A fluid and heat flow problem arising in the soup-canning industry

In this paper we consider the problem of heat flow at large Peclet number through viscous fluid (containing an air-bubble) in a rotating circular cylinder. Gravity is assumed to act in a plane perpendicular to the axis of the cylinder, but end effects (due to the finite length of the cylinder) are ignored. A one-dimensional diffusion equation for the transfer of heat between streamlines, valid for any steady flow with closed streamlines, is derived. The implications of our results for the UHT sterilization of canned liquid foods are discussed.