Green coffee beans, after harvesting, are dried and roasted in a fluidized-bed roaster. This type of roaster has hot air typically at 2500C, and the air blows through a screen or perforated plate above which the beans float in an agitated suspension (fluidization) in the hot air as they get heated. As the beans heat up, they get dried and roasted to the required condition. They are typically flat ellipsoids that have an average volume of 44 mm3 and an average surface area of 66 mm2. For a flavorful and aromatic medium roast, the beans have to be heated to 2000C. If the beans are initially at 220C at the time they enter the roaster and the convective heat transfer coefficient of the heating air is 20 W/(m2 K), determine the required roasting time. Coffee bean thermophysical properties are
k=0.184 W/(m K), c=2.564 kJ/(kg K) and ?=552 kg/m3
GIVEN
• Green coffee beans with average volume V=44 mm3 and average surface area As=66 mm2
• Initial temperature of beans(To) = 22°C
• Roaster hot air temperature(T?) = 250°C
• Heat transfer coefficient ( ch ) = 20 W/(m2 K)
• Length of the oven(L)=3.5 m
FIND
• The heating time required for beans to reach to 200°C
ASSUMPTIONS
• Constant thermal conductivity
• End effects are negligible
SKETCH
PROPERTIES AND CONSTANTS
Given For beans Thermal conductivity (k) = 0.184 W/(m K)
Density (?) = 552 kg/m3 Specific heat (c) = 2.564 kJ/kg=2564 J/kg
The characteristic length of beans is given by
Lc=V/As
Lc=44/66=0.667 mm=0.000667 m
The Biot number is calculated first to check if the internal resistance is negligible
Therefore, the internal resistance of beans is negligible.
The temperature-time history of beans
Solving for the time
The time required to reach 88°C is
You might also like to view...
What are tides?
What will be an ideal response?
When an object 1.15 cm tall is placed 12 cm from a lens, the lens produces an upright image of the object that is 5.75 cm tall. What is the focal length of the lens?
A) 24 cm B) 18 cm C) 60 cm D) 15 cm E) 9.0 cm
When the equation Al + O2? Al2O3 is balanced, the coefficient of Al2O3 is
a. 1 b. 2 c. 3 d. 4
If a star is twice as hot as the sun and only half the sun's diameter, it will be less luminous than the sun
Indicate whether the statement is true or false