AbstractThe purpose of the present theoretical analysis is to provide explicit solutions for the problem of condensation of vapours on the lateral surface of a long vertical plate fin of variable cross‐section. The formulation yields solutions to the Limiting cases so that the results can be employed in the design of the condenser section of a flat plate heat pipe in which the fin is considered to be an essential element in transporting heat liberated by the condensing vapours. It is observed that the local and average Nusselt numbers depend on fin parameter, fin profile index, Rayleigh number and degree of subcooling.