The exact analytical solution of the unsteady impulsive Thermo-Fluid Dynamic field arising in a two-dimensional channel with thick solid walls is presented when the thermal field in the fluid is coupled with the thermal field in the solid (conjugated heat transfer). The cases studied in this paper depend on the boundary conditions imposed on the unwetted sides of the channel walls: assigned temperature and adiabatic condition. Moreover the case of a given heat loss at the unwetted wall is also considered in an appendix. The temperature and heat flux at the solid-fluid interface are analyzed as function of time and of the nondimensional parameters governing the problem. (C) 2011 Elsevier Ltd. All rights reserved.