Thermoelastic stability of duplex heat exchanger tubes

When duplex tubes are used for heat exchange purposes, thermal distortion affects the contact pressure and, hence, the thermal contact resistance at the interface. The resulting coupling between the thermal and thermoelastic fields for the system can lead to instability and non-uniqueness of the steady-state solution and, hence, to erratic heat transfer performance. Stability of the system is investigated by determining the conditions under which a small (axisymmetric or non-axisymmetric) perturbation on the steady state can grow exponentially in time. Substitution into the governing heat conduction and thermoelastic equations enables the unknown functions to be determined except for a set of arbitrary constants, which are then determined from the thermal and mechanical boundary conditions, including a statement of the relation between thermal contact resistance and pressure, linearized for small perturbations about the steady state. Results are presented for a range of material combinations and for both directions of steady state heat flux. It is shown that unstable axisymmetric perturbations can only occur for inward heat flow and, hence, the stability boundary for outward heat flow is always associated with a non-axisymmetric mode. In the latter case, the circumferential wavelength of the critical mode is generally about twice the tube thickness and a good approximation to the stability boundary can be obtained using previously published results for the stability of two plane layers in thermoelastic contact. For inward heat flow, the critical heat flux for axisymmetric perturbations is independent of the mean contact resistance, whereas that for non-axisymmetric modes increases with contact resistance. Thus, the stability boundary in this case is determined by non-axisymmetric modes for small values of contact resistance and by axisymmetric modes for large contact resistance.