Conductivity-temperature profiles

Ehase Inversion Temperatures It was possible to determine the Phase Inversion Temperature (PIT) for the system under study by reference to the conductivity/temperature profile obtained (Figure 2). Rapid declines were indicative of phase preference changes and mid-points were conveniently identified as the inversion point. The alkane series tended to yield PIT values within several degrees of each other but the estimation of the PIT for toluene occasionally proved difficult. Mole fraction mixing rules were employed to assist in the prediction of such PIT values. Toluene/decane blends were evaluated routinely for convenience, as shown in Figure 3. The construction of PIT/EACN profiles has yielded linear relationships, as did the mole fraction oil blends (Figures 4 and 5). The compilation and assessment of all experimental data enabled the significant parameters, attributable to such surfactant formulations, to be tabulated as in Table II. 

Figure 3. Conductivity/temperature profiles for toluene/decane blends...

Characteristic time required to establish a conductive temperature profile... 

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

Figure 5 shows conduction heat transfer as a function of the projected radius of a 6-mm diameter sphere. Assuming an accommodation coefficient of 0.8, h 0) = 3370 W/(m -K) the average coefficient for the entire sphere is 72 W/(m -K). This variation in heat transfer over the spherical surface causes extreme non-uniformities in local vaporization rates and if contact time is too long, wet spherical surface near the contact point dries. The temperature profile penetrates the sphere and it becomes a continuum to which Fourier s law of nonsteady-state conduction appfies. 

VFO works well in gas turbines. In a nine-month test program, the combustion properties of VFO were studied in a combustion test module. A gas turbine was also operated on VFO. The tests were conducted to study the combustion characteristics of VFO, the erosive and corrosive effects of VFO, and the operation of a gas turbine on VFO. The combustion tests were conducted on a combustion test module built from a GE Frame 5 combustion can and liner. The gas turbine tests were conducted on a Ford model 707 industrial gas turbine. Both the combustion module and gas turbine were used in the erosion and corrosion evaluation. The combustion tests showed the VFO to match natural gas in flame patterns, temperature profile, and flame color. The operation of the gas turbine revealed that the gas turbine not only operated well on VFO, but its performance was improved. The turbine inlet temperature was lower at a given output with VFO than with either natural gas or diesel fuel. This phenomenon is due to the increase in exhaust mass flow provided by the addition of steam in the diesel for the vaporization process. Following the tests, a thorough inspection was made of materials in the combustion module and on the gas turbine, which came into contact with the vaporized fuel or with the combustion gas. The inspection revealed no harmful effects on any of the components due to the use of VFO. 

An implicit assumption of the foregoing treatment is that A// remains independent of temperature over the range investigated. This is very nearly correct in general, and is particularly the case given that studies of reactions in solution are usually conducted over a temperature interval of only some 30-50°. In certain circumstances the temperature profiles show curvature outside the experimental error. Such cases have, or appear to have, temperature-dependent activation enthalpies. Here we explore one of the reasons for that another is given in Section 7.3. 

The heat transfer problem which must be solved in order to calculate the temperature profiles has been posed by Lee and Macosko(lO) as a coupled unsteady state heat conduction problem in the adjoining domains of the reaction mixture and of the nonadiabatic, nonisothermal mold wall. Figure 5 shows the geometry of interest. The following assumptions were made 1) no flow in the reaction mixture (typical molds fill in <2 sec.) ... 

Figure 4. Temperature profiles in transient heat conduction.

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. 

With decreasing cell size, the temperature difference between the wall of the cell and the eatalyst partiele in the cell would decrease to zero. For sufficiently small cell dimensions, we may assume the two temperatures are the same. In this case, the heat conduction through the wall becomes dominant and affects the axial temperature profile. As the external heat exchange is absent and the outside of the reactor is normally insulated, the temperature profile is flat along the direction transverse to the reactant flow, and the conditions in all channels are identical to each other. The energy balance is... 

Figure 2.31 Characteristic temperature profiles in a counter-current micro heat exchanger for a very low (left), intermediate (middle) and very high (right) thermal conductivity of the wall material and equal volume flows inside the two channels, reproduced from [125],...

A metal rod is in contact with a constant temperature source at each end. At steady state the heat conducted towards the center is balanced by the heat loss by radiation. This leads to a symmetrical temperature profile in the rod, as shown. 

Figure 5.243. The temperature profile is symmetrical for this heat conduction problem.

A simplified version of the model in Table IX, neglecting accumulation of mass and heat as well as dispersion and conduction in the gas phase, predicts dynamic performance of a laboratory S02 converter operating under periodic reversal of flow direction quite well. This is shown by Fig. 13 taken from Wu et al. (1996). Data show the temperature profiles in a 2-m bed of the Chinese S101 catalyst once a stationary cycling state is attained. One set of curves shows the temperature distribution just after switching direction and the second shows the distribution after a further 60 min. Simulated and experimental profiles are close. The surprising result is that the experimental maximum temperatures equal or exceed the simu-... 

We now repeat the derivation of the steady-state heat transport limited moisture uptake model for the system described by VanCampen et al. [17], The experimental geometry is shown in Figure 9, and the coordinate system of choice is spherical. It will be assumed that only conduction and radiation contribute significantly to heat transport (convective heat transport is negligible), and since radiative flux is assumed to be independent of position, the steady-state solution for the temperature profile is derived as if it were a pure conductive heat transport problem. We have already solved this problem in Section m.B, and the derivation is summarized below. At steady state we have already shown (in spherical coordinates) that... 

The burning of a column of delay composition takes place by the passage of a reaction front along the column. The temperature profile of this reaction front can be measured by the use of suitable thermocouples and recording instruments. By analysing the shape of the front it can be shown that the reaction is a solid/solid reaction initiated by thermal conduction of heat through the unreacted material. It follows that to obtain reproducible reaction rates there must be (1) constant amount of solid to solid contact and (2) constant thermal conductivity. 

Temperature Profiles of Adiabatic Polymerizations. Experiments were conducted to characterize the adiabatic temperature profiles of photocured composites... 

To overcome thermal entry effects, the segments may be virtually stacked with the outlet conditions from one segment that becomes the inlet conditions for the next downstream section. In this approach, axial conduction cannot be included, as there is no mechanism for energy to transport from a downstream section back to an upstream section. Thus, this method is limited to reasonably high flow rates for which axial conduction is negligible compared to the convective flow of enthalpy. At the industrial flow rates simulated, it is a common practice to neglect axial conduction entirely. The objective, however, is not to simulate a longer section of bed, but to provide a developed inlet temperature profile to the test section. 

Fig. 9 shows comparisons of CFD results with experimental data at a Reynolds number of 986 at three of the different bed depths at which experiments were conducted. The profiles are plotted as dimensionless temperature versus dimensionless radial position. The open symbols represent points from CFD simulation the closed symbols represent the points obtained from experiment. It can be seen that the CFD simulation reproduces the magnitude and trend of the experimental data very well. There is some under-prediction in the center of the bed however, the shapes of the profiles and the temperature drops in the vicinity of the wall are very similar to the experimental case. More extensive comparisons at different Reynolds numbers may be found in the original reference. This comparison gives confidence in interstitial CFD as a tool for studying heat transfer in packed tubes. 

---