Straight overall heat transfer coefficient

When true scale formation occurs, the overall heat-transfer coefficient may be related to the time the evaporator has been in operation by the straight-line equation ... 

Of course, if the equilibrium curve is straight (as it will be in dilute solutions), then m is its slope. This is similar to the expression for overall heat transfer coefficients for a double-pipe heat exchanger ... 

The temperature of the steam-cooled reactor shown is 285°F. The heat that must be transferred from the reactor into the steam generation system is 2.5 X 10 Btu/hr. The overall heat transfer coefficient for the cooling coils is 300 Btu/lir ft- F. The steam discharges into a 25-psia steam header. The enthalpy difference between saturated steam and liquid condensate is 1000 Btu/lb, . The vapor pressure of water can be approximated over this range of pressure by a straight line. 

Thus a plot of the logarithm of the ratio of the instantaneous temperature difference to the initial temperature difference, as a fimction of time, should give a straight line, as far as cooling is Newtonian. The slope of this line is the thermal time constant of the reactor, from which the overall heat transfer coefficient U can be calculated. 

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