Liquid solid interface, heat transfer

Heat transfer by nucleate boiling is an important mechanism in the vaporization of liqmds. It occurs in the vaporization of liquids in kettle-type and natural-circulation reboilers commonly usea in the process industries. High rates of heat transfer per unit of area (heat flux) are obtained as a result of bubble formation at the liquid-solid interface rather than from mechanical devices external to the heat exchanger. There are available several expressions from which reasonable values of the film coefficients may be obtained. 

The experimental and theoretical work reported in the literature will be reviewed for each of the five major types of ga s-liquid-particle operation under the headings Mass transfer across gas-liquid interface mass transfer across liquid-solid interface holdup and axial dispersion of gas phase holdup and axial dispersion of liquid phase heat transfer reaction kinetics. 

When (a) there are no external mass-transfer resistances (such as gas-liquid, liquid solid, etc.), (b) catalysts are all effectively wetted, (< ) there is no radial or axial dispersion in the liquid phase, (d) a gaseous reactant takes part in the reaction and its concentration in the liquid film is uniform and in excess, (e) reaction occurs only at the liquid-solid interface, (/) no condensation or vaporization of the reactant occurs, and (g) the heat effects are negligible, i.e., there is an isothermal operation, then a differential balance on such an ideal plug-flow trickle-bed reactor would give... 

In the past, there have been two major approaches to analyze the problem of heat and mass transfer across the liquid-solid interface. The first approach can be broadly classified as "Analogies." This method essentially consists of (von Karman ( ) and Wasan and Wilke ( )) (i) development of velocity profile near the interface, (ii) suitable assumption for the variation of eddy diffusivity with respect to the distance from the interface, and... 

Fischer-Tropsch (FT) synthesis is accompanied by an extremely large heat evolution (exothermic). To improve the characteristics of heat transfer, liquid phase synthesis using a slurry-type reactor has been developed. Although liquid phase synthesis has been operated using pulverized catalysts (ref. 1), it is interesting to use a catalyst of smaller particles, so-called ultrafine particle (UFP), for the purpose of enhancing the gas-liquid-solid interface contact. 

Several methods can be used to rapidly freeze foods. The most efficient is to immerse the product in a veiy cold liquid. This permits a liquid-solid interface for rapid heat transfer. Liquid nitrogen (LNj) and liquid Freon freezant (LFF) are the most commonly used, the latter being the most popular because... 

The most catalytic or noncatalytic processes involving reactions in multiphase systems. Such processes include heat and mass transfer and other diffusion phenomena. The applications of these processes are diverse and its reactors have their own characteristics, which depends on the type of process. For example, the hydrogenation of vegetable oils is conducted in a liquid phase slurry bed reactor, where the catalyst is in suspension, the flow of gaseous hydrogen keeps the particles in suspension. This type of reaction occurs in the gas-liquid-solid interface. 

The processes are transport of the gaseous reactant A in the vicinity of the liquid, transfer of this reactant through the gas-liquid interface into the liquid, transport of the dissolved gaseous reactant and of the liquid reactant B in the vicinity of the solid, transfer of both reactants at the external surface of the catalyst, through the liquid-solid interface, diffusion and reaction into the pores of the catalyst. The product undergoes similar mass transfer steps from the catalytic active sites to the liquid phase. In the case of a reaction with a heat effect, heat transfer steps associated to the proceeding mass transfer steps have to be considered. 

Three-phase packed bed reactors generally have a lower specific capacity than slurry reactors, for two reasons Much larger catalyst particles are used, so that for rapid reactions, with diffusion or mass transfer limitations, much larger catalyst volumes are required. Also, the maximum specific gas/liquid interfacial area is generally smaller. On the other hand, the volumetric mass transfer coefficients at the gas/liquid and at the liquid/solid interfaces are of comparable magnitude, so they are better adapted to one another. Heat transfer rates to the walls are quite limited. 

At an interface between gas and liquid or solid or between liquid and solid, convective heat transfer can take place when those media have a temperature difference. It can be in the form of free convection, such as in the case of a central heating radiator, or it can be forced convection, for example, an air flow from a blower. Owing to the resistance to heat transfer, a heat gradient will occur. In the model that describes this interface transfer, it is assumed, as shown in Fig. 2.8, that the temperature gradient restricts itself to a boundary layer. The bulk outside this boundary layer has a uniform temperature as a result of convection or mixing. Fig. 2.8 shows two possibilities. 

In a recent paper, Pruppacher carried this analysis still ftirther in order to analyze the results of field experiments on ice nucleation in clouds. He took four additional properties for which there is no evidence of singular behavior at -45°C (heat of melting, heat of evaporation, surface tension, and liquid-solid surface free energy) and fit them to power laws that led to a vanishing of the first and the last and a divergence of the second and third of these properties. With these functional forms, he then took nucleation rate data and used them to fit the only other parameter, the activation free energy for mass transfer across the liquid-solid interface. The result was that this quantity increased as the water was cooled down to -30°C and then began to decrease sharply. 

