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Pedagogy

Thermal Contraction Resistance

Forward Problem

Authors: G Rozza & AT Patera

in collaboration with DBP Huynh & NC Nguyen

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**Q1**
Develop a 1D resistance model for the wavy part in series with the straight part. Is this model an upper
bound or lower bound (or neither)?
*Hint*: Assume that *T* = *T*(*x*) (a function of *x* only) and require
that the heat transfer across any *x*-plane is constant.

**Q2**
Assess the accuracy of the model of Part Q1 as a function of the parameters (in particular the waviness amplitude
and *y*-conductivity).

**Q3**
Predict/confirm the *x*-extent of the region
after the wavy portion over which the temperature distribution is
not 1D.

**Q4**
Develop a model for how to connect the curvy
("tailpiano") geometry with an infinitely long straight segment.