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The shipping of live biological materials requires very close monitoring and perhaps active control of the temperature of the materials. This paper presents the results of a numerical study of 2-D transient natural convection inside a rectangular cavity. The cavity is intended to simulate a typical biological shipping container in which the biomaterials are encased in a chamber surrounded by a phase change material. The rectangular cavity is filled with air (Pr ap 0.69). Initially, the air is at uniform temperature and zero velocity. The top and side walls of the rectangular cavity are fixed at a low temperature and the bottom wall is coupled to the top wall of the heated solid block. For the lower solid block, the side and bottom wall are assumed adiabatic and filled with solid biomaterials. The biomaterial is subjected to a step heat input at time zero. A finite volume approach is used to solve the generic transport equations with the Boussinesq approximation. The flow inside the rectangular cavity is divided into three transient regimes: 1) initial transient stage; 2) quasi-steady stage; and 3) late quasi-steady stage. The results of the parametric study are included for shallow cavities, Ar = 0.5, Ar = 0.25, Ar = 0.125. The transient regimes and fluid flow structure were found to be functions of Rayleigh number, aspect ratio, Prandtl number, thermal capacity parameter (Q*), and nondimensional time (t*).