The liquid phase reactor shown in Fig. P.4.8 is operated at 250°C and is agitated with a propeller mounted on a 10-cm-diameter steel shaft with a thermal conductivity k = 50 W/m K. The agitator shaft is driven by a belt-pulley system, whose maximum operating temperature is 75°C. A design concern is that the belt must be located on the shaft at a distance sufficiently far away from the reactor so that this maximum temperature will not be exceeded. The total length of the shaft from the reactor up is 1 m. The air is at 20°C, and the convective heat transfer coefficient is estimated to be 10 W/m² K. Neglect any effects of friction.

(a) Write the differential energy balance and boundary conditions needed to address this design concern.

(b) Determine the minimum distance from the reactor at which the belt must be placed.

(c) Determine the rate of total heat loss from the reactor through the stirrer shaft.

FIGURE P.4.8:

Transcribed Image Text:

1 m 10 cm diam. solid steel shaft in air at 20 C Well insulated reactor at 250 C