A technical issue with fluid flow heating is the relatively small temperature increase as the fluid passes through the heating surface. The fluid does not spend enough time inside the heating source to significantly raise its temperature, despite the heating source itself experiencing a substantial increase. To address this challenge, the concept of the multiple circular heating of air was developed, forming the basis of this work. Two PTC heaters with longitudinal fins are located within a closed channel inside housing composed of a thermal insulation material. Air flows circularly from one finned surface to another. Analytical modeling and experimental testing were used in the analysis, with established restrictions and boundary conditions. An important outcome of the analysis was the methodology established for the optimization of the geometric and process parameters based on minimizing the transient thermal entropy. In conducting the analytical modeling, the temperature of the PTC heater was assumed to be constant at 150 °C and 200 °C. By removing the restrictions and adjusting the boundary conditions, the established methodology for the analysis and optimization of various thermally transient industrial processes can be applied more widely. The experimental determination of the transient thermal entropy was performed at a much higher air flow rate of 0.005 m3s−1 inside the closed channel. The minimum transient entropy also indicates the optimal time for the opening of the channel, allowing the heated air to exit. The novelty of this work lies in the controlled circular heating of the fluid and the establishment of the minimum transient thermal entropy as an optimization criterion.

: The intensity of convective electric heating of the fluid is mainly determined by its volumetric flow, the installed power of the heater and the geometric characteristics of the channel through which it flows. The temperature of the surface of the heating source, and its power is limited by the maximum allowed value. The constant convective surface of the electric heating source, with the above limitations, results in a wide range of electric convective heaters. The thermal efficiency of these heaters depends on a case-by-case basis, while the temperature of the fluid varies in some intervals in relation to the required temperature that needs to be achieved. During fast transient fluid heating processes, convective electric heaters are thermally inert, low efficiency, while in some cases their application is unjustified. Therefore, the thermally generated entropy of the described convective heaters and fluids increases, from case to case, while their energy efficiency is minimized.

The novel segment electric in-line process electric heaters heater designed to heat various fluids analyzed in this work. The complete electric heater consists of several hollow cylindrical segment heating elements. The segment heating elements can vary positioned in relation to the fluid flow. The total power of the segment process heater is equal to the sum of the power of all heating segments and is 0.756kW. Volumetric air flow variations in the amount of 0.001m3s-1, 0.002m3s-1 and 0.003m3s-1. The heating elements are positioned in the three combinations in relation to the direction of the fluid flow. The comparative numeric analysis, conducted for this work, has the goal to determine the influence of the arrangement of segment heaters on the overall energy efficiency of the segment electric heater. In order to verify the results of the numeric simulations carried out and experimental investigations of the segment electric heater. Keywords: In-line heater Energy efficiency Segment elements Fluid flow, Convective heating

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.

Liquid impinging jet at the bottom of the annular cavity is a typical case in the process industry. The jet could have an impact at the bottom center or its peripheral section. The profiled annular cylindrical cavity with the installed electricity heater source is investigated in this paper. Thermal contact irreversibility and liquid drag irreversibility are generated within the profiled cavity. Through analytical modeling and experimental verification, a valid model of the entropy generation is established for both states. The results show that the total entropy between the liquid and the bottom is many times greater for the case of the central jet impingement. Within the annular vertical walls are the locations of the maximum or minimum of the entropy. The effectiveness of the liquid heating is greater in the peripheral impact of the liquid. The method and the results are the basis for optimizing the profiled cavity in various optimization geometry parameters. The optimal geometry of the annular cavity exists in such a way that the balance between thermal irreversibility and liquid drag irreversibility leads to the total minimum rate of the entropy generation for the annular cavity.

In this paper, a discussion of results is presented for the dimensionless analysis of generating irreversibility of vessels in which mixing and heating of fluid are done simultaneously. In the first case, the impeller inside the mixing vessel is the heating body, and in the second case heating body is a fixed ring and the impeller inside the vessel provides only mixing of the fluid. The paper presents a comparative analysis of typical irreversible dimensionless parameters in both cases. A mathematical model is established to describe the thermal-hydraulic irreversibility of heating-mixing vessel which indirectly gives them the ability to minimize and maximize the efficiency of such a system. Also, the paper established typical relations between the dimensionless entropic values and power number, as for the water heater impeller and also for impeller, combined with a heating ring, which will enable comparison of the required power numbers