The heat transfer coefficient for hydrogen flowing over a sphere is to be determined by observing the temperature–time history of a sphere fabricated from pure copper. The sphere, which is 20.0 mm in diameter, is at 70°C before it is inserted into the gas stream having a temperature of 27°C. A thermocouple on the outer surface of the sphere indicates 50°C 97 s after the sphere is inserted into the hydrogen. Find

a) What is the value of the specific heat of the copper at the average temperature of the process, in J/kg·K?

b) What is the value of the lumped thermal capacitance of the sphere, in J/K?

c) Solve for the thermal time constant, in sec.

d) What is the value of the heat transfer coefficient, in W/m2· K?

e) What is the value of the Biot number?