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You have been asked to cook a 6 kg joint of beef in a conventional oven preheated to 200°C. The joint of meat is roughly spherical and therefore the joint can be modelled as a uniform sphere. i) Normal cooking times for beef state you should cook for at least 60 minutes per kg plus an additional 30 minutes. Estimate the normal cooking time for the beef. ii) Estimate the heat flux into the joint needed to raise the temperature of the joint from 25 °C to a minimum cooked temperature of 70 °C. Given: a. The heat capacity for beef is: 1. 67 kJ/kg/K. b. The density of beef is 1033 k/m'. iii) Assuming only heat transfer occurs through a solid, calculate the rate of accumulation of heat in the meat. iv) Derive a simple expression for the temperature profile in the radial direction through the meat. Given: a. The thermal conductivity of the beef is 0.45 W/m/K. v) Calculate the minimum time needed to reach the minimum temperature of 70 °C using your expression. vi) Compare your answer in part v) with that in part i) and comment on your observations.

You have been asked to cook a 6 kg joint of beef in a conventional oven preheated to 200°C. The joint of meat is roughly spherical and therefore the joint can be modelled as a uniform sphere. i) Normal cooking times for beef state you should cook for at least 60 minutes per kg plus an additional 30 minutes. Estimate the normal cooking time for the beef. ii) Estimate the heat flux into the joint needed to raise the temperature of the joint from 25 °C to a minimum cooked temperature of 70 °C. Given: a. The heat capacity for beef is: 1. 67 kJ/kg/K. b. The density of beef is 1033 k/m'. iii) Assuming only heat transfer occurs through a solid, calculate the rate of accumulation of heat in the meat. iv) Derive a simple expression for the temperature profile in the radial direction through the meat. Given: a. The thermal conductivity of the beef is 0.45 W/m/K. v) Calculate the minimum time needed to reach the minimum temperature of 70 °C using your expression. vi) Compare your answer in part v) with that in part i) and comment on your observations.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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You have been asked to cook a 6 kg joint of beef in a conventional oven preheated to 200°C. The joint of meat is roughly spherical and therefore the joint can be modelled as a uniform sphere. i) Normal cooking times for beef state you should cook for at least 60 minutes per kg plus an additional 30 minutes. Estimate the normal cooking time for the beef. ii) Estimate the heat flux into the joint needed to raise the temperature of the joint from 25 °C to a minimum cooked temperature of 70 °C. Given: a. The heat capacity for beef is: 1. 67 kJ/kg/K. b. The density of beef is 1033 k/m'. iii) Assuming only heat transfer occurs through a solid, calculate the rate of accumulation of heat in the meat. iv) Derive a simple expression for the temperature profile in the radial direction through the meat. Given: a. The thermal conductivity of the beef is 0.45 W/m/K. v) Calculate the minimum time needed to reach the minimum temperature of 70 °C using your expression. vi) Compare your answer in part v) with that in part i) and comment on your observations. vii) The meat is actually cooked in a fan assisted convection oven and is observed to cook at a much quicker rate than that calculated either by part i) or part v). What does this tell you about the mode of heat transfer and the controlling mechanisms?
Transcribed Image Text:You have been asked to cook a 6 kg joint of beef in a conventional oven preheated to 200°C. The joint of meat is roughly spherical and therefore the joint can be modelled as a uniform sphere. i) Normal cooking times for beef state you should cook for at least 60 minutes per kg plus an additional 30 minutes. Estimate the normal cooking time for the beef. ii) Estimate the heat flux into the joint needed to raise the temperature of the joint from 25 °C to a minimum cooked temperature of 70 °C. Given: a. The heat capacity for beef is: 1. 67 kJ/kg/K. b. The density of beef is 1033 k/m'. iii) Assuming only heat transfer occurs through a solid, calculate the rate of accumulation of heat in the meat. iv) Derive a simple expression for the temperature profile in the radial direction through the meat. Given: a. The thermal conductivity of the beef is 0.45 W/m/K. v) Calculate the minimum time needed to reach the minimum temperature of 70 °C using your expression. vi) Compare your answer in part v) with that in part i) and comment on your observations. vii) The meat is actually cooked in a fan assisted convection oven and is observed to cook at a much quicker rate than that calculated either by part i) or part v). What does this tell you about the mode of heat transfer and the controlling mechanisms?
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