Applied sciences

Archives of Thermodynamics

Content

Archives of Thermodynamics | 2025 | vol. 46 | No 2

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Abstract

This work describes examples of the use of cryogenic lines and their designs, referring in detail to typical structural nodes found in cryogenic transfer lines. As a special case, multichannel cryogenic transfer lines are described, in which the process pipes are made of Invar. This has a significant impact on the number of internal supports and the method of thermal shrinkage compensation, which directly impact into reduced heat input during the transfer of cryogenic media. The second law of thermodynamics and the Gouy-Stodola theorem are discussed from the perspective of their application in optimizing and evaluating heat and mass transfer devices. The next part of the work presents the internal structure of the selected 250 m multichannel cryogenic transfer line. Several variants of the method of supporting process pipes have been presented and compared with the solution using Invar. For each solution, an entropy analysis was carried out in order to select the best design in terms of the entropy generated in the process pipes. From the examples presented, it is proven that entropy minimization method can be used for complex optimization of entire cryogenic distribution systems, as well as their indi-vidual components.
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Authors and Affiliations

Pawel Duda
1
Maciej Chorowski
1
Ziemowit Malecha
1
Jarosław Poliński
1

  1. Wroclaw University of Science and Technology, Wybrzeże Stanisława Wyspiańskiego 27, 50-370 Wrocław, Poland
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Abstract

Atmospheric conditions, such as for example ambient temperature, may have the influence on temperature of a photovoltaic (PV) module. The greatest impact is exerted by solar radiation intensity, leading to an increase in the temperature of pho-tovoltaic cells. As the temperature of the module increases, the efficiency and thus the generated power decreases. The cooling systems capable of lowering the temperature of the module, thus improving its efficiency may be promising solu-tion to this problem. This paper presents the results of a study on the effect of water cooling of a photovoltaic module. The experiments were conducted in Poland using the test stand composed of two photovoltaic modules. One module was equipped with a water cooling system at its front surface while the second module was treated as the reference. Thanks to such a test setup design it was possible to study the influence of atmospheric conditions on the change of photovoltaic module temperature, power output and amount of energy generated by the cooled and reference module. Two cooling methods concerning the timing of cooling water flow activation/deactivation were investigated. The first method involved a fixed cooling time and intervals, while the second method adjusted the cooling water flow activation and deactivation time based on the surface temperature of the module. As a result of the conducted research, a maximum decrease of 17.6 K of photovoltaic module temperature and a maximum power increase of ca. 5%, using the cooling system, was achieved. Furthermore, a correlation between cooling efficiency and cloud cover was described, as well as a method for determining cooling water flow. It was found that better cooling results are obtained when employing a cooling activation and deacti-vation method based on temperature dependence.
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Authors and Affiliations

Weronika Janowicz
1
Michał Pomorski
1
Piotr Kolasiński
1

  1. Department of Thermodynamics and Renewable Sources of Energy, Wrocław University of Science and Technology, Wybrzeże Stanisława Wyspiańskiego 27, Wrocław 50-370, Poland
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Abstract

Thermal conductivity and transition are the two stages of a closed loop pulsating heat pipe's operation. A device called a closed loop pulsating heat pipe transfers heat at various heat inputs. The thermal performance of the closed loop pulsating heat pipe is impacted by various types of modifications. Heat transfer characteristics of the closed loop pulsating heat pipe are to be ob-served using computational fluid dynamics analysis. The aim of this study is to improve the heat conductivity of the closed loop pulsating heat pipe with the changing filling ratio. This study presents the closed loop pulsating heat pipe modeling by using ANSYS Workbench. ANSYS Fluent is considered to model the above stated phenomenon and computational fluid dy-namics simulations are performed for different variations of temperature and filling ratio. The model is analyzed at 200W300W heat flux for 100400 iterations and the vaporized form is obtained. The temperature and iterations variations are the key parameters of the study. It is concluded that the temperature of the evaporator increased more at different levels of time as compared to the temperature of the condenser. In this analysis, by giving different heat inputs and evaporator sections, the heat flux in the condenser section is observed. It is concluded that the time and heat flux are the most affecting parameters in this study.
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Authors and Affiliations

Haider Ali
1
Muhammad Amjad
1
Muhammad Ishaq
1
Mohammed Marshad R. Alharbi
2
Krzysztof Kędzia
3
Ahmed Zubair Jan
3

