A 1 in. o.d. (outer diameter) tube reactor is insulated with a 3 inch layer of asbestos. If the temperature of the outer surface of the insulation is 100 °F and the rate of heat loss per foot of reactor length is 50 BTU/hr, what must the temperature of the inside of the reactor be? [for asbestos, k = 0.105 BTU/hr ft °F]

A 0.5-in.-diameter steel [E= 30,000 ksi] bolt (1) is placed in a copper tube (2). The copper [E= 16,000 ksi] tube has an outside diameter of 1.00 in., a wall thickness of 0.125 in., and a length of L= 8.0 in. Rigid washers, each with a thickness of t= 0.125 in., cap the ends of the copper tube. The bolt has 20 threads per inch. This means that each time the nut is turned one complete revolution, the nut advances 0.05 in. (i.e., 1/20 in.). The nut is hand-tightened on the bolt until the bolt, nut, washers, and tube are just snug, meaning that all slack has been removed from the assembly but no stress has yet been induced. What stresses are produced in the bolt and in the tube if the nut is tightened an additional quarter turn past the snug-tight condition?

The assembly shown below consists of a brass shell (1) fully bonded to a ceramic core (2). The brass shell [E = 115 GPa; α = 18.7 x 10-6 /°C] has an outside diameter of 50 mm and an inside diameter of 35 mm. The ceramic core [E = 290 GPa; α = 3.1 x 10-6 /°C] has a diameter of 35 mm. At a temperature of 15°C, the assembly is unstressed. Determine the largest temperature increase that is acceptable for the assembly if the normal stress in the longitudinal direction of the brass shell must not exceed 80 MPa.