Convection stationary

Fig. 8.5. The product of the total rate of dissipation times temperature (solid line) in Js and the time derivative of excess work (dashed line) vs. time in the following processes for the Lorenz model (a) Gravity is initially set in the direction along which the temperature decreases, and the system is at a stable motionless conductive stationary state at t = 0, invert the direction of gravity the motionless conductive state becomes unstable and the system approaches the convective stationary state, (b) The reverse process. The temperature difference is AT = 4K for both cases...

There may be several reasons for a lack of quantitative agreement. First, the convective stationary state in the theory is a focus, not a node. (A node is approached with an eigenvalue that is real and negative and hence provides for a damped monotonic approach, whereas a focus is approached with a complex eigenvalue with the real part negative, that is a damped oscillatory approach.) In the experiments, however, the convective stationary state is a node due to the rigid boundaries. Second, because of the truncation to the first order in Fourier modes in the Lorenz model, this model can be a good approximation... 

Containerized ice cream is hardened on a stationary or continuous refrigerated plate-contact hardener or by convection air blast as the product is carried on a conveyor or through a tunnel. Air temperatures for hardening are —40 to —50° C. The temperature at the center of the container as well as the storage temperature should be <—26°C. Approximately one-half of the heat is removed at the freezer and the remainder in the hardening process. 

The packed-bed reactors discussed in Chapters 9 and 10 are multiphase reactors, but the solid phase is stationary, and convective flow occurs only through the fluid phase. The reaction kinetics are pseudohomogeneous, and components balances are written only for the fluid phase. 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

Two examples will now be given of solution of the convective diffusion problem, transport to a rotating disk as a stationary case and transport to a growing sphere as a transient case. Finally, an engineering approach will be mentioned in which the solution is expressed as a function of dimensionless quantities characterizing the properties of the system. 

Kast, W., 1964, Significance of Nucleating and Non-stationary Heat Transfer in the Heat Exchanger during Bubble Vaporization and Droplet Condensation, Chem. Eng. Tech. 36(9) 933-940. (2) Katto, Y., 1981, General Features of CHF of Forced Convection Boiling in Uniformly Heated Rectangular Channels, Ini. J. Heat Mass Transfer 24.14131419. (5)... 

The lack of hydrodynamic definition was recognized by Eucken (E7), who considered convective diffusion transverse to a parallel flow, and obtained an expression analogous to the Leveque equation of heat transfer (L5b, B4c, p. 404). Experiments with Couette flow between a rotating inner cylinder and a stationary outer cylinder did not confirm his predictions (see also Section VI,D). At very low rotation rates laminar flow is stable, and does not contribute to the diffusion process since there is no velocity component in the radial direction. At higher rotation rates, secondary flow patterns form (Taylor vortices), and finally the flow becomes turbulent. Neither of the two flow regimes satisfies the conditions of the Leveque equation. 

This expression applies to the transport of any conserved quantity Q, e.g., mass, energy, momentum, or charge. The rate of transport of Q per unit area normal to the direction of transport is called the flux of Q. This transport equation can be applied on a microscopic or molecular scale to a stationary medium or a fluid in laminar flow, in which the mechanism for the transport of Q is the intermolecular forces of attraction between molecules or groups of molecules. It also applies to fluids in turbulent flow, on a turbulent convective scale, in which the mechanism for transport is the result of the motion of turbulent eddies in the fluid that move in three directions and carry Q with them. 

Forced convection can be used to achieve fast transport of reacting species toward and away from the electrode. If the geometry of the system is sufficiently simple, the rate of transport, and hence the surface concentrations cs of reacting species, can be calculated. Typically one works under steady-state conditions so that there is no need to record current or potential transients it suffices to apply a constant potential and measure a stationary current. If the reaction is simple, the rate constant and its dependence on the potential can be calculated directly from the experimental data. 

For laminar conditions of slow flow, as in candle flames, the heat transfer between a fluid and a surface is predominately conductive. In general, conduction always prevails, but in the unsteadiness of turbulent flow, the time-averaged conductive heat flux between a fluid and a stationary surface is called convection. Convection depends on the flow field that is responsible for the fluid temperature gradient near the surface. This dependence is contained in the convection heat transfer coefficient hc defined by... 

In normal atmospheric conditions, fire usually is initialed by a combustible material coming in contact with a heat source. The spread of fire occurs due to direct flame impingement or the transfer of heat to the surrounding combustible materials. Heat transfer occurs by three principal mechanisms - conduction, convection, and radiation. Conduction is the movement of heat through a stationary medium, such as solids, liquids or gases. Steel is a good conductor of heat as is aluminum, therefore they can pass the heat of a fire if left unprotected. 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

A CV voltammogram can be recorded under either a dynamic or a steady state depending on the electrode design and solution convection mode. In a stationary solution with a conventional disk electrode, if the scan rate is sufficiently high to ensure a non-steady state, the current will respond differently to the forward and backward potential scan. Figure 63 shows a typical CV for a reversible reduction.1... 

If we neglect migration, experiments can be performed under conditions of minimal convection, which are thus dominated by diffusion. Since S increases with time t in such a case, nonstationary conditions exist. On the other hand, if convection dominates in the electrolyte bulk, S 7 /( ), and we approach stationary conditions, as far as diffusion is concerned. 

In Section 7.2, we looked at electroanalytical systems where the electrode rotates while the bulk of the solution remained still. In this present section, we will reverse this experimental concept by considering the case where it is the solution which flows - this time past a stationary electrode. Here, we shall be looking at flow ceils and channel electrodes. The principal mode of mass transport in both cases is convection, since the solution moves relative to the electrode. 

Convective measurements using stationary electrodes again show that / im a Canaiytc, provided that the solution flow is laminar. In this case, the limiting current... 

The particle is first levitated stably in the absence of convective forces or phoretic forces by adjusting the ac and dc voltages and the ac frequency to keep it stationary at the midplane of the balance, as observed through a microscope or video imaging system. The ratio g/m is written in terms of the measured value of applying Eq. (15), and the result is used to eliminate qlm in Eq. (19). The result is... 

When a fluid is heated, the hot less-dense fluid rises and is replaced by cold material, thus setting up a natural convection current. When the fluid is agitated by some external means, then forced convection takes place. It is normally considered that there is a stationary film of fluid adjacent to the wall and that heat transfer takes place through this film by conduction. Because the thermal conductivity of most liquids is low, the main resistance to the flow of heat is in the film. Conduction through this film is given by the usual relation (74), but the value of h is not simply a property of the fluid but depends on many factors such as the geometry of the system and the flow dynamics for example, with tubes there are significant differences between the inside and outside film coefficients. 

Dne to the macroporons strnctnre of monolithic stationary phases (flow channels), the solvent is forced to pass the entire polymer, leading to faster convective mass transfer (compared to diffnsion), which provides for analyte transport into and out of the stagnant pore liqnid, present in the case of microparticulate columns. 

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