Heat exchanges during fast transient are very complex phenomena. Many studies have been led in this field, trying to quantify the heat exchanges between a heating wall, under fast increasing power, and a coolant. This kind of situation is encountered for instance during RIA (Reactivity-Initiated Accidents) in nuclear reactors, whose characteristics times of wall heat flux excursion can be as low as orders of 1 ms. The CABRI reactor, an experimental pulse reactor funded by the french Institute for Radiological protection and Nuclear Safety (IRSN) and operated by CEA at the Cadarache nuclear center (France), was build in order to study and thus to better understand RIA effects on nuclear fuels. Heat exchanges characterization is definitely one of major points to tackle in the understanding and modeling of such transients, involving single and two phase flows. This paper broaches the question of single phase heat exchanges coefficients during fast transient power excursions in the CABRI reactor. The single phase pure convection is the overlap of two main mechanisms: the advection (wall axial supply in upstream cold water) and the turbulent mixing inside the boundary layer. This latter phenomenon is due to vortices in boundary layers inducing radial mixing through the velocity boundary layer. In most cases involving turbulent flows, the turbulent mixing phenomenon is preponderant. To these mechanisms is added a pure conduction heat exchange mechanism through the thermal boundary layer. Convection and conduction overlap defining a conducto-convective heat transfer coefficient, improperly only called "convection" coefficient. This paper suggests a way to model this coefficient during a CABRI-RIA transient by a non-linear superposition of transient pure conduction and convection mechanisms. Two distinct transient phases are considered; the first one presenting a wall heat flux of exponential shape followed by the second one during which the wall heat flux remains constant. The potency of this analytical model, which is implementable into computational system tools, is demonstrated.