41. Transient Conduction for Two Plates in Contact Suppose that two plates of indefinite thickness, initially at different temperatures, are brought into contact at t=0. Plate 1 , with thermal properties 1 and k1, is at x0 and has initial temperature T2. Determine the temperatures in both plates, expressed as =(TT2)/(T1T2). Is the temperature at x=0 constant or does it vary with time? (Hint: It will be helpful to use similarity variables of the form i=x/[2(it)1/2].)