Q3
A plate of material with a thickness of 4.0 cm, surface area 2.0 m2, and mass 320 kg is suddenly heated, at both sides equally, in a convection oven for a period of time . In this time period the midplane temperature of the plate is still lower than the air temperaturein the oven..
a. Sketch and label accurately on T-x coordinates the following temperature distributions: initial, steady state ( ),, and at two intermediate times between.(take x=0 at the midplane)
b. Sketch and label, on T-t coordinates, the midplane and exposed surface temperature distributions.
c. Repeat parts a. and b. for the case Bi<<1
d. Give at least three factors which affect the Bi number in the above case.
Q4
A 1.0 Liter can containing solid like food (diameter 12.0 cm) has to be sterilized. It is demanded that the temperature in the middle of the can should have reached a minimum temperature of at least 110 0C. The initial temperature is homogeneous and 20 0C. At time t=0, the wall of the can immediately reaches a (constant) temperature of 120 0C due to treatment with saturated steam. The density of the food material is 1200 kg/m3, the heat capacity cp=4000 J/kg K. and the heat conductivity is k=0.71 W/m K.
a. What can you say about the magnitude of the Biot number in this case?
b. Estimate the temperature at the center after 60 min, if you assume the can to be a sphere.
c. Estimate the temperature at the center by assuming the can is an infinite cylinder.
d. Estimate the temperature reached after 60 min if you use the formula for the cross section of a slab and a cylinder.
e. Discuss the differences you found in b. c. and d.
f. What is the total total sterilization time needed? Which assumptions do you make?
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