XXVII.The heat loss from a cylinder embedded in an insulating wall

Abstract

The problem discussed is that of the steady flow of heat from an infinitely long circular cylinder with an isothermal boundary, embedded in an infinitely long wall with a rectangular isothermal boundary. For this two-dimensional problem the method of conformal representation is employed, taking the rectangular outer boundary and an imaginary inner isothermal boundary of such dimensions and shape that it yields a particular isothermal approximating, as closely as may be, with the required circle. Formulae are derived for calculating the overall heat loss for cases where the axis of the cylinder lies either outside or in the mid-plane of the wall, and a complete distribution of isothermals and flow lines is calculated for two such cases. The distribution in these latter cases is compared with that given by a method of graphical estimation, and a determination of overall heat loss, based on electrical analogy, is given for one of the cases. An alternative method of theoretical treatment is also discussed.