Mathematical modeling of heat transfer, condensation, and capillary flow in porous insulation on a cold pipe

Porous insulation used on pipes carrying cold fluids suffers thermal degradation due to condensation of water vapor and the build up of water in the insulation. Recently, it has been suggested that the thermal degradation can be significantly reduced by wrapping a hydrophilic wick fabric on the cold pipe. The capillary action of the fabric, aided by gravity, allows the condensed moisture to move to the outer surface of the insulation, from where, if ambient conditions are right, it evaporates. This paper presents the details of a mathematical model for condensation in the insulation in the presence of the wick fabric. The model is based on the volume-averaged equations for unsteady transport of heat, water vapor, and liquid water in a porous medium. The wick is modeled as an anisotropic porous medium. The model also allows for the presence of a vapor retarder jacket that is used to reduce the ingress of water vapor into the insulation. The model has been applied to an insulation layer around a horizontal pipe. The presence of the wick is shown to significantly reduce the amount of liquid water in the insulation. The results of the model have been verified using laboratory experiments and field tests.