Velocity of convection

The quasireversible case. When Eq. (5.4.22) cannot be simplified as described under alternatives 2 and 3, then it should be considered that the first term on its right-hand side increases compared to the second term as the potential becomes more positive and decreases at more negative potentials. As the velocity of convection increases, the second term increases compared to the first term. 

Vx Velocity of convective heat exchange front (see Section lV,3,a)... 

This velocity of diffusion must be added to the velocity of convection. 

When a sample is injected into the carrier stream it has the rectangular flow profile (of width w) shown in Figure 13.17a. As the sample is carried through the mixing and reaction zone, the width of the flow profile increases as the sample disperses into the carrier stream. Dispersion results from two processes convection due to the flow of the carrier stream and diffusion due to a concentration gradient between the sample and the carrier stream. Convection of the sample occurs by laminar flow, in which the linear velocity of the sample at the tube s walls is zero, while the sample at the center of the tube moves with a linear velocity twice that of the carrier stream. The result is the parabolic flow profile shown in Figure 13.7b. Convection is the primary means of dispersion in the first 100 ms following the sample s injection. 

Convection Heat Transfer. Convective heat transfer occurs when heat is transferred from a soHd surface to a moving fluid owing to the temperature difference between the soHd and fluid. Convective heat transfer depends on several factors, such as temperature difference between soHd and fluid, fluid velocity, fluid thermal conductivity, turbulence level of the moving fluid, surface roughness of the soHd surface, etc. Owing to the complex nature of convective heat transfer, experimental tests are often needed to determine the convective heat-transfer performance of a given system. Such experimental data are often presented in the form of dimensionless correlations. 

The effective thermal conductivity of a Hquid—soHd suspension has been reported to be (46) larger than that of a pure Hquid. The phenomenon was attributed to the microconvection around soHd particles, resulting in an increased convective heat-transfer coefficient. For example, a 30-fold increase in the effective thermal conductivity and a 10-fold increase in the heat-transfer coefficient were predicted for a 30% suspension of 1-mm particles in a 10-mm diameter pipe at an average velocity of 10 m/s (45). 

The maximum velocity at the axis is twice the average, whereas the velocity at the wall is zero. The effect of the burner wall is to cool the flame locally and decrease the burning velocity of the mixture. This results in flame stabilization. However, if the heat-transfer processes (conduction, convection, and radiation) involved in cooling the flame are somehow impeded, the rate of heat loss is decreased and the local reduction in burning velocity may no longer take place. This could result in upstream propagation of the flame. 

Convective heat transfer occurs when a fluid (gas or liquid) is in contact with a body at a different temperature. As a simple example, consider that you are swimming in water at 21°C (70°F), you observe that your body feels cooler than it would if you were in still air at 21°C (70°F). Also, you have observed that you feel cooler in your automobile when the air-conditioner vent is blowing directly at you than when the air stream is directed away from you. Both ot these observations are directly related to convective heat transfer, and we might hypothesize that the rate of energy loss from our body due to this mode of heat transfer is dependent on not only the temperature difference but also the typie of surrounding fluid and the velocity of the fluid. We can thus define the unit heat transfer for convection, q/A, as follows ... 

In most cases where convective heat transfer is taking place from a surface to a fluid, the circulating currents die out in the immediate vicinity of the surface and a film of fluid, free of turbulence, covers the surface. In this film, heat transfer is by thermal conduction and, as the thermal conductivity of most fluids is low, the main resistance to transfer lies there, Thus an increase in the velocity of the fluid over the surface gives rise to improved heat transfer mainly because the thickness of the film is reduced. As a guide, the film coefficient increases as (fluid velocity)", where 0.6 < n < 0.8, depending upon the geometry. 

Figure 9.22. Film coefficients of convection for flow of air through a tube at various velocities...

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

Convection due to the solar heating of the Earth s surface. Upward velocities of 2-20 cm/ s occur. 

Langmuir, I., The velocity of reactions in gases moving through heated vessels and the effect of convection and diffusion, J. Am. Chem. Soc., 30, 1742-1754 (1908). 

In Chapter 6.4, J. Chomiak and J. Jarosinski discuss the mechanism of flame propagation and quenching in a rofating cylindrical vessel. They explain the observed phenomenon of quenching in ferms of the formation of fhe so-called Ekman layers, which are responsible for the detachment of flames from the walls and the reduction of fheir width. Reduction of the flame speed with increasing angular velocity of rofation is explained in terms of free convection effects driven by centrifugal acceleration. 

A booth should be of sufficient size to contain any naturally occurring emissions and so minimize escape via the open face. An air velocity of 0.56 m/s is required over the whole open face a higher velocity is needed if there is significant air movement within the booth or to cope with convection currents. Booths should be deep enough to contain eddies at the rear corners baffle plates or multiple offtakes may be necessary with shallow booths. 

Similar convection-diffusion equations to the Navier-Stokes equation can be formulated for enthalpy or species concentration. In all of these formulations there is always a superposition of diffusive and convective transport of a field quantity, supplemented by source terms describing creation or destruction of the transported quantity. There are two fundamental assumptions on which the Navier-Stokes and other convection-diffusion equations are based. The first and most fundamental is the continuum hypothesis it is assumed that the fluid can be described by a scalar or vector field, such as density or velocity. In fact, the field quantities have to be regarded as local averages over a large number of particles contained in a volume element embracing the point of interest. The second hypothesis relates to the local statistical distribution of the particles in phase space the standard convection-diffusion equations rely on the assumption of local thermal equilibrium. For gas flow, this means that a Maxwell-Boltzmann distribution is assumed for the velocity of the particles in the frame-of-reference co-moving with the fluid. Especially the second assumption may break dovm when gas flow at high temperature or low pressure in micro channels is considered, as will be discussed below. 

In aqueous solutions Dj = lO cmVs a typical value of 5 is 10 cm. It follows that the convective and diffusional transport are comparable even at the negligible linear velocity of 10 cm/s of the liquid flow. At larger velocities, convection will be predominant. 

The development of the equations for the dynamic dispersion model starts by considering an element of tube length AZ, with a cross-sectional area of Ac, a superficial flow velocity of v and an axial dispersion coefficient, or diffusivity D. Convective and diffusive flows of component A enter and leave the element, as shown by the solid and dashed arrows respectively, in Fig. 4.12. 

The spatial temperature distribution established under steady-state conditions is the result both of thermal conduction in the fluid and in the matrix material and of convective flow. Figure 2. 9.10, top row, shows temperature maps representing this combined effect in a random-site percolation cluster. The convection rolls distorted by the flow obstacles in the model object are represented by the velocity maps in Figure 2.9.10. All experimental data (left column) were recorded with the NMR methods described above, and compare well with the simulated data obtained with the aid of the FLUENT 5.5.1 [40] software package (right-hand column). Details both of the experimental set-up and the numerical simulations can be found in Ref. [8], The spatial resolution is limited by the same restrictions associated with spin... 

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