A stainless-steel plate, 1.0 m² in area and 5.0 cm thick, is to be attached to a glass substrate with a thermosetting glue. For this purpose, a thin layer of the glue is applied to the glass and the stainless-steel plate is then laid on top of it. The glue sets when the temperature reaches 120°C.

The initial temperature is 20°C. Two cases are considered. In the first case

(I), a metal plate kept at 150°C is firmly pressed against the stainless-steel plate. In the second case (II), air at 200°C is blown over the stainless-steel plate resulting in a heat transfer coefficient h = 300 W/m2 K. Assuming that the glass substrate serves as a perfect insulator:

(a) Write down the differential equations and initial and boundary conditions needed to describe each of the two cases making sure that you define all of the variables appearing in your equations.

(b) Determine the time required to set the glue in case I as well as the amount of heat transferred to the stainless-steel plate when the glue setting temperature is reached. (c)

Determine the time required to set the glue in case II as well as the temperature at the stainless steel–air interface when the glue temperature reaches 150°C.