  1. Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan
  2. Ministry of Education, Saudi Arabia
  3. Faculty of Mechanical Engineering, Wroclaw University of Science and Technology, Wroclaw, Poland
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Abstract

District heating systems commonly utilize pre-insulated pipes arranged in either a parallel or TwinPipe configuration. This study compares the temperature distribution in the ground, as determined by a numerical 3D model, with experimental meas-urements conducted on a dedicated test setup. The analysis includes several district heating pipe variants (DN40, DN50 and DN65), and their counterparts in a single parallel pre-insulated system. The results obtained from laboratory experiments and numerical simulations show strong agreement, confirming the reliability of the proposed approach. The novelty of this work lies in the integration of experimental data and numerical simulations to improve the accuracy of heat loss estimations. The relative error between the computational and experimental models remains below 10%, ensuring high precision in the findings. The presented results provide valuable design insights for optimizing insulation thickness and pipe layout configurations in district heating networks. These findings contribute to the development of more efficient and sustainable thermal energy dis-tribution systems.
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Authors and Affiliations

Dariusz Jakubek
1
Marzena Nowak-Ocłoń
1
Petar Sabev Varbanov
2
Maciej Sułowicz
3
ORCID: ORCID

  1. Energy Department, Cracow University of Technology, al. Jana Pawła II 37, Cracow, 31-864, Poland
  2. Sustainable Process Integration Lab, NETME Centre, Brno Univ. of Technology, Technická 2896/2, Brno, 616 69, Czech Republic
  3. Faculty of Electrical and Computer Engineering, Cracow University of Technology, Warszawska 24, Cracow, 31–155, Poland
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Abstract

The paper presents a concept of an innovative test stand for converting waste heat into electricity using wet steam. Two expanders will be tested, i.e. a rotary blower and a scroll compressor, which have been adapted for reverse cycle operation. The main objective of the stand is to verify experimentally the feasibility of the effective use of an innovative wet steam cycle for waste heat recovery. To verify the design assumptions, as well as the stand configuration and parameters, prelim-inary simulations were carried out in Ebsilon software. The solution innovation lies in using wet steam to enhance waste heat recovery. Wet steam is generated on the test stand by injecting water into saturated steam using a specially designed nozzle system. In this way, steam dryness can be controlled precisely and proper conditions are created for the expander operation. Saturated steam is generated in the boiler installed at the laboratory of the Department of Energy of the Cracow University of Technology. The test stand will enable the system operation and an assessment of the system’s potential applications. This will help to improve the energy efficiency of waste heat utilization and reduce emissions.
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Authors and Affiliations

Wiesław Zima
1
Artur Cebula
1
Karol Morański
1
Jerzy Cisek
2

  1. Department of Energy, Cracow University of Technology, Al. Jana Pawła II 37, Cracow 31-864, Poland
  2. Mechanical Department, Cracow University of Technology, Al. Jana Pawła II 37, Cracow 31-864, Poland
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Abstract

This study investigates the influence of chemical reactions, heat sources, and magnetohydrodynamic effects on the flow of hyperbolic tangent fluid over a nonlinear stretching sheet in a porous medium. Despite significant research on magnetohydro-dynamic flows, the combined effects of magnetohydrodynamics, chemical reactions and heat on hyperbolic tangent fluid flow in porous media have not been fully explored, especially under varying electromagnetic conditions. This gap is critical in applications such as geothermal energy extraction, petroleum recovery, polymer processing and cooling systems for electron-ics. The governing equations for mass, momentum, energy and species transport are transformed into a dimensionless system using similarity transformations and solved numerically using the implicit finite difference method with MATLAB’s ”bvp4c” solver. Key parameters, including magnetic field strength, porosity, chemical reaction rate and heat source/sink are analysed for their effects on velocity, temperature and concentration profiles. Notably, varying magnetic field strengths significantly influence flow characteristics, offering insights into the behaviour of hyperbolic tangent fluid under different electromagnetic conditions. Results of this study show that magnetohydrodynamic interactions, chemical processes and thermal effects signif-icantly affect the flow dynamics and heat transfer. Additionally, as the Darcy number increases and the permeability of the porous medium rises, so do the shear rates within the pores. This observation underscores the intricate relationship between the shear-thinning behaviour of heat transfer fluids and permeability, providing valuable insights for optimizing flow dynamics in porous media relevant to energy extraction and material processing applications.
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Authors and Affiliations

