The forced-convection longitudinal flow of a viscous and heat-conducting fluid in a system of thin parallel cylinders, arranged in regular patterns, is studied. The aim of the study is to determine both the velocity field and temperature field between the system of thin cylinders. A new way of calculating i.e. the use of a complex number is proposed. The final results are analytical formulas for determining the longitudinal permeability and the Nusselt number of the fluid and the system of thin cylinders. (c) 2007 Elsevier Ltd. All rights reserved.