We are interested in predicting the time it will take for popcorn kernels to pop in a fluidized bed. The superficial air velocity inside the bed is 3 m/s, which is above the minimum fluidization velocity for popcorn kernels. The air temperature is maintained constant at 520 K (247°C) by heating coils placed around the fluidization vessel. The average diameter of the popcorn kernels is 0.5 cm. When the temperature of a kernel reaches 175°C, it will pop. At 25°C, the thermal conductivity of popcorn is 0.2 W/m · K, the specific heat is 2000 J/kg · K, and the density is 1300 kg/m³.
a. What is the convective heat-transer coefficient for air flow around each popcorn kernel?
b. What is the Biot number for a popcorn kernel? Is a lumped parameter model valid?
c. If we assume that the popcorn kernel pops when its center line temperature reaches 175°C, how long after entering the bed will it take for the popcorn kernel to pop? Initially, the popcorn kernels are at 25°C.