Internal flow combined convection

Commercial dryers differ fundamentally by the methods of heat transfer employed (see classification of diyers, Fig. 12-45). These industrial-diyer operations may utihze heat transfer by convection, conduction, radiation, or a combination of these. In each case, however, heat must flow to the outer surface and then into the interior of the solid. The single exception is dielectric and microwave diying, in which high-frequency electricity generates heat internally and produces a high temperature within the material and on its surface. 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

Another area of rapid growth for particle separation has been that of Field-Flow Fractionation (FFF) originally developed by Giddings (12,13>1 1 ) (see also papers in this symposium series). Like HDC, the separation in field-flow fractionation (FFF) results from the combination of force field interactions and the convected motion of the particles, rather than a partitioning between phases. In FFF the force field is applied externally while in HDC it results from internal, interactions. 

The bed and the fluid are considered as a pseudo-homogeneous medium, and the heat transfer in the bed up to the internal side of the wall is represented by two parameters, the radial effective conductivity snd the internal wall heat transfer coefiident aw,int- The introduction of aw.mt allows us to take into account a weaker heat transfer (smaller effective radial heat transfer coefficient X ad) close to the wall due to less mixing and a higher void fraction of the bed (Figure 4.10.64). Thus, combines the interplay of convective flow at the wall and of conduction by contact between the bed and the heat exchange surface (internal wall), and assumes a jump in temperature direcily at the wall. For relative simple modeling, the consequence of the introduction of mt is also that we use a constant value of within the bed. 

The first term on the right is convection, whereas the second is heat flow. Combination of these results yields the following balance equation for the internal energy... 

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