Suppose that two plates of indefinite thickness, initially at different temperatures, are brought into contact at t = 0. plate 1, with thermal properties a 1 and kb is at x < 0 and has initial temperature t1; plate 2, with properties a 2 and k2, is at x > 0 and has initial temperature t2. determine the temperatures in both plates, expressed as @ = (t- t2)j(t1 - t2). is the temperature at x = 0 constant or does it vary with time? (hint: it will be to use similarity variables of the form tji = xj[2(ait) 112 ] .)