Integral methods are suited to solve a non-linear system of differential equations where the
non-linearity can be found either in the differential equations or in the boundary conditions
. Though they are approximate methods, they have proven to give simple solutions with acceptable
accuracy for transient heat transfer in He II. Taking in account the temperature dependence
of thermal properties, direct solutions are found without the need of ajusting a parameter.
Previously, we have presented a solution for the clamped heat flux and in the present study
this method is used to accommodate the clamped-temperature problem. In the case of constant
thermal properties, this method yields results that are within a few percent of the exact
solution for the heat flux at the axis origin. We applied this solution to analyze recovery
from burnout and find an agreement within 10% at low heat flux whereas at high heat flux the
model deviates from the experimental data suggesting the need for a more refined thermal
model.
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