Heat transfer in cryogenic bottles involves conduction, convection and radiation modes. Dewar invented the vacuum flask at the beginning of the twentieth century to minimize heat transfer and contain low or high-temperature fluids in it.

In this example, a cryogenic bottle with a stainless steel inner tube, a vacuum gap and an outer insulation layer will be utilized to store liquid nitrogen. The bottle will have a venting system to release the evaporating nitrogen. Heat transfer from the sides of the cryogenic bottle will be considered. The top and the bottom surfaces of the bottle are assumed to be well-insulated. The temperature of the inner wall of the inner tube is assumed to be that of liquid nitrogen, namely a negligible convection heat transfer resistance between the liquid nitrogen and the inner wall of the inner tube.