We have hot dogs that we can approximate as cylinders, with length 15 cm and diameter 2.4 cm. It has a uniform, constant conductivity of 0.53 W/m-C. The density of the hot dog is 1020 kg/m3, and the heat capacity is 4200 J/kg-C.
Here is the design problem: We want to cook our hot dogs for 5 minutes at a grill flame temperature of 400 C, such that the inside of the hot dog reaches 75 C, and the outside does not exceed 105 C. The heat transfer coefficient for the heat reaching the hot dog is 20 W/m2-C. At what initial temperature should we start the hot dog before putting it on the grill?
a) Evaluate the initial temperature, assuming a lumped analysis, that gives T = 105 C. Do we want to take them straight out of the freezer, or let them come to room temperature? Is a lumped analysis valid here (explain)?
initial T of hot dog (lumped analysis) = __________ C
start at (choose one and explain): freezer temperature / room temperature
lumped analysis valid (choose one, and briefly explain). yes / no
b) For this part of the problem, we will use the Heisler charts. If we cook the hot dog at 400 C, starting at T = 25 C, for 5 minutes (as in (a) above), what is the final centerline temperature, and outer temperature? COMMENT: We won't do any iterations on this problem, but you can see how our knowledge of heat transfer would reduce the trial and error of getting the "perfect hot dog cooking process".
centerline T of hot dog (Heisler charts) = __________ C
outside T of hot dog (Heisler charts) = __________ C