A heat exchanger, perhaps a cross flow heat exchanger, has first and second passages. During dehumidification (adsorption of moisture) in the first passages, water is evaporated from the second passages. This water can be introduced to the second passages during reactivation (desorption of moisture) in the first passages or at another time. If the water is introduced to the second passages during reactivation, the first and second passages have therein first and second moisture adsorbents. During a first time period, air to be dehumidified is passed through the first passages of the heat exchanger and cooling air is passed through the second passages of the heat exchanger to remove heat generated in the first passages and to desorb moisture adsorbed by the second moisture adsorbent. During a second time period, a heating fluid is passed through the second passages of the heat exchanger to heat the first passages and supply moisture for adsorption to the second moisture adsorbent. Also during the second time period, removal air is passed through the first passages of the heat exchanger to eliminate water adsorbed by the first moisture adsorbent during the first time period. If water is introduced to the second passages at a time other than during reactivation, it is not necessary for the second passages to have a moisture adsorbent therein. The water could be introduced to the second passages as a spray during the first time period (during dehumidification).