Final Solution

                 The thermodynamic model of this system is based on the concept of a thermal heat exchanger.  Though the filter has many channels, it was decided to initially make the model of the system as simple as possible in order to obtain clearer measurements.  In order to achieve this, the thermodynamic model of the system was simplified into a simple hollow cylinder open on both ends that was made of cordierite with identical mass to the actual filter.  The exhaust gases pass through the center of the cylinder and deposit particulate matter on the inner surface of the cylinder.  The gases also transmit heat to the cylinder.  This simple model is an accurate reflection of the actual Diesel Particulate Filter system.  Following is a diagram of the model.

 

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The Temperature Measurement Method

Thermodynamic Model

Cummins

Diesel Particulate Filter

The yellow cylinder represents the filter.  The red arrow represents the exhaust gases.  The dark grey interior represents the diesel soot being deposited on the walls of the filter.