4 2 pts heat loss from a tube consider a tube containing a fluid of ma

Question

5. (2 pts) Heat Sterilization of Canned Food (Adapted from Welty et al., Problem 18.22)
In the canning process, sealed cans of food are sterilized with pressurized steam to kill any
microorganisms initially present in the food and thereby prolong the shelf life of the food. A
cylindrical can of food has a diameter of 4 cm and height of 4 cm. The food material can be treated
as a solid with heat capacity of 4000 J/kgK, density of 1200 kg/m³, and thermal conductivity of 0.6
W/mK. In the process, steam at 120°C is used to sterilize the can. The convective heat-transfer
coefficient is 60 W/m² K. The can and contents initially are at a uniform temperature of 20 °C.
A. If the heat-transfer resistance offered by the thin can walls is neglected and the can ends are
thermally insulated, how long will it take for the center of the can to reach a temperature of 80
°C, which is sufficient to kill all microorganisms? Hint: You will need to use one of the charts
in Appendix F of Welty et al.
B. What is the required time if the ends of the can are not insulated but are instead exposed to the
steam? Hint: See Section 18.2 of Welty et al. for an approximate approach to this two-
dimensional problem. It is tricky, though, as you know the left-hand-side of Eq. 18.24, but not
the two terms on the right-hand-side. Thus, you will need iterate by making two educated guesses
for the time required, then calculate the right-hand-side and then interpolate (or extrapolate) to
get an improved estimate. Also, the variable a for this equation is the half-height of the can.