A bearing piece in the form of half of a hollow cylinder of 60 mm ID, 90 mm OD and 100 cm long is to be cooled to –100 C from 30 C using a cryogenic gas at –150 C with a heat transfer coeffi cient of...

A bearing piece in the form of half of a hollow cylinder of 60 mm ID, 90 mm OD and 100 cm long is to be cooled to –100C from 30C using a cryogenic gas at –150C with a heat transfer coeffi cient of 70 W/m²
K, density = 8900 kg/m³, specific heat = 444 J/kgK, conductivity = 17.2 W/mK. Determine the time required.

Find the volume of the piece

Establish Bi =
  less than 0.1 and then use

the lumped parameter model from Eq. (3.3).

Find t.