A heat transfer apparatus (400) which uses a heat source to generate a cooling effect. The apparatus comprising: a first adsorber vessel (4) containing an adsorbent material (10) and having an aperture (9) in the base through which a pipe (8) passes. The pipe having perforations (12) covered with mesh (14) to allow vapour to pass to and from the adsorbent; a second heat exchanger vessel (37) having heat exchanger tubing (40) connected by a conduit (440) to the first adsorber vessel. The conduit providing a fluid passage between the vessels and the vessels and the conduit forming a sealed volume; a quantity of working substance within the sealed volume capable of being strongly adsorbed by the adsorbent material in a fluid stream as the working substance passes from the second heat exchanger vessel to the first adsorber vessel during adsorption of the working substance; a separator (430) connected to the conduit between the first and second vessels to separate at least a part of the working substance from the fluid stream to reduce the amount of working substance actually adsorbed in the first adsorber vessel. The quantity of working substance is not greater than the adsorbing capacity of the adsorbent material at a selected temperature and pressure of the sealed volume such that the working substance is capable of being substantially completely adsorbed by the adsorbent material. Also claimed are the apparatus for use with a Stirling engine, with a thermal voltaic device, with a turbine positioned in the conduit between the two vessels, with the apparatus comprising a refrigeration unit with two heat exchanger vessels in a refrigeration chamber, with an electrical heating element within the pipe within the adsorber vessel, with a fluid circulated through the adsorber vessel to regulate the adsorbent material temperature, with a ferromagnetic member in the adsorber vessel and a magnet to regulate temperature, an apparatus for removing heat and water from a hydrogen-oxygen fuel cell and methods of operating the apparatus.    USE -   An absorbent refrigerator with a separator.    ADVANTAGE -   The heat transfer apparatus is capable of adsorbing a working substance from the solid phase as well as the liquid phase eliminating the need for brine or additives which reduce the freezing point of the working substance. The amount of adsorbent material is balanced to adsorb substantially all the working substance maximising the cooling effect of the working substance contained within the heat transfer apparatus. The efficiency of the adsorption cycle is increased by retaining the working substance in a vessel which does not burst when the working substance solidifies permitting adsorption to continue after the working substance has solidified. The separator reduces the amount of working substance actually adsorbed by the adsorbent material in the adsorbent vessel.