Southwicks value for the conductivity of empty comb is with the comb horizontal i.e. 90 dgrees to the orientation in nests You should rather use :

Humphrey, J.A.C. and Dykes, E.S. 2008. Thermal energy conduction in a honey bee comb due to cell-heating bees. Journal of Theoretical Biology. 250(1), pp.194–208.

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