7. Simulink Responses

In this last part of the chapter, the Simulink responses will be presented for both the semiinfinite and the finite aluminum media. For both cases, the exact system is implemented on

Simulink.

So, Figure 20 shows the Simulink system whereas Figure 21 represents the temperature variation with respect to time for different values of the sensor placement.

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Figure 20. Simulink representation for the semi-infinite homogeneous plane.

Note that, when comparing Figure 6 to Figure 21, a small time variation of about appears due to the simulation time needed in Simulink that didn’t show up when

using Matlab.

As for the finite medium, Figure 22 and Figure 23 show the Simulink system and the temperature variation with respect to time for different values of the sensor placement and for two values of :

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Figure 22. Simulink representation for the finite homogeneous plane.

Conclusion

In this chapter we have studied the thermal interface behavior using the fractional order approach. The identification of the diffusion phenomena as well as the optimization of their process control were made easier using the fractional order approach, especially when both operational and frequency domains are considered. In fact, based on the pseudo-state (Sabatier, 2013) equations of the conduction phenomenon, representative models for both semi-infinite and finite media were easily developed.

On the other hand, when it comes to time responses, it is more complicated as the analytical solutions of Inverse Laplace transforms don’t exist for all the types of equations.

Nevertheless, approximations do exist and others are still a contemporary research subject of our interest; they are the core of advanced studies related to fractional order applications.

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