Srinivas Reddy Kallem
1
Siva Reddy Sheri
1
Alfunsa Prathiba
2
Gollapalli Shankar
3

  1. Department of Mathematics, GSS, GITAM (Deemed to Be University), Hyderabad, Telangana-502329, India
  2. Department of Mathematics, CVR College of Engineering, Telanagana-501510, India
  3. Department of Mathematics, B V Raju Institute of Technology, Narsapur, Medak, Telanagana-502313, India
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Abstract

In this study, we investigate the potential impacts of the thermo-diffusion and diffusion-thermo effects on electro-osmotic flow of Maxwell nanofluid across the stretching sheet. Magnetic and electric field over Darcy-Forchheimer flow and chem-ical reaction are also included. This study is vital in areas such as microfluidics, medical applications, and thermal man-agement, where manipulating nanofluids under electromagnetic fields is essential. Through similarity transformation, the governing equations are turned into a collection of non-linear ordinary differential equations. The numerical results for the changed equations are obtained using the fifth order Runge-Kutta-Fehlberg technique with a shooting method. It has been established that if the Forchheimer number and electro-osmotic parameter increase, the velocity profile drops. As the dif-fusion-thermo effect grows so does the temperature profile. Similarly, the thermo-diffusion effect increases along with the concentration profile. The skin friction coefficient decreases by 10% and 23%, for the magnetic parameter increases from 0.4 to 2 and the Forchheimer number rises from 1 to 5, respectively. Additionally, with an increase in the Dufour number from 1.5 to 2, the Nusselt number decreases by 9%, while the Sherwood number increases by 33%. This research provides a more comprehensive analytical framework by integrating multiple physical effects such as Soret and Dufour effects, magnetic and electric fields, and porous media, thereby enhancing applications in microfluidic devices for precise fluid control, biomedical engineering for improved drug delivery and tissue engineering, thermal management for more efficient electronic cooling systems, environmental remediation for effective pollution control, and materials science for developing smart materials and nanocomposites.
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Authors and Affiliations

Amudhini M
1
Poulomi De
1

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai-600127, Tamilnadu, India
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Abstract

The present paper targets the flow of fluid with Fe3O4 particles as nanomaterial over a non-linear elongated sheet with changing width. The process holds vital importance in various industries like paper manufacturing, extrusion of dyes and filaments, atomic reactors and many more. Nanofluids depict special features which give them the potential to be also used in power engines, refrigerators, power plants as well as pharmaceutical processes. Hence, the presented model is designed to intensify the rate of heat transfer and to reduce energy wastage, and tailor for the optimal selection of parameters like conductivity as well as viscosity, which will improve the effectiveness of the heat transfer process. The main idea behind this investigation is to calculate the effect of electromagnetohydrodynamics, Biot number, Eckert number, radiation along with the absorption factor. In this paper, the flow is modelled by using Navier-Stokes equations which are customised to Prandtl boundary layer equations. The Adams-Bashforth predictor-corrector is used to obtain numerical solutions. The present study helps to potentially improve and achieve the desired quality of the stretching sheet. Moreover, a negligible amount of activation energy is required, finding an economical way to get suitable out-puts.
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Authors and Affiliations

Pragya Pandey
1
Dhatchana Moorthy Kavitha
2
Thangaraju Lawany
2

  1. Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai – 600 089, Tamil Nadu, India
  2. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha Nagar, Thandalam, Chennai – 602 105, Tamil Nadu, India
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Abstract

The heat transfer optimization for magnetohydrodynamic unsteady stagnation-point flows and the thermal progress with the effect of heat generation is performed using the response surface methodology. The first step in this study involves reducing the mathematical model of partial differential equations and boundary conditions into non-linear ordinary differential equations via similarity transformations. Numerical solutions of the emerged system are obtained using the bvp4c solver. As observed from this study, the magnitude of the skin friction coefficient and heat transfer rate rises with the suction parameter. The statis-tical analysis and optimization done using the response surface methodology revealed that the suction parameter highly impacts the local Nusselt number. The maximum sensitivity of the heat transfer rate is towards the magnetic and suction parameters.
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Authors and Affiliations

