Modelling the optimum distribution of insulation material

The optimum insulation thickness is determined according to investment and operation and maintenance costs using various economic analysis techniques. Calculation of thickness distribution according to maximum temperature differences may give undesired results if the temperature differences varies during time. Thus, the variation of temperature differences should be taken into account by optimizing the distribution of insulation material according to total amount of heat transfer. Also, neighboring volumes are kept at constant temperatures by means of cooling and heating by refrigerators and heat pumps. Therefore, total energy cost for both sides of the wall (heated/cooled one side and cooled/heated at the other side) should be considered. In this study, a general solution of the optimum distribution of thermal insulation material for a given investment cost or material volume is provided for the volumes confined with environments at different temperatures considering the total amount of heat transfer and total energy cost. Also a case study is given to explain the usage of the new method.