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This paper presents a simplified thermal model for round catalytic converters in steady state operation. Using this model, the analytic solution for the temperature distribution in the monolithic substrate is obtained. This analytic solution in the substrate is, then, combined with those in the intumescent mat [1] and the metal shell to obtain the temperature profile in the radial direction of the converter except for three unknown temperatures at the three material interfaces, which can be solved using an Excel application program. This analytical temperature solution facilitates the studies of the effects of various design parameters such as the exhaust gas temperature, exhaust gas flow rate, substrate cell geometry, converter dimensions, and ambient temperature and flow, etc.

In the catalytic converter, the thermal conductivity of the insulation material (intumescent mat) placed between the ceramic catalyst and the metal shell is strongly dependent on the temperature, resulting in the solving of non-linear heat conduction equations. In this paper, the analytic solution for the steady heat flow in a cylinder with temperature dependent conductivity is given. Using this analytic solution for the mat and including convection and radiation at the converter skin, an analytical expression for calculating converter skin temperature is obtained. This expression can be easily incorporated in a Fortran code to calculate the temperatures.