Amirul Zaqwan Azman
1
Norihan Md Arifin
1
Nur Syahirah Wahid
1
Mohd Ezad Hafidz Hafidzuddin
2

  1. Department of Mathematics & Statistics, Faculty of Science, Universiti Putra Malaysia, 43400, UPM Serdang, Selangor, Malaysia
  2. Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor
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Abstract

To prepare mullite porous ceramics with low thermal conductivity and high strength, taking kyanite tailings and α-Al2O3 as the main raw materials, the mixture after adding sawdust and foaming agents was cast into shape and heated at different temperatures. The bulk density, porosity and mechanical properties of the sample were tested at room temperature. The phase composition and microstructure were analyzed using X-ray diffraction and scanning electron microscopy. The results show that as the sawdust addition increased, the apparent porosity of the sample increased; the compressive strength and the thermal conductivity decreased. Increasing the firing temperature can promote the densification, improve the compressive strength and increase the thermal conductivity of the sample. When the firing temperature was increased to 1500°C, the ceramic reaction was basically completed. When the sawdust content was low, the sawdust was almost surrounded by the material, and the pore distribution was relatively dispersed. As the sawdust content increased, the pore distribution became more con-centrated, and there were more connected pores. When the sawdust addition was 10% (w) and the heat treatment temperature was 1500°C, the mullite porous ceramics would have high compressive strength and low thermal conductivity.
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Authors and Affiliations

Huayun Sun
1

  1. School of Metallurgy, Shandong Vocational College of Industry, Zibo, 256414, China
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Abstract

Evaporative cooling can be an answer to the growing global demand for energy efficient and sustainable air conditioning. Direct evaporative cooling is the traditional method of cooling air to wet-bulb temperature. Indirect evaporative cooling uses heat exchangers with wet and dry channels to cool air indirectly, avoiding an increase in humidity. The Maisotsenko cycle is a dew point indirect evaporative cooling that allows air to be cooled below wet-bulb temperature using a heat and mass ex-changer with a coupled wet and dry channel. It can be used as a stand-alone system, or as coupled with traditional refrigerant-based cooling systems, or as a heat recovery process to improve the efficiency in the power industry applications. A Python-based computational tool for simulating of 1D heat and mass transfer in the Maisotsenko cycle is presented here. It uses a spatially discretised differential equation solver and a psychrometric chart. The 1D model and experimental data from the study of Pakari were used as a reference for the initial testing. The comparison results are promising, suggesting a potential application in the design of sustainable cooling.
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Authors and Affiliations

Jan Pokorný
1
Paweł Madejski
2
Jan Fišer
1

  1. Faculty of Mechanical Engineering, Department of Thermodynamics and Environmental Engineering, Brno University of Technology (BUT), Technická 2896/2, Královo Pole, 61669, Brno, Czech Republic
  2. Faculty of Mechanical Engineering and Robotics, Department of Power Systems and Environmental Protection Facilities, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
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Abstract

The issue of reducing energy consumption and the negative impact on the environment caused by vapour-compression refrig-erating machines through the use of adiabatic air cooling technologies is considered in the paper. The climatic features of the use of adiabatic air cooling are determined using the example of four cities of Ukraine (Lviv, Kyiv, Kharkiv, Odesa). It is shown that the maximum cooling effect is observed in Kharkiv, although in terms of maximum temperatures and the duration of the warm period, this city is 6.3% inferior to Odesa. However, due to low relative humidity, the cooling efficiency was 5.4% higher. To conduct a comparative study of the effectiveness of the use of adiabatic technologies, field tests were con-ducted on two identical refrigerating units working under the same operating conditions, one of which was additionally equipped with an evaporative cooling system. A monitoring system, which was installed on both the original and the modern-ized refrigerating units, was developed to collect, accumulate and pre-process experimental data. It was determined that when using adiabatic technologies, the mass flow rate of the refrigerant is reduced compared to the original vapour-compression machine while ensuring the same cooling capacity, which in turn leads to a decrease in the load on the compressor. In turn, this leads to a decrease in the rotation frequency of the compressor electric motor, which resulted in a decrease in energy consumption by 25–28 % for the considered type of refrigerating units.
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Authors and Affiliations

