Mean temperature difference in condensation

The pressure drop of condensing steam is therefore a function of steam flow rate, pressure and temperature difference. Since the steam pressure drop affects the saturation temperature of the steam, the mean temperature difference, in turn, becomes a function of steam pressure drop. This is particularly important when vacuum steam is being used, since small changes in steam pressure can give significant alterations in the temperature at which the steam condenses. 

Mean temperature difference the condensation range is small and the change in saturation temperature will be linear, so the corrected logarithmic mean temperature... 

Mean temperature difference in the main heat exchangers, melter and condenser 5° F. 

A pure, saturated, vapour will condense at a fixed temperature, at constant pressure. For an isothermal process such as this, the simple logarithmic mean temperature difference can be used in the equation 12.1 no correction factor for multiple passes is needed. The logarithmic mean temperature difference will be given by ... 

If the degree of superheat is large, it will be necessary to divide the temperature profile into sections and determine the mean temperature difference and heat-transfer coefficient separately for each section. If the tube wall temperature is below the dew point of the vapour, liquid will condense directly from the vapour on to the tubes. In these circumstances it has been found that the heat-transfer coefficient in the superheating section is close to the value for condensation and can be taken as the same. So, where the amount of superheating is not too excessive, say less than 25 per cent of the latent heat load, and the outlet coolant temperature is well below the vapour dew point, the sensible heat load for desuperheating can be lumped with the latent heat load. The total heat-transfer area required can then be calculated using a mean temperature difference based on the saturation temperature (not the superheat temperature) and the estimated condensate film heat-transfer coefficient. 

It is normal practice to assume that integral condensation occurs. The conditions for integral condensation will be approached if condensation is carried out in one pass, so that the liquid and vapour follow the same path as in a vertical condenser with condensation inside or outside the tubes. In a horizontal shell-side condenser the condensate will tend to separate from the vapour. The mean temperature difference will be lower for differential condensation, and arrangements where liquid separation is likely to occur should generally be avoided for the condensation of mixed vapours. 

Where integral condensation can be considered to occur, the use of a corrected logarithmic mean temperature difference based on the terminal temperatures will generally give a conservative (safe) estimate of the mean temperature difference, and can be used in preliminary design calculations. 

In a condenser, the rate of heat flow (Q) is proportional to the condenser area (A), the mean temperature difference (A7"m) between the coolant and vapour streams and the overall coefficient of heat transfer ( ) ... 

In practice, condenser temperatures are as shown in Figure 6.1(b) (both vapour and coolant temperatures change) and in the equation for (0, the log mean temperature difference should be used for A Tm. 

This means that for the same work/heat ratio, the turbine inlet pressure must also be higher as is clearly demonstrated in Figure 5. Other trends associated with increasing TB include the decreasing of the maximum temperature difference in the condenser, an increase in pump efficiency (Figure 3), and an increase in the system s Second Law efficiency. 

The methods presented above are applicable only for conditions in which the heat transferred is a straight-line function of temperature. For systems that do not meet this condition, the total heat-release curve can be treated in sections, each section of which closely approximates the straight-line requirement. A log mean temperature difference can then be calculated for each section. Common examples in which this approach is encountered include (1) total condensers in which the condensate is subcooled after condensation, and (2) vaporizers in which the fluid enters as a subcooled liquid, the liquid is heated to the saturation temperature, the fluid is vaporized, and the vapor is heated and leaves in a superheated state. 

But, when there is a phase change involved in the process — for example, condensation (Fig. lb), or vaporization (Fig. Ic), or both (Fig. Id), LMTD cannot be used directly. In this case, the designer must break the exchanger into two or more zones, and analyze each section separately. The resultant AT is called the weighted mean-temperature-difference (WMTD), and is expressed as ... 

This s a little less than the arithmetic mean temperature difference of j(8 + 16) = 12°C. Then the heat transfer rate in Ihe condenser is determined from... 

Superheat of a pure vapor is removed at the same coefficient as for condensation of the saturated vapor if the exit coolant temperature is less than the saturation temperature (at the pressure existing in the vapor phase) and if the (constant) saturation temperature is used in calculating the mean temperature difference. But see note k for vapor mixtures with or without noncondensable gas. 

The coefficients cited for condensation in the presence of noncondensable gases or for multicomponent mixtures are only for very rough estimation purposes because of the presence of mass transfer resistances in the vapor (and to some extent, in the liquid) phase. Also, for these cases, the vapor-phases temperature is not constant, and the coefficient given is to be used with the mean temperature differences estimated using vapor-phase inlet and exit temperatures, together with the coolant temperatures. 

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