Interfaces between hot and cold magnetized plasmas exist in various astrophysical contexts, for example, where hot outflows impinge on an ambient interstellar medium. It is of interest to understand how the structure of the magnetic field spanning the interface affects the temporal evolution of the temperature gradient. Here, we explore the relation between the magnetic field topology and the heat transfer rate by adding various fractions of tangled versus ordered field across a hot-cold interface that allows the system to evolve to a steady state. We find a simple mathematical relation for the rate of heat conduction as a function of the initial ratio of ordered-to-tangled field across the interface. We discuss potential implications for the astrophysical context of magnetized wind blown bubbles around evolved stars.
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