In this work we test the capability of an exact solution found in the framework of a non linear extension of the Israel-Stewart theory to fit the supernovae Ia data. This exact solution is a generalization of one previously found in the context of the near equilibrium description of dissipative processes, where a dissipative unified dark matter model is studied, considering that such generalized solution does not represent the full regime of the non linear picture. We restrict the solution to the case where a positive entropy production is guaranteed. It is found that for some specific values of the parameter that characterizes the non linear effects, namely k, the model fits the supernovae Ia data slightly better than the ΛCDM model.