A simple perturbation technique is used to reformulate the energy equations which describe the treatment thermal behaviour of a radially lumped conjugate that transfer problem is annular and dissimilar parallel plate ducts of finite wall thickness. The simplified perturbation tecnique 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 the fluid and the solid-wall are in thermal equilibrium. It is found that seven dimensionless parameters control the state of the thermal equilibrium between the fluid and the solid domains.