Suppose that two plates of indefinite thickness, initially at different temperatures, are brought into contact at t = 0. plate 1, with thermal properties a1 and k1, is at x < 0 and has initial tempera- ture t1 ; plate 2, with properties a2 and k2 , is at x > 0 and has initial temperature t2 . 1222 determine the temperatures in both plates, expressed as q = (t - t )> (t - t ). is the tem- 212 perature at x = 0 constant or does it vary with time? (hint: it will be to use similarity vari- ables of the form hi = x/[2(ait)^(1/2)].)