Evaporation temperature distribution

Estimate temperature distribution in the evaporator, taking into account boiling-point elevations. If all heating surfaces are to be equal, the temperature drop across each effect will be approximately inversely proportional to the heat-transfer coefficient in that effect. 

The quasi-one-dimensional model of flow in a heated micro-channel makes it possible to describe the fundamental features of two-phase capillary flow due to the heating and evaporation of the liquid. The approach developed allows one to estimate the effects of capillary, inertia, frictional and gravity forces on the shape of the interface surface, as well as the on velocity and temperature distributions. The results of the numerical solution of the system of one-dimensional mass, momentum, and energy conservation equations, and a detailed analysis of the hydrodynamic and thermal characteristic of the flow in heated capillary with evaporative interface surface have been carried out. 

The velocity, pressure and temperature distribution in a heated capillary with evaporative interface surface are determined by the following parameters ac-... 

The temperature distribution has a characteristic maximum within the liquid domain, which is located in the vicinity of the evaporation front. Such a maximum results from two opposite factors (1) heat transfer from the hot wall to the liquid, and (2) heat removal due to the liquid evaporation at the evaporation front. The pressure drops monotonically in both domains and there is a pressure jump at the evaporation front due to the surface tension and phase change effect on the liquid-vapor interface. 

The temperature distribution along the micro-channel axis is not monotonic. It has a maximum that is located within the liquid domain. An extraordinary form of the temperature profile is a result of the influence of two opposite factors, namely, absorbs heat from the wall and heat transfer from liquid to the front in order to establish the evaporation process. An increase of heat flux on the wall leads to displacement of the point corresponding to maximum temperature towards the inlet cross-section. 

The position of the meniscus within the micro-channel defines the type of temperature distribution. In the first case, when the meniscus is near the outlet, the temperature gradient of the vapor region is small. The rate of evaporation is determined mainly by the heat flux in the liquid region. Therefore, the necessary condition of the evaporation consists of the existence of the region (near the meniscus), where the water is overheated (its temperature is higher than the temperature of boiling). The heat losses to the inlet tank cause the existence of the temperature maximum. 

The temperature distribution in a heated micro-channel is not uniform (Fig. 11.2, Peles et al. 2000). The liquid entering the channel absorbs heat from the walls and its temperature increases. As the liquid flows toward the evaporating front it reaches a maximum temperature and then the temperature begins to decrease up to the saturated temperature. Within the vapor domain, the temperature increases monotoni-cally from saturation temperature Ts up to outlet temperature Tg.q. 

Water returns to the atmosphere via evaporation from the oceans and evapotranspiration from the land surface. Like precipitation, evaporation is largest over the oceans (88% of total) and is distributed non-uniformly around the globe. Evaporation requires a large input of energy to overcome the latent heat of vaporization, so global patterns are similar to radiation balance and temperature distributions, though anomalous local maxima and minima occur due to the effects of wind and water availability. 

In this study, an integrated methanol reformer including an evaporator and a combustor was fabricated and tested. Previous tests of the reformer with a number of on-off cycles revealed that non-uniform temperature distribution caused hot spots within the combustion plate, resulting in cracking of the welded region of the reformer. Therefore, emphasis was made to achieve a uniform temperature distribution within the reformer. In addition, start-up characteristics of the complete reforming system were investigated. 

Rolfgaard [2.2] compares the types of trays and heating systems The ribbed trays are said to have an uneven temperature distribution, because the distances between shelf and tray vary between 0.1 mm and 1 mm. The ribs could compensate this only partially. The variation in distances is correct, but Rolfgaard overlooks that the thermal conductivity in the bottom of the tray is so effective that practically no temperature differences are established in the bottom. Even with an evaporation of 3 kg ice/m2 h and the assumption that all heat is Transmitted only in the center of the tray (8 cm from the border of the tray), the temperature difference between border and center is approx. 5 °C. During the drying under actual conditions, no measurable temperature differences can exist. 

