Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport

Pedagogy

Thermal Contraction Resistance
Forward Problem

Authors: G Rozza & AT Patera
in collaboration with DBP Huynh & NC Nguyen


 

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.

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