A mercury bath at 60°C is to be heated by immersing cylindrical electric heating rods, each 20 cm tall and 2 cm in diameter. Calculate the maximum electric power rating of a typical rod if its maximum surface temperature is 140°C.

Question

GIVEN

• Cylindrical heating rods in a mercury bath

• Mercury temperature (T?) = 60°C

• Rod diameter (D) = 2 cm = 0.02 m

• Rod height (L) = 20 cm = 0.2 m

• Maximum surface temperature (Ts) = 140°C

FIND

• The maximum electric power rating ( q e) of a rod

ASSUMPTIONS

• Steady state

• The rods are in a vertical position

SKETCH



PROPERTIES AND CONSTANTS

for mercury at the mean temperature of 100°C

Thermal conductivity (k) = 10.51 W/(m K) Kinematic viscosity (?) = 0.093 × 10–6 m2/s Prandtl number (Pr) = 0.0162 Also Density at 50°C (?50) = 13,506 kg/m3

Density at 15°C (?150) = 13,264 kg/m3 To find the thermal expansion coefficient (?),

Answer 1

The Grashof number at the top of the cylinder is



Therefore, the boundary layer is turbulent and the average heat transfer coefficient is



The maximum electric power rating of a rod is equal to the maximum rate of heat transfer from a rod