Serhii Molskyi
1
Oleksandr Molskyi
2
Anna Vorontsova
3

  1. Public Union “Refrigeration Association of Ukraine”, Druzhkivska St., 10, 03113, Kyiv, Ukraine
  2. State Biotechnological University, Alchevskikh St., 44, 61000, Kharkiv, Ukraine
  3. Anatolii Pidhornyi Institute of Power Machines and Systems, National Academy of Sciences of Ukraine, Komunalnykiv St., 2/10, 61046, Kharkiv, Ukraine
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Abstract

Integration of a Stirling engine in a biomass boiler can be an interesting renewable alternative for the supply of heat and electricity in isolated homes located in areas where local biomass is available and during months when sunlight is low. Since this integration requires a careful coupling of the engine and boiler, an integrated model of these two devices is a relevant issue. In this case, a modular integrated model of a 25 kWth biomass pellet boiler, fire-tube with a cylindrical water jacket, coupled to a 1 kWe free piston Stirling engine is presented. To model the boiler, and take into account the location of the Stirling head, the zonal method was chosen, which allows estimating this temperature from an additional set of surrounding temperatures. For the Stirling engin, a model widely used to evaluate those engines was used. Various software tools have been used to integrate the model sequentially. The integrated model predicts the thermal and electrical production based on different opera-tion parameters, such as the boiler load in 5% fractions of its load from 50 to 100%. The obtained results, which will be validated with the experimental setup, show a maximum output of approximately 600 W for the engine and a decreasing tem-perature profile in the combustion chamber, as a function of the partial load.
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Authors and Affiliations

Javier Uche
1
Sergio Usón
2
Juan Anat Gómez
3

  1. ENERGAIA Institute and Department of Mechanical Engineering, University of Zaragoza. Mariano Esquillor 15, 50018 Zaragoza, Spain
  2. ENERGAIA Institute and Department of Mechanical Engineering, University of Zaragoza. Maria de Luna 5, 50018 Zaragoza, Spain
  3. ENERGAIA Institute, University of Zaragoza. Mariano Esquillor 15, 50018 Zaragoza, Spain
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Abstract

This study investigates the improved heat transfer process of multi-nozzle arrangements through numerical analysis. A dis-crete phase based numerical model is developed to analyse the secondary atomization and heat transfer characteristics under different conditions. The effects of pressure, spacing and tilt angle of the nozzle group on the atomization cooling perfor-mance are evaluated. The results indicate that increasing the pressure can significantly improve the heat transfer capacity. The higher the pressure, the lower the hot wall temperatures and the higher the heat transfer coefficient. The nozzle tilt angle also has a significant impact. The heat transfer performance for a 30° tilt angle is optimal, while for a 15° tilt angle is poor. Increasing the number of nozzles can improve the cooling to a limited extent. In addition, nozzle spacing will affect temper-ature distribution, thereby achieving optimal cooling at intermediate distances. The results can provide valuable insights for optimizing multi-nozzle configurations of efficient heat transfer in industrial applications.
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Authors and Affiliations

Li Li
1 2
Rong Li
1 2
ORCID: ORCID
Lei Zhang
1 2

  1. Hebei Key Laboratory of Man-machine Environmental Thermal Control Technology and Equipment, Xingtai, 054000, China
  2. Hebei Vocational University of Technology and Engineering, Xingtai, 054000, China
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Abstract

This study investigates heat transfer under conditions of limited (undeveloped) convection within a narrow 5 cm gap between a centrally positioned heater and the inner walls of a closed chamber. A simplified approach − the linear method − is proposed for estimating Newton’s heat transfer coefficient, assuming a weak linear dependence on temperature. Experimental data and known convection models were used to verify the method. The convective component obtained using the linear method was compared to experimental values and theoretical bounds, showing that the linear method slightly overestimates but remains within a valid range. Artificial neural networks supported the estimation of steady-state temperatures and voltages. This work is a continuation of earlier research and confirms the practical value of the linear method in constrained thermal environments. Further development of the experimental rig is planned to expand the study.
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Authors and Affiliations

Ewa Pelińska-Olko
1
Emilija Zagórska
1

  1. Department of Thermodynamics and Renewable Energy Sources, Faculty of Mechanical and Power Engineering, Wroclaw University of Science and Technology, Wybrzeże Stanisława Wyspiańskiego 27, 50-370 Wrocław, Poland
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Abstract

