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

Question

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

Answer 1

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