UNSTEADY CONJUGATED HEAT-TRANSFER IN LAMINAR PIPE-FLOW

This study analyses the transient conjugated heat transfer in laminar pipe flow, where the flow is both hydrodynamically and thermally fully developed. Two cases are considered: a prescribed constant wall temperature and a constant heat flux at the wall. A non-standard method of separation of variables is applied, which treats the fluid and the solid as one region with certain discontinuities. The resulting eigenfunctions, which are not orthogonal to each other with respect to the usual weight function according to the Sturm-Liouville theorem, are made orthogonal to each other with respect to a special weight function. It is concluded that the degree of conjugation and viscous dissipation may have a great impact on the temperature distribution in the fluid.