Gradient temperature profile

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

At the outer edge of the thermal boundary layer, the temperature is 9S and the temperature gradient (36/dy) = 0 if there is to be no discontinuity in the temperature profile. 

Figure 2.6 shows a typical temperature profile.t l The temperature boundary layer is similar to the velocity layer. The flowing gases heat rapidly as they come in contact with the hot surface of the tube, resulting in a steep temperature gradient. The average temperature increases toward downstream. 

The wall boundary condition applies to a solid tube without transpiration. The centerline boundary condition assumes S5anmetry in the radial direction. It is consistent with the assumption of an axis5Tnmetric velocity profile without concentration or temperature gradients in the 0-direction. This boundary condition is by no means inevitable since gradients in the 0-direction can arise from natural convection. However, it is desirable to avoid 0-dependency since appropriate design methods are generally lacking. 

The associated temperature profiles are shown in Figures 10 through 12. Metal in contact with Dowtherm is at 240°C, whereas in the middle of the plate, the metal temperature ranges from 226 to 234°C. Because of this effect, as well as the relatively low thermal conductivity of polymer melt, large temperature gradients exist along the y and z directions. At the walls the polymer temperature reaches 240°C, whereas at the center of the channel the polymer temperature is only 213°C, at the outlet. 

Figure 3 shows the profiles induced in a bulk system by an applied temperature gradient. These Monte Carlo results [ 1 ] were obtained using the static probability distribution, Eq. (246). Clearly, the induced temperature is equal to the applied temperature. Also, the slopes of the induced density and energy profiles can be obtained from the susceptibility, as one might expect since in the linear regime there is a direct correspondence between the slopes and the moments [1]. 

Figure 13.6 indicates that very large temperature gradients exist near the beginning of the bed and that the higher the inlet temperature, the greater the difference between this temperature and the maximum temperature achieved in the bed. Catalyst effectiveness factor profiles mirror the temperature profiles in an opposite... 

Fig. 2.6 I nverted temperature gradients in microwave versus oil-bath heating [12]. Temperature profiles (finite element modeling) after 1 min as affected by microwave irradiation (left) compared to treatment in an oil bath (right). Microwave irradiation raises the...

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