Mode of heat transfer between two cubes and to its surroundings

Hi all, I am trying to mathematically proof that one can neglect convection and radiation when two cubes (paraffin-based, 1x1x1cm) are in direct contact on one side whilst the other 5 sides are perfectly insulated. Any ideas on how to calculate the Nusselt number here? How do you justify that radiation can be neglected? Can they actually be neglected? How would the mode of heat transfer be changed if the cubes were not perfectly insulated, but instead were surrounded by air?
It would be fantastic if anyone could give me any hint! Many warm wishes and thanks so much in advance!