Steady state heat conduction in a circular homogeneous rod of infinite length is analyzed. The rod is composed of an isotropic heat conducting material and is subjected to a multi-cascade wall condition with no heat source or sink. By using the Fourier integral transform, the temperature field in the rod is obtained. To represent the total heat flow, a dimensionless heat flow coefficient at the cross section corresponding to the wall temperature discontinuity is defined and its value is calculated. The procedure for obtaining the temperature field for a multi-cascade wall temperature case is also discussed.
