Question

2.- In the inspection of a sample of meat intended for human consumption, it was found that certain undesirable organisms were present. In order to make the meat safe for consumption, it is ordered that the meat be kept at a temperature of at least 121°C for a period of at least 20 min during the preparation. Assume that a 2.5-cm- thick slab of this meat is originally at a uniform temperature of 27°C; that it is to be heated from both sides in a constant temperature oven; and that the maximum temperature meat can withstand is 154°C. Assume furthermore that the surface coefficient of heat transfer remains constant and is 10 W/(m²K). The following data may be taken for the sample of meat: cp = 4184 J/(kg K); p= 1280 kg/mº; k = 0.48 W/( mK). Using analytical one-term approximation method (not the Heisler charts) calculate the oven temperature and the minimum total time of heating required to fulfill the safety regulation. (Hint: be careful, the requirement is not at the same time, the least temperature can no be the final temperature due a time requirement) Comprehension (State Definition, Free Body Diagram and/or Diagram Sketch.) [10 points]

Answer 1

Given:- Now, by one-term analytical approximation, we have -

h = 10 m/mºk; Cp 4184 J/kgk; K = 0.48 w/mk; Slab thickness, 2 0.025m p= 1280 kg/mº; time, t = 20 x 60 = 1200 seconds. Now, since a = k/pCp = 0.0896191 x 10-6

T Tz,t) – T. T; -T = erf | 2at

Since, $T_i, T_s\ given\ and \ surface \ temperature \ has \ to \ be \ at \ least \ 121\degree C\\ And \ meat \ can \ withstand \ temperature< 154\degree C, we \ get-$