Using the Fourier transform to solve a one-dimensional heat conduction model with temperature f(t) as the boundary requires complex integral transformation operations. According to the property of the Fourier transform, f(t) is regarded as a symbol in the process operation, and the universal theory resolution of such a problem is established without directly solving the f(t) transformation. f(t) is then substituted into the theoretical solution to obtain the solution of the actual model. Using the theo-retical solution, the solutions of 3 types of common functions are given. Combined with the characteristics of the model, precautions during the solving process are proposed. The example application demonstrates the establishment and application process of inversing model parameters based on the inflection point of temperature variation over time.
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Authors and Affiliations

Dan Wu
1
Yao Wang
2
Yuezan Tao
3
Xian Li
3
ORCID: ORCID
Honglei Ren
3
Qiang Yang
4

  1. School of Urban Construction and Transportation, Hefei University, Hefei, 230601 China
  2. School of Environment and Energy Engineering, Anhui Jianzhu University, Hefei 230601, China
  3. School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei, 230009 China
  4. Northwest Engineering Corporation Limited, Xi’an 710065, China
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Abstract

The aim of this study is to analyse the presence and activity of users in individual households by means of quantitative and qualitative research – questionnaires and interviews. The users’ behaviour has a significant impact on the thermal-flow processes taking place in the building, so their verification, ultimately, makes it possible to reduce the difference between the calculated and actual energy consumption of the building. The literature review revealed a lack of updated building occupancy schedules, which changed significantly after the COVID-19 pandemic. Based on the data collected, 6 household occupancy profiles were proposed, which, when combined, form a model describing behaviours (occupancy profile, profile of electrical appliances, lighting, natural ventilation, heating installations and supporting appliances). The model took into account the effect of internal heat gains on the energy balance of the building, including the working system – home office mode. The collected data was fed into a reference building model and an hourly dynamic simulation was carried out using commercial DesignBuilder software. Using outdoor climate parameters for selected cities, the reference building's annual heat demand was demonstrated and an assessment of the building’s indoor microclimate was provided. The multi-criteria empirical approach resulting in a set of revised data can be generalised and adapted to a larger group of actors, a selected area and a building.
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Authors and Affiliations

Alicja Wiącek
1
Sebastian Werle
2
Mariusz Ruszel
3
ORCID: ORCID

  1. Ignacy Łukasiewicz Doctoral School of Rzeszów University of Technology, Powstańców Warszawy 12, Rzeszów, 35-959, Poland
  2. Silesian University of Technology, Akademicka 2A, Gliwice, 44-100, Poland
  3. Rzeszow University of Technology, Powstańców Warszawy 12, Rzeszów, 35-959, Poland
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Abstract

Monitoring power plants necessitates sophisticated methods and reliable dynamic models, especially with the increasing flexibility demand. The primary challenge of this work is to develop a modelling strategy for heat recovery steam genera-tors (HRSG) that enables simple yet accurate simulation of their dynamic behaviour, accounting for the delayed response of their heat exchangers to load variations caused by high thermal inertia. The proposed modelling methodology aims to build models suitable for monitoring power plants based on a set of sensor measurements, which can realistically be found in a power plant. This approach eliminates the need for extensive system design information, which may not always be accessible to the modeller. First, fully detailed, pseudo three dimensional Modelica model of the monophasic heat exchang-ers is developed. The model is then simplified progressively while the impact on accuracy is assessed. A more simplified model is later developed by assuming a lumped global heat transfer coefficient and a mass. The simplified model provides promising results, demonstrating a good compromise between simple calibration process and accuracy. A model of the evaporator is also presented and validated based on literature. Finally, a qualitative analysis of the full HRSG model is conducted. The dynamic behaviour as well as the time constants of the heat exchangers are analysed. The results demon-strate a good agreement with the expected physical behaviour.
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Authors and Affiliations

Nabil Youssef
1 2
Assaad Zoughaib
1
Valentin Drouet
2

  1. Mines Paris − PSL, 60 Boulevard Saint Michel, 75006 Paris, France
  2. Metroscope, 63 Boulevard Haussmann, 75008 Pairs, France
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Abstract

