ah, 1995).

In this paper we will first describe a fast-response infrared reactor system which is capable of operating at high temperatures and pressures. We will discuss the reactor cell, the feed system which allows concentration step changes or cycling, and the modifications necessary for converting a commercial infrared spectrophotometer to a high-speed instrument. This modified infrared spectroscopic reactor system was then used to study the dynamics of CO adsorption and desorption over a Pt-alumina catalyst at 723 K (450°C). The measured step responses were analyzed using a transient model which accounts for the kinetics of CO adsorption and desorption, extra- and intrapellet diffusion resistances, surface accumulation of CO, and the dynamics of the infrared cell. Finally, we will briefly discuss some of the transient response (i.e., step and cycled) characteristics of the catalyst under reaction conditions (i.e.,... 

A fast-response infrared spectroscopic reactor system has been described which is capable of operating at high temperatures (e.g., 450-500°C). The infrared reactor system was successfully used to monitor the response of the surface concentration of CO to step changes or oscillations in the feedstream composition, under both reactive and nonreactive conditions. 

The apparatus s step change from ambient to desired reaction conditions eliminates transport effects between catalyst surface and gas phase reactants. Using catalytic reactors that are already used in industry enables easy transfer from the shock tube to a ffow reactor for practical performance evaluation and scale up. Moreover, it has capability to conduct temperature- and pressure-jump relaxation experiments, making this technique useful in studying reactions that operate near equilibrium. Currently there is no known experimental, gas-solid chemical kinetic method that can achieve this. 

Example 5.2 Semi-infinite Solid with Constant Thermophysical Properties and a Step Change in Surface Temperature Exact Solution The semi-infinite solid in Fig. E5.2 is initially at constant temperature Tq. At time t — 0 the surface temperature is raised to T. This is a one-dimensional transient heat-conduction problem. The governing parabolic differential equation... 

Example 5.3 The Semi-infinite Solid with Variable Thermophysical Properties and a Step Change in Surface Temperature Approximate Analytical Solution We have stated before that the thermophysical properties (k, p, Cp) of polymers are generally temperature dependent. Hence, the governing differential equation (Eq. 5.3-1) is nonlinear. Unfortunately, few analytical solutions for nonlinear heat conduction exist (5) therefore, numerical solutions (finite difference and finite element) are frequently applied. There are, however, a number of useful approximate analytical methods available, including the integral method reported by Goodman (6). We present the results of Goodman s approximate treatment for the problem posed in Example 5.2, for comparison purposes. 

Example 5.4 Melting of a Semi-infinite Solid with Constant Thermophysical Properties and a Step Change in Surface Temperature The Stefan-Neumann Problem The previous example investigated the heat conduction problem in a semi-infinite solid with constant and variable thermophysical properties. The present Example analyzes the same conduction problem with a change in phase. 

We assume that the temperature profile in each phase has the form of the temperature profile in a semi-infinite solid with a step change in surface temperature as derived in Example 5.2. Thus we get the following temperature profiles for melt and solid phases, respectively,... 

The break-point temperature in dehydration (above which the rate was temperature insensitive) matched the maximum temperature for dehydrogenation, suggesting that a common intermediate exists for each reaction, and that the product selectivity is determined by interactions with other molecules and the surface. Above 650 K, the catalytic dehydration channel dominates, but the rate-determining step changes above 700 K. Below 700 K, the reaction rate is nearly independent of the partial pressure of formic acid (ca. 0.2 order). Above 700 K, the rate of the reaction is essentially independent of temperature, implying that reaction is limited by formic acid adsorption and dissociation thus, above 700 K, the rate becomes first-order with respect to the partial pressure of formic acid. Higher pressures of formic acid over the crystal surface should therefore increase the transition temperature - this behavior was observed by Iwasawa and coworkers, and the turnover frequency for catalytic dehydration approached the collision frequency of formic acid at high... 

Note that the inner surface temperature of the Trombe wall dropped by I C and the outer surface temperature rose by 6.5°C during the first time step vrhile the temperatures at the interior nodes remained the same. This is typical of transient problems in mediums that involve no heat generation. The nodal temperatures at the following time steps are determined similarly with the help of a computer. Note that the dala for ambient temperature and the incident solar radiation change every 3 hours, which corresponds to 12 time steps, and this must be reflected in the computer program. For example, the value o( must be taken to be = 360 for / = 1 12, = 763 for i =... 

J is a coupling constant that gives the energy cost of a step change in the surface height. For a vicinal surface, roughening may occur by proliferation of kinks at a temperature given implicitly by... 

Typical resistance responses to a step change in the gas composition are illustrated in Figure 1. The experimental results (open circles, labels 1, 2, 3) and the theoretical calculations (dash-dot lines, labels 1, 2, 3 ) are plotted in this figure. The resistance response to gas was measured in several sensors in which the rate parameters of the surface chemical reaction were made different by modification with the metallic catalyst. The temperature of the sensors was fixed at about 600 K long before the tests. 

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