By Jaan Kalda (TalTech).
The space between two parallel infinite metallic plates is filled with homogeneous material of heat conductivity \kappa. The heat conductivity of the metallic plates is much larger than \kappa, the distance between the plates is L. One of the plates is kept at temperature T_1, and the other – at temperature T_2. There is a spherical cavity of radius R in the medium between the plates, at equal distance L/2 from the both plates; assume that R\ll L . Initially, the cavity is filled with a gas of negligibly small heat conductivity (much smaller than \kappa). By how much will change the total heat flux P between the plates (measured in watts) if the spherical cavity is filled with a material of very large heat conductivity (much larger than \kappa)?
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