Transfer factor

Figure 2 Flow diagram of the DHT with N=8, P=3. Broken lines represent transfer factors -1 while full lines represent unity transfer factor. The crossover boxes perform the sign reversal called for by the shift theorem which also requires the sine and cosine factors Sn, Cn.

Example 2 Calculation of j Factors in an Annulus Calculate the heat-transfer / factors for both walls of an annulus for the following condi-... 

A heat transfer factor (a) between the fluid and surface is defined as... 

If steam condenses on a surface, there is no boundary layer the resistance to heat flow is due to scale, metal thickness, and the condensed liquid layer, resulting in a high heat transfer factor. A thin layer of air or other noncondensing gas forms at the surface through which the steam diffuses. The heat transfer factor diminishes rapidly but is considerably higher than in dry convection. 

The net heat transfer between two surfaces according to Eq. (4.159) is proportional to the first or second power of the temperature difference hence the radiation heat transfer dominates at a high temperature or for large temperature differences. When the temperature difference is small, a heat transfer factor is used similar to that used for convective heat transfer ... 

For conduction the heat resistance is the distance divided by the heat conductivity, R = 8/X.A, and the heat conductance is heat conductivity divided by distance, U = X.A/8. For convection and radiation the heat resistance is 1 divided by the heat transfer factor, 1/aA, and the heat conductance is the same as the heat transfer factor, U aA. A coefficient of heat flow is also used, the K value, which is the total conductance ... 

FIGURE 4.33 Heat transfer factor representing blackbody radiation for various mean temperatures and temperature differences. 

Figures 4.34 and 4.35 represent two extreme cases. Drying processes represent the case shown in Fig. 4.34 and distillation processes represent Fig. 4.35. Neither case represents a convective mass transfer case while the gas flow is in the boundary layer, other flows are Stefan flow and turbulence. Thus Eqs. (4.243) and (4.244) can seldom be used in practice, but their forms are used in determining the mass transfer factor for different cases.

Considering the case of Eq. (4.244), it is normal to describe a real mass transfer case by taking into consideration the boundary layer flows and the turbulence by using a mass transfer factor which is defined by... 

Based on this, it is normal to define a mass transfer factor consistent with this case, analogous with Eq. (4.245) ... 

With the use of Eqs. (4.255) and (4.256a), the following relationships between the mass transfer factors are obtained ... 

In practice the mass transfer factors are often presented without stating the experimental assumptions by which = -/g or /g = 0 has been obtained. The designer has to decide on the suitability of the experiments from which the quantity or is measured. 

We can apply this result to determine the analogy between mass and heat transfer factors. Mass flow density /a (mol/m s) can be given as... 

Strictly speaking, a new mass transfer factor should be defined that represents the situation Ma/a = 3. 

The dimensionless quantity Sh is called the Sherwood number. The heat transfer factor a is defined bv... 

The preceding discussion has attempted to formulate the situation for laminar boundary layer flow as accurately as possible and to obtain precise correlation between the heat transfer and mass transfer factors. 

This allows the mass transfer factor to be calculated. The above equation can be refined to... 

To calculate the conductance of the boundary layer we first calculate rhf mass transfer factor using Eq. (4.300) ... 

Heat Transfer Factors. These involve the removal, or addition of the heat of reaction. 

Surfaces will absorb radiant heat and this factor is expressed also as the ratio to the absorptivity of a perfectly black body. Within the range of temperatures in refrigeration systems, i.e. - 70°C to + 50°C (203-323 K), the effect of radiation is small compared with the conductive and convective heat transfer, and the overall heat transfer factors in use include the radiation component. Within this temperature range, the emissivity and absorptivity factors are about equal. 

Pressure losses due to pipe friction can be calculated from the basic formulas established by Reynolds and others. However, as with the calculation of heat transfer factors, this would be a time-consuming process and some of the parameters are not known accurately. Recourse is usually made to simplified estimates or tables published in works of reference [32, 33]. 

As discussed in Section 9.4.3, heat transfer data are conveniently correlated in terms of a heat transfer factor j/ again modified by the viscosity correction factor ... 

It may be noted that whilst Figure 9.77 is similar to Figure 9.24, the values of ji, differ due to the fact that Kern(28) and other workers define the heat transfer factor as ... 

Figure 9.77. Heat transfer factor for flow inside tubes...

Figure 9.81. Shell-side heat-transfer factors with segmental baffles1 ...

The MRLs are derived from data from supervised residue trials that are generally carried out in the context of food production. Specific conditions of feed production are not considered. Therefore, many practical problems for the official control of feed must be solved in future, e.g., application of transfer factors and the calculation of MRLs for mixed feed. 

Using transfer factors derived for uptake into plants and animals, Friberg and Vesanen (1999) have listed critical activity levels for americium and other nuclides deposited on soil and pasture vegetation from a nuclear accident required to exceed the action level for foodstuffs recommended by the IAEA. Experiments have been conducted to assess uptake of241 Am and other radionuclides from fallout or nuclear facilities in plants. 

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