Energetically optimal dimensions of parallelepiped-shaped industrial structures

Technical structures with a parallelepiped form are frequently used in various areas of industry. For example, as fluid containers, ice and minerals piles, underground and surface storages and cooling chambers. A task of determining the optimum dimensions of the structure to minimize the energy expenses to support a normative temperature in the structure arises. The minimum surface area of the structure at a given volume is accepted as a criterion of optimality. A problem of unconstrained optimization for a structure with a parallelepiped form was formulated and solved. Equations to determine the optimum dimensions of width, height and length of the structure were obtained. It was determined that a cube is the most optimal form.