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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.

Entransy Dissipation Analysis and New Irreversibility Dimension Ratio of Nanofluid Flow Through Adaptive Heating Elements