Acounterflow double-pipe heat exchanger is used to heat water from 20 to 40◦c by cooling an oil from 90 to 55◦c. the exchanger is designed for a total heat transfer of 59 kw with an overall heat-transfer coefficient of 340 w/m2 · ◦c. calculate the surface area of the exchanger.

The temperature in gavin's oven is a sinusoidal function of time. gavin sets his oven so that it has a maximum temperature of 280°f and a minimum temperature of 240°. once the temperature hits 280°, it takes 20 minutes before it is 280° again. gavin's cake needs to be in the oven for 30 minutes at temperatures at or above 270°. he puts the cake into the oven when it is at 260° and rising. how long will gavin need to leave the cake in the oven? (round your answer to the nearest minute.)