A mathematical model of natural convection in three-dimensional enclosures containing respiring fruits or vegetables is presented. The agricultural produce is treated media exhibiting transversely orthotropic permeability in which local temperature dependent respiration heat generation occurs. In the numerical investigations conducted, both adiabatic and isothermal boundary conditions are considered for the cooling and storage process. The influence of size, respiration rate and permeability on natural convection is discussed. Numerical experimental results for temperature distribution, velocity distribution, true and storage process are presented. It was found that the style of packaging of the agricultural produce and the size container were likely to have significant effects on the storage characteristics.