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A detailed description of a numerical method for computing unsteady flows in engine intake and exhaust systems is given. The calculations include the effects of heat transfer and friction. The inclusion of such calculations in a mathematically simulated engine cycle is discussed and results shown for several systems. In particular, the effects of bell-mouth versus plain pipe terminations and the effects of a finite surge tank are calculated. Experimental data on the effect of heat transfer from the back of the intake valve on wave damping are given and show the effect to be negligible. Experimental data on wave damping during the valve closed period and on the temperature rise of the air near the valve are also given.