This Note presents the study of transient flow under forced convection in buried coaxial exchanger. The wall temperature as well as the wall heat flux and the heat transfer coefficient are unknown. A hybrid model consisting of a finite element method at the boundary (BEM) for the heat transfer problem on the boundary and a finite volume method (FVM) to solve the laminar flow inside solves this problem. The development of the BEM method is based on the Green's function theory. This conjugate method allows one to have fast results and to foresee the thermal behaviour of the exchanger. The heat transfer coefficients are investigated. The results are compared to those obtained using the commercial CFD package Fluent.