Conductive heat transfer, lateral surface

If conduction or radiation is the predominant mode of heat transfer, the surface (and possibly the interior) moisture may literally boil regardless of the temperature or the humidity of the environment. This may be readily demonstrated by microwave drying. Thus, if control of granulation temperature is important, direct heat (convection) dryers usually offer greater control and product safety since the material s surface does not exceed the wet-bulb temperature during the steady state period. However, it will be shown later in this chapter that properly controlled dielectric drying may also be used to dry heat sensitive materials. 

Conductive Heat Transfer across the Lateral Surface ... 

The instantaneous rate of thermal energy transport into the reactive fluid across the wall at radius R is given by dQ/dV in (4-34), with units of energy per volume per time. The differential control volume of interest that contains the reactive fluid is t/V = itR dz, where z is the spatial coordinate that increases in the primary flow direction. Four possibilities allow one to determine this rate of conductive heat transfer across the lateral surface of the reactor ... 

Constant Outer Wall Temperature. If the chemical reaction is exothermic and the outer wall temperature of the reactor is lower than the temperature of the reactive fluid, then conductive heat transfer across the lateral surface will provide the necessary cooling. This condition is required to prevent thermal runaway. The differential rate of thermal energy transport d Q into the reactor across the lateral surface is given by the product of (1) an overall heat transfer coefficient that accounts for resistances in the thermal boundary layer within the reactive fluid, as well as the tube wall itself (2) an instantaneous temperature difference Twaii — T, where T is the bulk temperature of the reactive fluid at axial position z and (3) the differential lateral surface area, 2nR dz. Hence,... 

At this point it is important to note that this equation assumes that the controlling mechanism for heat transfer is conduction. Later, Hartley and Richards(H) developed a diffusion model for the hot surface drying of sheet materials. 

A common way of measuring the thermal conductivity of a material is to sand-v/ich an electric thermofoil heater between two identical samples of the material, as shown in Fig. 1-30. The thickness of the resistance heater, including its cover, v/hich is made of thin silicon rubber, is usually less than 0.5 mm. A circulating fluid such as tap water keeps the exposed ends of the samples at constant temperature. The lateral surfaces of the samples are well insulated to ensure that heat transfer through the samples is one-dimensional. Two thermocouples are embedded into each sample some distance L apart, and a... 

Using extended surfaces is addressed in several later sections on specific types and applications of heat exchangers. This section analyzes the efficiency of these surfaces, which is a problem of heat conduction, with the additional consideration of heat transfer to or from the surrounding fluid by convection. 

E, 31-2 XI, vi, II, 25-7. Later experimenters found that only in the case of the detonation wave is the flame velocity independent of the material of the tube, but Holm, Phil. Mag., 1932, xiv, 18 1933, XV, 329, thought the inability of flame to pass through narrow tubes is due to the extreme curvature of the flame-surface and consequent large heat loss from burnt to unbumt gas. The critical tube diameter is the same for glass as copper, with a thermal conductivity 400 times that of glass. The rate of heat transfer to the wall depends on the thermal conductivity of the gas, so that the assumption that the arrest of the flame is due to cooling by the wall rather than in the gas would not be satisfactory. 

These results were used as the starting conditions for the heat transfer calculation. They gave a maximum temperature of 820°K in the TNT and 910°K in the Plexiglas. The temperature in the gas was lowered to a maximum of 2000°K within 3 /nsec, and insufficient reaction had occurred to make the first cell decompose. At later times the explosive surface cooled as heat was being conducted away faster than it was furnished by the hot gas and explosive decomposition. 

In order to incorporate the shape of the p>articles (e.g. cylinders) and the interaction between the particles, extensions of this Maxwell model were later developed by (Hamilton and Grosser, 1962) and (Hui et al., 1999). However, these classical models were found to be unable to accurately predict the anomalously high thermal conductivity of nanofluids (Murshed et al., 2008a). Thus, researchers have proposed several mechanisms to explain this phenomenon. For example, (Kebflnski et al., 2002) systematized the four different mechanisms for heat transfer to explain these enhancements, namely (i) Brownian motion of the nanoparticles (ii) liquid layering at the liquid/ particle interphase, (iii) the nature of the heat transport in the nanoparticles and (iv) the effect of nanoparticle clustering. From the analysis made in an exhaustive review paper on nanofluids (Murshed et al., 2008a) and other publications cited, therein, it is our belief that the effect of the particle surface chemistry and the structure of the interphase partide/fluid are the major mechanisms responsible for the unexpected enhancement in nanofluids. 

In considering the heat that is transferred, the method first put forward by NussELT(%i and later modified by subsequent workers is followed. If the vapour condenses on a vertical surface, the condensate film flows downwards under the influence of gravity, although it is retarded by the viscosity of the liquid. The flow will normally be streamline and the heal flows through the film by conduction. In Nusselt s work it is assumed that the temperature of the film at the cool surface is equal to that of the surface, and at the other side was at the temperature of the vapour. In practice, there must be some small difference in temperature between the vapour and the film, although this may generally be neglected except where non-condensable gas is present in the vapour. 

Fast pyrolysis occurs in time of few seconds or less. Therefore, not only chemical reaction kinetics but also heat and mass transfer processes, as well as phase transition phenomena, play important roles. The critical issue is to bring the reacting biomass particle to the optimum process temperature and minimise its exposure to the intermediate (lower) temperatures that favour formation of charcoal. This objective can be achieved by using small particles, thus reducing the time necessary for heat up. This option is used in fluidised bed processes that are described later. Another possibility is to transfer heat very fast only to the particle surface that contacts the heat source. Because of the low thermal conductivity the deeper parts of the particles will be maintained at temperatures lower than necessary for char production. The products that form on the surface are immediately removed exposing that way consecutive biomass layers to the contact with the heat source. This second method is applied in ablative processes that are described later. 

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