A monster turnip (assumed spherical) weighing in at 0.45 kg is dropped into a cauldron of water boiling at atmospheric pressure. If the initial temperature of the turnip is 17°C, how long does it take to reach 92°C at the center? Assume that
GIVEN
FIND
Time needed to reach 92°C at the center
ASSUMPTIONS
SKETCH
The radius of the turnip is given by
Therefore, internal resistance is significant and the approximate solution method will be used.
Using approximate solution, we have
For the center r=0, the term becomes indeterminate, so using L Hospital’s rule we get.
For Bi=153 which can be considered ? From Table 3.1 for sphere we have
solving for the time
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