Exact solutions for the problem of drying with coupled phase change in a porous medium with a heat flux condition on x = 0 of the type - q0/ , with q0 > 0, for any value of the Luikov number Lu is obtained. This solution can be only obtained when q0 verifies a certain inequality. Besides, for large Luikov number (more precisely, Lu > ), we obtain that the temperature distribution t2 reaches to a minimum value which is smaller than its initial temperature or limit value reached at +¥.