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a)
The heat transfer coefficient at the surface of the rib.
a)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Mass of the rib
Initial temperature
Temperature maintained at the oven
Temperature at the center of the meat
Time taken to roast the rib
Calculation:
Write the given properties of the rib.
Calculate the radius of the roast
Calculate the Fourier number
The Fourier number is nearly close to 0.2
Calculate the dimensionless temperature of the roast
Solve Equation (I) by trial and error method using Table 18-2, Coefficients used in the one-term approximate solution of transient one-dimensional heat conduction in plane walls, cylinders, and spheres”.
Equation (I) is satisfied when the Biot number,
Calculate the heat transfer coefficient at the surface of the rib
Thus, the heat transfer coefficient at the surface of the rib is
b)
The temperature at the surface of the rib.
b)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Calculation:
Calculate the temperature at the surface of the rib
Thus, the temperature at the surface of the rib is
c)
The amount of heat transferred to the rib.
c)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Calculation:
Calculate the maximum amount of heat transferred to the rib
Calculate the amount of heat transferred to the rib
Thus, the amount of heat transferred to the rib is
d)
The time taken to cook the medium-done rib.
d)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Calculation:
It is given that the innermost temperature of the rib is
Calculate the Fourier number
Calculate the time taken to cook the medium-done rib
Thus, the time taken to cook the medium-done rib is
The calculated cooking time
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Chapter 18 Solutions
Fundamentals of Thermal-Fluid Sciences
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