A hollow electric heating cylinder is inserted inside a thermo-insulating cylindrical body of larger diameter, together representing a single cylindrical heating element. Three cylindrical heating elements, with an independent electrical source, are arranged alternately one after the other to form a heating duct. The internal diameters of the hollow heating cylinders are different, and the cylinders are arranged from the largest to the smallest in the nanofluid’s flow direction. Through these hollow heating cylinders passes nanofluid, which is thereby heated. The material of the hollow heating cylinders is a PTC (positive temperature coefficient) heating source, which allows maintaining approximately constant temperatures of the cylinders’ surfaces. The analytical analysis used three temperatures of the hollow heating cylinders of 400 K, 500 K, and 600 K. The temperatures of the heating cylinders are varied for each of the three cylindrical heating elements. In the same arrangement, the inner diameters of the hollow cylinders are set to 15 mm, 11 mm, and 7 mm in the nanofluid’s flow direction. The basis of the analytical model is the entransy flow dissipation rate. Furthermore, a new dimension irreversibility ratio is introduced as the ratio between entransy flow dissipation and thermal-generated entropy. This paper provides a suitable basis for optimizing the geometric and process parameters of cylindrical heating elements. An optimization criterion can be maximizing the new dimensionless irreversibility ratio, which implies minimizing thermal entropy and maximizing entransy flow dissipation.

By insulating the vortex of the liquid with a hollow cylinder, the level of liquid inside the cylinder is raised. This phenomenon is caused by an air vacuum between the liquid vortex and the inside of the cylinder. At the bottom of the cylinder, a heat source is installed while the outer surface of the cylinder is thermally insulated. In this way, the cylinder can be considered as a hollow cylindrical fin. The heat from this fin is partially transmitted to the liquid. The analysis of the entransy of this system is based on the variation in the size of the inner convective cylinder surface and the angular velocity of the liquid vortex. In addition, an analysis of the entransy, efficiency, and thermal resistance of this system was carried out for the partial and complete filling of the cylinder with liquid. The novelty of this entransy analysis is in simultaneously raising and heating the liquid vortex within the hollow cylinder. By innovatively using an air vacuum above the liquid vortex, the hollow cylinder sucks the liquid vortex and the same is heated. The contribution of this research includes an established mathematical model of the entransy dissipation, which can be used in the case where the hollow cylinder is completely filled with liquid or when it is completely filled with air. The results obtained in this study are a good basis for further investigations and optimization of the various thermotechnical systems, especially in the chemical, mechanical, and process industries.