In the inspection of a sample of meat intended for human consumption, it was found that certain undesirable organisms were present. 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/(m2 K). The following data can be assumed for the sample of meat: specific heat = 4184 J/(kg K); density = 1280 kg/m3; thermal conductivity = 0.48 W/(m K). Calculate the oven

Question

temperature and the minimum total time of heating required to fulfill the safety regulation.



GIVEN

• A slab of meat is heated in constant temperature over

• Meat be kept at a temperature of at least 121°C for a period of at least 20 min during the preparation

• Slab thickness (2L) = 2.5 cm = 0.025 m

• Initial uniform temperature (To) = 27°C

• The maximum temperature meat can withstand is 154°C

• Specific heat (c) = 4184 J/(kg K)

• Density (?) = 1280 kg/m3

• Thermal conductivity (k) = 0.48 W/(m K)

FIND

• The minimum total time of heating required to fulfill the safety regulation

ASSUMPTIONS

• The surface heat transfer coefficient ( h c)= 10 W/(m K)

• Edge effects are negligible

• One dimensional conduction

SKETCH

Answer 1

The Biot number for the meat is



Therefore, the internal resistance is significant and the transient conduction charts will be used to find a solution.

The highest temperature will occur at the surface of the meat while the lowest will occur at the center of the meat. Therefore, the maximum possible oven temperature (T?) can be obtained from approximate solutions. For Bi=0.26,

for infinite slab we have



for x= L, we have



The actual oven temperature must be less than this so the center temperature can remain above 121°C without the surface temperature exceeding 154°C. The oven temperature and cooking time must be found by iterating the steps below

1. Pick an oven temperature. 2. Use Figure approximate solution to find the Fourier number which determines the time required for the center temperature to reach 121°C.

3. Add 20 min to the time and calculate a new Fourier number.

4. Use the new Fourier number and approximate solution to find the center temperature at the end of the cooking period.

5. Use (T(ro, t) – T?)/(T(0, 2t) – T?) = 0.91 to find the surface temperature at the end of the cooking period.





Solving for the time for the center to reach 121°C: