Summary: To maintain the quality of cereal grains during storage, it is necessary to keep the grain cool and free from insects, and typical methods for dealing with these problems are considered in this paper. In particular the insect population is controlled by fumigating the grain bed with carbon dioxide gas and the grain is cooled by forcing ambient air through the bed. In both problems, the equations which describe the physical processes contain a mixture of advection and diffusion or conduction terms. This paper explores the relationship between traverse time and heat and mass transfer and gains an insight into the grain storage processes that are controlled by forced convection. When heat and mass transport is dominated by the advection terms, the equations are simplified by changing variables from the (x,y) space coordinates to \((\psi,\tau)\), where \(\psi\) is the stream function for the problem and the traverse time \(\tau\) at a point in the storage bin is the time taken for the air to travel to the point from the inlet duct. The conditions are described for the equations to be independent of \(\psi\), with the main condition being that the derivatives of the metrics \(g_{11}\), \(g_{12}\) and \(g_{22}\) with respect to \(\psi\) are small enough. If the equations are independent of then the dependent variable (concentration or temperature) will be constant on lines of constant traverse time \(\tau\). This relationship between traverse time and the cooling or fumigation pattern can be used in the design of storage bins since it implies that the best outlet surface is a line of constant \(\tau\).