Explicit Solution to a Two-Phase Stefan Problem with a Robin Condition at the Fixed Face and a Similarity-Type Exponential Heat Source
DOI:
https://doi.org/10.70567/mc.v42.ocsid8419Keywords:
Stefan problem, Convective boundary condition, Heat source, Similarity-type solutionAbstract
We consider a one-dimensional two-phase Stefan problem in a semi-infinite domain, modeling the melting of a material imposing a convective (Robin-type) boundary condition at the fixed face and to an internal exponential-type heat source. This formulation realistically represents thermal exchange with the environment, incorporating an additional heating mechanism through a source depending on a similarity variable. The exponential self-similar structure of the source allows for the derivation of analytical solutions. Existence and uniqueness of similarity-type solutions are established under certain conditions on the problem parameters. As an application, a computational example simulating paraffin melting is presented, showing good agreement with the expected physical behavior.
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