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.