Hot polymer beads are being cooled by allowing them to settle slowly in a long cylindrical tank of water maintained at 30°C as shown in the figure. In this process, 1-cm-diameter spherical beads settle at a terminal velocity of 3 cm/s, which is based on the size of the bead and density of the bead material relative to the density of water. Properties of water can be taken at its bulk temperature of 30°C, where the Prandtl number is 4.33, the kinematic viscosity is 6.63 × 10^-7m²/s, and the thermal conductivity is 0.633 W/m · K. The thermal conductivity of the polymer bead is 0.08 W/m · K. If the polymer beads are at a temperature of 100°C, what is the total heat-transfer rate from one bead?

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polymer bead water column 1.0 cm Ts = 100°C 3.0 cm/sec T = 30°C