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Abstract
The theoretical problem of determining critical conditions for an asymmetrically self-heating circular cylinder is considered here and some temperature distributions are obtained using the method of conformal mapping. In particular, the family of asymmetric temperatures is determined whose critical Frank-Kamenetskii parameter is δc = 2. It is shown that for a general surface temperature and specified δ the interior solution is unique, but that there exist exceptional cases for which there are just two interior solutions. The problem of determining δc for general surface temperatures is discussed in terms of conformal mapping.
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