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

Pedagogy

The Thermal Fin "Tfin" Problem
Forward Problem

Authors: G Rozza & AT Patera
in collaboration with DBP Huynh, NC Nguyen and, previously, S Sen & S Deparis



 

Q1 As the Bi number increases, how does the temperature distribution in the fin change — in particular as regards variations in x1 and x2? When would you expect the classical 1D fin approximation to yield reasonable predictions for the temperature field in the fin?

Q2 Assume that the spreader plate is isothermal: what does the classical 1D fin approximation then predict for Tav(μ)? How accurate is this approximation in the limit that (i) κ is large (and hence there is little temperature drop in the base/spreader), and (ii) Bi is small (hence the temperature distribution in the fin is largely 1D)

Q3 Can you construct a simple lumped/analytical model that will be reasonably valid even for κ not too large? (Hint: consider a "constriction" resistance for the base/spreader and a classical 1D fin resistance placed in series.) How accurate is your approximation over the full range of parameters?

Q4 Are the results for large Bi of interest, and why or why not?

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