We have developed a simple method to calculate disk temperature profiles that is based on analytically solving the heat conduction equation in Hankel Transform Space. This method can be applied to disks that are mounted on multi-layered, water-cooled heat spreaders, which may include glue or solder layers and dielectric coating layers. This allows parametric optimization of the heat removal process in pumped solid state and semiconductor disks without having to use finite-element programs.
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N. Hodgson, A. Caprara, "Analytical calculation of temperature profiles in solid state laser disks mounted on multi-layered heat spreaders using Hankel transforms," Proc. SPIE 10082, Solid State Lasers XXVI: Technology and Devices, 100820I (17 February 2017);