This research investigates the mixed convection of an incompressible, non-Newtonian radiating Casson fluid in a Darcy-Forchheimer porous medium over a slippery, permeable, stretching surface. The study further examines the influences of thermal buoyancy and viscous dissipation. Through appropriate similarity transformations, the governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved using MATLAB with the fourth-order Runge-Kutta method combined with the shooting technique. This work aims to assess the influence of Casson parameter, porosity parameter, radiation parameter, suction parameter, Eckert number, mixed convection parameter, local inertia coefficient, Prandtl number and slip parameter on the velocity and temperature. The findings show that increasing Casson parameter results in decreased velocity and temperature, while an increase in the radiation parameter leads to a rise in temperature. Velocity decreases with an increase in slip parameter for velocity, but as the similarity variable exceeds 2.4, it experiences a slight increase due to the stretching effect of the sheet. Conversely, temperature is directly proportional to slip parameter for velocity.
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Authors and Affiliations

Shish Ram Dhwal
1
Rajendra Singh Yadav
1
Oluwole Daniel Makinde
2

  1. Department of Mathematics, University of Rajasthan, Rajasthan, Jaipur 302004, India
  2. Faculty of Military Science Stellenbosch University, Stellenbosch, Western Cape, South Africa
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Abstract

Entropic analysis makes it possible to determine the equilibrium of a system with its environment, but heat exchange at boundaries is a difficulty in this exercise. In this article, we establish the energy balance of a water liquid and air mixture: the Gibbs-Duhem equation is used to describe the balance. Diffusion terms are expressed while accounting for volume changes and their entropic contributions, leading to an expression for fugacity. After mixing, the mixture spontaneously evolves combining mechanical, chemical and thermal changes towards equilibrium. This latest is solved assuming either an isenthalpic or isentropic transformation in the balance, to highlight the energy exchange between the system and its environment. Some irreversibilities are included in transformations and primarily affect the chemical path. The comparison reveals heat transfer terms corresponding to uncompensated heat. This analysis illustrates the concept of uncompensated heat and introduces its complement, the apparent heat, which corresponds to enthalpy. The models explain the limiting phenomena involved in spray cooling, whose efficiency varies depending on whether the process follows an adiabatic or an isenthalpic path. The isenthalpic model was applied to literature data to estimate experimental cooling efficiencies over a wide range of operating conditions. However, further modelling work is needed to express the scaling factor for fugacity as a function of the droplet size distribution. The mechanical pathway also requires more attention and dedicated measure-ments are needed to include pressure drops in the analysis.
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Authors and Affiliations

Stephanie Lacour
1
Michel Feidt
2

  1. Université Paris-Saclay, INRAE - Unite de recherche FRISE, Pierre-Gilles de Gennes 1, CS 10030, Antony 92761, Cedex, France
  2. University of Lorraine, Laboratory LEMTA, 2 Av. de la Forêt de Haye, 54500 Vandoeuvre-lès-Nancy, France

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3. More important symbols used in the paper should be listed in Nomenclature, placed below Abstract and arranged in a column, e.g.:
u – velocity, m/s
v – specific volume, m/kg etc.

The list should begin with Latin symbols in alphabetical order followed by Greek symbols also in alphabetical order and with a separate heading. Subscripts and superscripts should follow Greek symbols and should be identified with separate headings. Physical quantities should be expressed in SI units ( Système International d’Unités). In the template a dedicated area is created to put the nomenclature.

4. All abbreviations should be spelled out first time they are introduced in the text. Abbreviations should also be listed in the Nomenclature.

5. The equations should be each in a separate line. Standard mathematical notation should be used. All symbols used in equations must be clearly defined. The numbers of equations should run consecutively, irrespective of the division of the paper into sections. The numbers should be given in round brackets on the righthand side of the column.

6. Particular attention should be paid to the differentiation between capital and small letters. If there is a risk of confusion, the symbols should be explained (for example small c) in the margins. Indices of more than one level (such as Bfa) should be avoided wherever possible.

7. Computer-generated figures should be produced using bold lines and characters. No remarks should be written directly on the figures, except numerals or letter symbols only. Figures should be as small as possible while displaying clearly all the information requires, and with all lettering readable. The relevant explanations can be given in the caption.

8. The figures, including photographs, diagrams, etc., should be numbered with Arabic numerals in the same order in which they appear in the text. Each figure should have its own caption explaining the content without reference to the text.

