Abstract: A method is provided for estimating the heat exchange rate related to the exothermic oxidation reactions of a catalytic converter in an internal combustion engine. Exhaust gases flow through the catalytic converter, the method includes, but is not limited to providing a thermal model of a catalytic converter where no oxidation reactions take place.

Abstract: A method is provided for the diagnosis of the EGR cooler efficiency in a Diesel engine that includes but is not limited to construction of a model for determining the temperature drop y=?T in the EGR cooler, the model having a parameter vector ? and an input vector x; performing a model calibration phase in order to estimate the bias h0 of the system; calculation of a set of primary residuals ?(?0, x, ?T), staffing from the model equation and using the results of the calibration phase; calculation of a set of improved residuals ?N(?0): ? N ? ( ? 0 ) = 1 N ? ? k = 1 N ? ( ? ? ( ? 0 , x k , y k ) - h 0 ) where N is the number of samples on which the diagnostic testis performed; calculation of a diagnostic index S: S=?TNR0?1?N and, use of the diagnostic index S in order to diagnose the efficiency of the EGR cooler.