A simple perturbation technique is used to reformulate the energy equations which describe the transient thermal behaviour of a radially lumped conjugated heat transfer problem in circular and parallel plate ducts of finite wall thickness. The simple perturbation technique is used to eliminate the coupling between the fluid and the solid-wall energy equations when the temperature difference between the fluid and the solid wall is a small perturbed quantity, which is true when the interface convective heat transfer coefficient between the fluid and the solid wall is high. A mathematical criterion is derived to determine the conditions under which fluid and solid wall are in thermal equilibrium. It is found that there are four dimensionless parameters that control the state of thermal equilibrium between the fluid and the solid domains.