Thermal energy conduction in a honey bee comb due to cell-heating bees

Theoretical analysis and numerical calculations are performed to characterize the unsteady two-dimensional conduction of thermal energy in an idealized honey bee comb. The situation explored corresponds to a comb containing a number of brood cells occupied by pupae. These cells are surrounded by other cells containing pollen which, in turn, are surrounded (above) by cells containing honey and (below) by vacant cells containing air. Up to five vacant cells in the brood region can be occupied by cell-heating bees which, through the isometrical contraction of their flight muscles, can generate sufficient energy to raise their body temperatures by a few degrees. In this way, the cell-heating bees alter the heat flux and temperature distributions in the brood region so as to maintain conditions that benefit the pupae. The calculations show that the number of cell-heating bees significantly affects the magnitude, time rate of change, and spatial distribution of temperature throughout the comb. They also reveal a vertically aligned asymmetry in the spatial distribution of temperature that is due to the large heat capacity and thermal conductivity of honey relative to air, whereby air-filled cells experience larger temperature increases than honey-filled cells. Analysis shows that convection and radiation represent negligible modes of thermal energy transfer at all levels in the problem considered. Also, because of its small thickness, the wax wall of a comb cell simultaneously presents negligible resistance to conduction heat transfer normal to it and very large resistance along it. As a consequence the walls of a cell play no thermal role, but simply serve as mechanical supports for the materials they contain.