Temperature gradient, liquid film

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

EfiBdent hydrogen supply iiom decalin was only accomplished by the si terheated liquid-film-type catalysis under reactive distillation conditions at modaate heating tempaatures of 210-240°C. Caibcm-supported nano-size platinum-based catalysts in the si ietheated liquid-film states accelerated product desorption fixjm file catalyst surface due to its temperature gradient under boiling conditions, so that both hi reaction rates and conversions were obtained simultaneously. 

Brown (1967) noted that a vapor bubble in a temperature gradient is subjected to a variation of surface tension which tends to move the interfacial liquid film. This motion, in turn, drags with it adjacent warm liquid so as to produce a net flow around the bubble from the hot to the cold region, which is released as a jet in the wake of the bubble (Fig. 4.10). Brown suggested that this mechanism, called thermocapillarity, can transfer a considerable fraction of the heat flux, and it appears to explain a number of observations about the bubble boundary layer, including the fact that the mean temperature in the boundary layer is lower than saturation (Jiji and Clark, 1964). 

Temperature gradient among reactor wall, catalyst-layer, and reactant solution under superheated liquid-film conditions. 

In the adequate case (1.0 or 2.0 mL tetralin), the catalyst appeared to be wet differently from dry sand-bath or suspension states. As in the case of decalin dehydrogenation under the superheated liquid-film conditions, the catalyst temperature is higher than the boiling point, exhibiting a temperature gradient, and the substrate liquid is limited in amount to... 

The more recent Thomas model [209] comprises elements of both the Semenov and Frank-Kamenetskii models in that there is a nonuniform temperature distribution in the liquid and a steep temperature gradient at the wall. Case C in Figure 3.20 shows a temperature distribution curve from self-heating for the Thomas model. The appropriate model (Semenov, Frank-Kamenetskii, or Thomas) is determined by the ratio of the heat removal from the vessel and the thermal conductivity in the vessel. This ratio is determined by the Biot number (Nm) which has been described previously as hx/X, in which h is the film heat transfer coefficient to the surroundings (air, cooling mantle, etc.), x is the distance such as the radius of the vessel, and X is the effective thermal conductivity. 

Consider a vertical flat plate exposed to a condensable vapor. If the temperature of the plate is below the saturation temperature of the vapor, condensate will form on the surface and under the action of gravity will flow down the plate. If the liquid wets the surface, a smooth film is formed, and the process is called film condensation. If the liquid does not wet the surface, droplets are formed which fall down the surface in some random fashion. This process is called dropwise condensation. In the film-condensation process the surface is blanketed by the film, which grows in thickness as it moves down the plate. A temperature gradient exists in the film, and the film represents a thermal resistance to heat transfer. In dropwise condensation a large portion of the area... 

The value of /i in a fluid film, i.e., that o h, is originally proportional to the value of A of the fluid itself As the value of the temperature gradient in a fluid film increases on account of the decrease in thickness of the film, however, the value of h increases even in the identical fluid. In other words, the value of hi of a liquid in which the forced convective flow is made is necessarily larger than that of the liquid in which the natural convective flow is allowed, because the thickness of the fluid film decreases with the increase in rate of the forced convective flow. Besides, it is also possible to point out a fact that the value of A of an ordinary liquid in general are much larger than that of an ordinary gas. 

Near the surface, a high gas content (polyhedral foam) is formed, with a much lower gas content structure near the base of the column (bubble zone). A transition state may be distinguished between the upper and bottom layers. The drainage of excess liquid from the foam column to the underlying solution is initially driven by hydrostatic pressure, which causes the bubble to become distorted. Foam collapse usually occurs from top to bottom of the column, with films in the polyhedral foam being more susceptible to rupture by shock, temperature gradient, or vibration. 

A correctly designed and constructed rotational viscometer is a convenient instrument for detecting departure from Newtonian viscosity behavior, since the rate of shear is readily computed by Eqn 4-27 from easily measured quantities such as Q, and R2. Barber, Muenger and Villforth [10] discuss the design and construction of an instrument which has the desired attributes and in addition operates so that the temperature gradient in the sheared film of liquid is only one or two degrees Kelvin. 

Film thidcness S is typically two or three orders of magnitude smaller than the tube diameter it can therefore be found, for flow either inside or outside a tube, from the equation for a flat plate, Eq. (5.77). Since there is a temperature gradient in the film, the properties of the liquid are evaluated at the average film temperature 7., given by Eq. (13.11). For condensation on a vertical surface, for which cos) = 1, Eq. (5.77) becomes... 

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