Multilayer insulation (MLI), commonly used in cryogenics, is typically composed of many layers of thin polymer sheets each coated with a thin film of highly reflective metal. The primary purpose of this insulation is to block radiative energy transfer. However, at very low temperatures where blackbody radiation occurs at long wavelengths, some energy may be transmitted through these layers, degrading the performance of the insulation. Traditional modeling techniques assume that the films are opaque and are not easily extended to include radiative transmission through the layers. In order to model the effect of wavelength dependent transmission on the thermal performance of MLI, an L1-norm energy vector is defined and combined with a square energy distribution matrix. The key here is that the energy distribution matrix describes one time step of the radiation—one set of reflections, transmissions, and absorptions—and since this matrix is square, it can be easily raised to a large power, describing the final state of the system quickly. This approach removes the need to track every reflected and transmitted radiation element, but instead determines the eventual location where the thermal radiation energy is deposited. This method can be generalized to model dependence of the reflection and transmission of the radiation on wavelength or angle of propagation, to include thermal conduction effects, and to model transient behavior. The results of this work predict the degree of transmission dependent degradation expected to be seen when using state-of-the-art MLI in low temperature cryogenic systems.

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