Polymer laminates are formed by “squeezing” two flat sheets of polymer together under high pressure. Consider the temperature profiles in two polymer sheets that are initially at temperatures T1o and T2o that are brought together at t = 0. The two polymers have different thermal conductivities (k1 and k2) but have the same density and heat capacity. A) Derive an expression for the temperature as a function of time and position in the two sheets which is valid at short times (i.e., at times for which the boundary at the far surface of the polymers can be taken as being at infinity). Although this problem can be solved analytically, I would strongly suggest using an integral solution

Polymer laminates are formed by “squeezing” two flat sheets of polymer together under high pressure. Consider the temperature profiles in two polymer sheets that are initially at temperatures T1o and T2o that are brought together at t = 0. The two polymers have different thermal conductivities (k1 and k2) but have the same density and heat capacity. A) Derive an expression for the temperature as a function of time and position in the two sheets which is valid at short times (i.e., at times for which the boundary at the far surface of the polymers can be taken as being at infinity). Although this problem can be solved analytically, I would strongly suggest using an integral solution