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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.

Accurately predicting converter assembly deformation and mat pressure is essential in converter packaging design and manufacturing. In stuffing packaging, the annulus between the deformed shell and the catalyst is larger than that between the stuffing cone and the catalyst. As a result, the mat expands and undergoes unloading process. Tests show that the mat exhibits different loading and unloading characteristics. Using such a hysteresis mat pressure vs density curve in finite element analysis, the computed converter deformations closely agree with test data. Conversly, neglecting the mat hysteresis behavior may overestimate the deformation and pressure by a factor of three to four.