9. The figures should also be submitted as separate graphic files in either vector formats (PostScript (PS), Encapsulated PostScript (EPS), preferable, CorelDraw (CDR), etc.) or bitmap formats (Tagged Image File Format (TIFF), Joint Photographic Experts Group (JPEG), etc.), with the resolution not lower than 300 dpi, preferably 600 dpi. These resolutions refer to images sized at dimensions comparable to those of figures in the print journal. Therefore, electronic figures should be sized to fit on single printed page and can have maximum 120 mm x 170 mm.

10. The references for the paper should be numbered in the order in which they are called in the text. Calling the references is by giving the appropriate numbers in square brackets. The references should be listed with the following information provided: the author’s surname and the initials of his/her names, the complete title of the work (in English translation) and, in addition:

The references should be placed after the acknowledgment section. The references citation in the manuscript body should be numbered: [1], [2], etc. Please use the following style of references in bibliography APA – 7th ed:

Journal citation (APA – 7th ed):
[1] Król, J., & Ocłoń, P. (2019). Sensitivity analysis of hybrid combined heat and power plant on fuel and CO2 emission allowances price change. Energy Conversion and Management, 196, 127–148.
doi.org/10.1016/j.enconman.2019.05.090

[2] Zhou, Y., Bi, H., & Wang, H. (2023). Influence of the primary components of the high-speed train on fire heat release rate. Archives of Thermodynamics, 44(1), 37–61.
doi.org/10.24425/ather.2023.145876

When citing scientific papers, it is needed to provide a DOI identifier if available.
Example of citation:
• Król and Ocłoń [1] studied a hybrid CHP sensitivity on fuel and CO2 emission allowances price change.
• Zhou et al. [2] studied the influence of the primary components of the high speed train on fire heat release rate.

Book citation (APA – 7th ed):
[3] Ocłoń, P. (2021). Renewable energy utilization using underground energy systems (1st ed.). Springer Nature.
Example of citation:
• Ocłoń et al. [3] presented renewable energy systems for heating cooling and electrical energy production in buildings.

Book chapter citation (APA – 7th ed):
[4] Ciałkowski, M., & Frąckowiak, A. (2014). Boundary element method in inverse heat conduction problem. In Encyclopedia of Thermal Stresses (pp. 424–433). Springer Netherlands.
Example of citation:
• Ciałkowski and Frąckowiak [4] presented a Boundary element method application for solving inverse heat conduction problems.

Conference proceedings (APA – 7th ed):
[5] Pourghasemi, B., & Fathi, N. (2023). Validation and verification analyses of turbulent forced convection of Na and NaK in miniature heat sinks. ASME 2023 Verification, Validation, and Uncertainty Quantification Symposium, 17-19 May, Baltimore, USA.
Example of citation:
• Pourghasemi and Fathi [5] validated and verified turbulent forced convection of Na and NaK in miniature heat sinks.
For works originally published in a language other than English, the language should be indicated in parentheses at the end of the reference. Authors are responsible for ensuring that the information in each reference is complete and accurate, including the DOI number.

11. As the papers are published in English, the authors who are not native speakers of English are obliged to have the paper thoroughly reviewed language-wise before submitting for publication. When the Editors or Reviewers assess that the writing English of the manuscript is poor, the authors are obliged to correct it, and provide a Certificate of English Editing as attachment in Editorial System.

Further information

All manuscripts will undergo some editorial modification. The paper proofs (as PDF file) will be sent by e-mail to the corresponding author for acceptance, and should be returned within two weeks of receipt. Within the proofs corrections of minor and typographical errors in: author names, affiliations, articles titles, abstracts and keywords, formulas, symbols, grammatical error, details in figures, etc., are only allowed, as well as necessary small additions. The changes within the text will be accepted in case of serious errors, for example with regard to scientific accuracy, or if authors reputation and that of the journal would be affected. Submitted material will not be returned to the author, unless specifically requested. A PDF file of published paper will be supplied free of charge to the Corresponding Author. Submission of the manuscript expresses at the same time the authors consent to its publishing in both printed and electronic versions.

Transfer of Copyright Agreement

All papers are published under lincense CC BY 4.0. Once a paper has been accepted for publication, as a condition of publication, the authors are asked to send a scanned copy of the signed original of the Transfer of Copyright Agreement, signed by the Corresponding Author on behalf of all authors.

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