Where heat transfer is taking place at the saturation temperature of a fluid, evaporation or condensation (mass transfer) will occur at the interface, depending on the direction of heat flow. In such cases, the convective heat transfer of the fluid is accompanied by conduction at the surface to or from a thin layer in the liquid state. Since the latent heat and density of fluids are much greater than the sensible heat and density of the vapour, the rates of heat transfer are considerably higher. The process can be improved by shaping the heat exchanger face (where this is a solid) to improve the drainage of condensate or the escape of bubbles of vapour. The total heat transfer will be the sum of the two components. 

The thermal conductivity of materials has been examined in Chapter 2 and Chapter 3. As we shall see in this chapter, in many cases, at very low temperatures, the heat conduction is not limited by the bulk thermal resistivity of the material but by the contact thermal resistance appearing at the interface of two materials. This is a particularly severe problem, below IK, in the case of the heat transfer between liquid He and a solid (see Section 4.3). Heat transfer by radiation will be considered in Section 53.2.2. 

Eleat transfer occurs not only within the solid surface, droplet and vapor phases, but also at the liquid-solid and solid-vapor interface. Thus, the energy-balance equations for all phases and interfaces are solved to determine the heat-transfer rate and evaporation rate. 

The radiative heat transfer across the vapor layer is neglected under the condition that the solid temperature is lower than 700 °C (Harvie and Fletcher, 2001 a,b). On the liquid-vapor interface, the energy-balance equation is... 

In subcooled impact, the initial droplet temperature is lower than the saturated temperature of the liquid of the droplet, thus the transient heat transfer inside the droplet needs to be considered. Since the thickness of the vapor layer may be comparable with the mean free path of the gas molecules in the subcooled impact, the kinetic slip treatment of the boundary condition needs to be applied at the liquid-vapor and vapor-solid interface to modify the continuum system. 

The impact process of a 3.8 mm water droplet under the conditions experimentally studied by Chen and Hsu (1995) is simulated and the simulation results are shown in Figs. 16 and 17. Their experiments involve water-droplet impact on a heated Inconel plate with Ni coating. The surface temperature in this simulation is set as 400 °C with the initial temperature of the droplet given as 20 °C. The impact velocity is lOOcm/s, which gives a Weber number of 54. Fig. 16 shows the calculated temperature distributions within the droplet and within the solid surface. The isotherm corresponding to 21 °C is plotted inside the droplet to represent the extent of the thermal boundary layer of the droplet that is affected by the heating of the solid surface. It can be seen that, in the droplet spreading process (0-7.0 ms), the bulk of the liquid droplet remains at its initial temperature and the thermal boundary layer is very thin. As the liquid film spreads on the solid surface, the heat-transfer rate on the liquid side of the droplet-vapor interface can be evaluated by... 

Increasing the temperature or lowering the pressure on a superheated liquid will increase the probability of nucleation. Also, the presence of solid surfaces enhances the probability because it is often easier to form a critical-sized embryo at a solid-liquid interface than in the bulk of the liquid. Nucleation in the bulk is referred to as homogeneous nucleation whereas if the critical-sized embryo forms at a solid-liquid (or liquid-liquid) interface, it is termed heterogeneous nucleation. Normal boiling processes wherein heat transfer occurs through the container wall to the liquid always occur by heterogeneous nucleation. 

The combustion wave of HMX is divided into three zones crystallized solid phase (zone 1), solid and/or liquid condensed phase (zone 11), and gas phase (zone 111). A schematic representation of the heat transfer process in the combustion wave is shown in Fig. 5.5. In zone 1, the temperature increases from the initial value Tq to the decomposition temperature T without reaction. In zone 11, the temperature increases from T to the burning surface temperature Tj (interface of the condensed phase and the gas phase). In zone 111, the temperature increases rapidly from to the luminous flame temperature (that of the flame sheet shown in Fig. 5.4). Since the condensed-phase reaction zone is very thin (-0.1 mm), is approximately equal to T . 

Chapter 1 reviews the concepts necessary for treating the problems associated with the design of industrial reactions. These include the essentials of kinetics, thermodynamics, and basic mass, heat and momentum transfer. Ideal reactor types are treated in Chapter 2 and the most important of these are the batch reactor, the tubular reactor and the continuous stirred tank. Reactor stability is considered. Chapter 3 describes the effect of complex homogeneous kinetics on reactor performance. The special case of gas—solid reactions is discussed in Chapter 4 and Chapter 5 deals with other heterogeneous systems namely those involving gas—liquid, liquid—solid and liquid—liquid interfaces. Finally, Chapter 6 considers how real reactors may differ from the ideal reactors considered in earlier chapters. 

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