The physical processes involved in a thermosyphon, whereby high rates of heat transfer can be obtained between surfaces that have only a small temperature difference between them, are described. Heat is transferred by means of evaporation and condensation, and gravity is used to return the liquid film to the evaporator as compared with capillary-driven designs which use a wick as described in ESDU 79012. ESDU 81038 relates to thermosyphons having (i) circular tubes of uniform cross section, (ii) a single component working fluid and no non-condensable gas, (iii) either no wick or a simple wick or insert in the evaporator wall and (iv) angles of inclination to the horizontal of 5 degrees to 90 degrees. The maximum overall rate of heat transfer depends on the overall temperature difference and the sum of the thermal resistances of the various solid, liquid and vaporous media and interfaces involved. Methods are given for calculating each thermal resistance. Advice and expressions are also given for the limits of vapour pressure, sonic velocity in the vapour, dry-out, boiling limit, and the counter-current flow limit.