Advanced Analytical Solution of Transient Heat Conduction

The sudden filling of an empty cryogenic liquid storage tank initially at atmospheric temperature with a cryogenic liquid at its saturation temperature will initiate a sudden high temperature difference between the terminals of the annular space containing the thermal insulating material. This high temperature difference is behind the dependence of thermal conductivity of the thermal insulation material on its temperature. In addition, it will initiate a potential for the evaporation of cryogenic liquid due to the transient heat transfer inside the cryogenic liquid storage tank. This energy loss is of a great economic interest especially when the size of cryogenic liquid storage tank is relatively big. Based on the authors’ own research and classroom experience, this book contains a text for researchers and for a graduate level coarse. The analytical solution of the non-linear partial differential equation in spherical & cylindrical coordinates of transient heat conduction through a thermal insulation material of a thermal conductivity temperature dependent is solved analytically using Kirchhoff’s transformation.