Figure 2.22 [2.6] demonstrates the method of a cooling circuit with recirculated flow An injector pump operated with just evaporated LN2 aspirates the warmer N2 coming from the condenser and feeds the mixture back in the condenser. The desired condenser temperature can be controlled by a throttle valve. To achieve a uniform temperature distribution, the gas mixture is alternately fed to one or the other end of the condenser. No results of such a system are given. 

A three-stage evaporator is fed with 1.25 kg/s of a liquor which is concentrated from 10 to 40 per cent solids. The heat transfer coefficients may be taken as 3.1,2.5, and 1.7 kW/m2 K in each effect respectively. Calculate the required steam flowrate at 170 kN/m2 and the temperature distribution in the three effects, if ... 

A triple-effect evaporator is fed with 5 kg/s of a liquor containing 15 per cent solids. The concentration in the last effect, which operates at 13.5 kN/m2, is 60 per cent solids. If the overall heat transfer coefficients in the three effects are 2.5, 2.0, and 1.1 kW/m2K, respectively, and the steam is fed at 388 K to the first effect, determine the temperature distribution and the area of heating surface required in each effect The calandrias are identical. What is the economy and what is the heat load on the condenser ... 

A precise theoretical solution is neither necessary nor possible, since during the operation of the evaporator, variations of the liquor levels, for example, will alter the heat transfer coefficients and hence the temperature distribution. It is necessary to assume values of heat transfer coefficients, although, as noted previously, these will only be approximate and will be based on practical experience with similar liquors in similar types of evaporators. 

Latent heat associated with phase change in two-phase transport has a large impact on the temperature distribution and hence must be included in a nonisothermal model in the two-phase regime. The temperature nonuniformity will in turn affect the saturation pressure, condensation/evaporation rate, and hence the liquid water distribution. Under the local interfacial equilibrium between the two phases, which is an excellent approximation in a PEFG, the mass rate of phase change, ihfg, is readily calculated from the liquid continuity equation, namely... 

Once the surface temperature distribution has been computed, using Eq. (151), the droplet evaporation rate is given by integrating the local mass flux over the droplet surface,... 

We shall find the temperature distribution in the gas in those layers adjacent to x — 0 in which the chemical reaction has not yet started. The evaporation heat or the heat of endothermic reaction of gas-formation, L, is equal to the jump in the thermal energy of the original substance. Thus, at x = 0 at the phase-boundary the magnitude of the thermal flux experiences a jump. Using one prime for the c-phase and two primes for the gas, we construct the equation... 

On the other hand, if the velocity of the heating wave is greater than the combustion velocity, a steady regime is impossible indeed, during combustion the surface of the liquid is heated to the temperature TB, however, at this temperature in the liquid a chemical reaction begins to run which heats the adjacent layers of the liquid before they are able to evaporate and burn. The temperature distribution in the liquid will turn out then to be non-steady. 

The approximate temperature distribution in a multiple-effect evaporator is under the control of the designer, but once built, the evaporator establishes its own equilibrium. Basically, the effects are a number of series resistances to heat transfer, each resistance being approximately proportional to The total available temperature... 

The numerical solution of governing equations of heat transfer for the evaporator and condenser regions allows determining the temperature distribution along the MHP axial direction. 

Heat pipe thermal resistanee (and the heat transfer eoeffieient in the evaporator and eondenser zones) was found using the data of the vapour temperature in the adiabatie zone and the mean temperature in the evaporator and in the eondenser. The heat transfer eoeffieients in the evaporator and eondenser of the flat mHPs depend on two- dimensional hydraulie (pore saturation, eapillary permeability, eapillary pressure) and thermal (temperature distribution along the heat pipe envelope) parameters of deviee. The temperature in the middle of the heated side (heat load input) of the evaporator ean exeeed the symmetrie point temperature on the opposite (non-heated) surfaee of the envelope by nearly 10 °C. 

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