Optimum insulation-thickness for thermal and freezing protection

Methods for protecting water pipes, in cold regions against freezing, by thermal insulation material and heating cable will be analyzed. Reliability of keeping the tube's wall temperature of a piping system at minimum value will be analyzed. A thermoeconomic optimization analysis is applied with a simple algebraic formula derived for estimating the optimum insulation thickness for tubes of different sizes. The optimization is based on a life-cycle cost analysis. The effects of design parameters on the optimum thickness are investigated. Predicted results of this study would provide useful reference data when considering design, practical operation or maintenance.