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Closed-Form Solutions for the Transient and Steady-State Temperature of a Lumped Mass Coupled to Linear and Radiant Boundaries

Exact closed-form solutions describing the transient and steady-state temperature of a lumped mass, linearly coupled to a fixed-temperature boundary and radiatively coupled to a second fixed-temperature boundary, with a constant impressed heat load, are derived. The results are verified by evaluation of limiting cases and comparison with commercial finite-difference heat transfer software.