Energy Balance Equation Research Articles

Active heating of greenhouse integrated semitransparent photovoltaic thermal system with series connected semitransparent photovoltaic thermal air collectors

In order to fulfill the demand of energy and food security, active heating of controlled environment greenhouse integrated semitransparent photovoltaic thermal (GiSPVT) system with N-semitransparent photovoltaic thermal (SPVT) air collector for cold climatic condition has been analyzed in this paper. The proposed SPVT air collectors are connected in series and integrated with GiSPVT. It is used to generate thermal as well electrical energy to meet daily requirement of users. Based on energy balance equation which is a function of design and climatic parameters, an analytical expression for various variable parameters namely plant, room air and solar cell temperatures have been derived. Numerical computation has been made in Matlab for computing thermal, electrical and overall exergy of the proposed system. Based on numerical computation, the following observations have been made: (i) From thermal point of view, the packing factor (0.5, 0.8) of semitransparent PV module plays an important role and it has to be optimized for maximum thermal heating. (ii) The selection of number of collector N is an important parameter to generate electrical energy as well as thermal heating of GiSPVT room air in an optimum way.

Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials

Abstract The calendering process is pivotal in enhancing various materials’ surface properties and characteristics, making them indispensable for achieving desired product quality and performance. Also, this process holds significant relevance in various industrial applications, such as polymer processing, food production, and the manufacturing of composite materials. So, the aim of this study is to theoretically examine the calendering process applied to third-grade materials. It specifically explores how temperature variations impact material behavior during passage through two counter-rotating heated rolls. Particular consideration is given to the influence of temperature-dependent viscosity via Reynold’s model. The complexities of mass, momentum, and energy balance equations are reduced through the application of the Lubrication approximation theory. Solutions to these equations for variables such as velocity, flow rate, and temperature fields are accomplished by combining perturbation and numerical techniques. In relation to the calendering process, the thickness of the exiting sheet is specifically explored. Furthermore, this study quantifies substantial engineering parameters such as roll-separating force, pressure distribution, and power transferal from the rolls to the fluid. The governing equations belong to three key dimensionless parameters, namely, the Brinkman number, which is a product of Eckert number and Prandtl number, the temperature-dependent consistency index μ \mu , and a parameter η \eta correlating to non-Newtonian behavior. The outcomes of this study are presented both graphically and in tabular form. It has been observed that a rise in the third-grade parameter decreases detachment point and sheet thickness due to increased material rigidity. Furthermore, established results in the literature regarding the calendering of Newtonian fluids are validated.

Integrated performance of a modular biomass boiler with a combined heat and power industrial Rankine cycle and supplementary sCO2 Brayton cycle

Abstract In this paper, the integrated performance of a modular biomass boiler with an existing industrial Rankine steam heat and power cycle and a supplementary supercritical-CO2 (sCO2) Brayton cycle is analyzed. The aim is to leverage the high efficiency supplementary sCO2 cycle to increase net generation and energy efficiency from the existing biomass boiler. Two sCO2 heater configurations situated within the flue gas flow path are investigated, namely a single convective-dominant heater, and a dual heater configuration with a radiative and a convective heater. A quasi-steady-state 1D model was developed to simulate the integrated cycle, including detailed component characteristics for the Rankine and Brayton cycles. The model solves the mass, energy, momentum, and species balance equations. The system is analyzed for three cases: (i) the existing Rankine cycle without the sCO2 integration, (ii) with the single convective-dominant sCO2 heater configuration, and (iii) the dual sCO2 heater configuration. The results show the required rate of overfiring for the sCO2 configurations, with a 15.3% increase in fuel flowrate resulting in an additional 21.2% in net power output. The model quantifies the impact of the sCO2 heaters, with reduced heat uptakes for downstream boiler heat exchangers. Furnace water wall heat uptake increased due to overfiring, offsetting the reduced heat uptakes at downstream evaporative heat exchangers. The dual configuration has more impact on Rankine cycle operation due to the radiative sCO2 heater placement in front of the second superheater, absorbing some of the direct radiation from the furnace.

Heat and Mass Transfer of Water During Activated Carbon Adsorption

AbstractIn order to investigate the dynamic process of the heat and mass transfer phenomenon of water vapor on activated carbon, a fixed‐column adsorption unit and two kinds of activated carbon were used as adsorbent for water vapor adsorption under the adsorption temperature 293.15 K, 303.15 K and 313.15 K, respectively. A coupled model was developed by mass and energy balance, mass transfer and simplified DO adsorption equilibrium equation. The effects of physical parameters on heat and mass transfer were theoretically investigated. Results show that the numerical model match well with the experimental data (R2>0.993). The axial diffusion coefficient (DL) increases from 1.226×10−6 m2 s−1 to 4.062×10−6 m2 s−1 for RAC and 1.425×10−6 m2 s−1 to 4.030×10−6 m2 s−1 for MAC, mass transfer coefficient (k) increases from 8.171 s−1 to 27.083 s−1 for RAC and 9.499 s−1 to 26.864 s−1 for MAC. Concurrently, the breakthrough time of adsorption water vapor gradually shorten from 1000 s to 780 s with temperature increasing from 293.15 K to 313.15 K. The effect of axial diffusion coefficient (DL) on mass transfer is not obvious. Furthermore, the influence of the mass transfer coefficient (k) on temperature variation rate surpasses that of the internal heat transfer coefficient (h).

Contact-angle hysteresis on rough surfaces: mechanical energy balance framework

Using as a starting point conservation of momentum, a multiphase mechanical energy balance equation is derived that accounts for multiple material phases and interfaces present within a moving control volume. This balance is applied to a control volume that is anchored to a three-phase contact line as it advances continuously over the surface of a rough and chemically homogeneous and inert solid. Using semi-quantitative models for the material behaviour occurring within the control volume, an order of magnitude analysis is performed to neglect insignificant terms, producing an equation for predicting contact-angle hysteresis from a knowledge of the interface dynamics occurring around the three-phase contact line. It is shown that the viscous energy dissipation that occurs during the ‘stick–slip’ motion of the three-phase contact line, being the cause of contact-angle hysteresis on rough surfaces, can be calculated from changes in intermediate equilibrium interface states. The balance is applied to the Wenzel, Cassie–Baxter and Fakir (super-hydrophobic) wetting states, showing for the Fakir case that significant dissipation occurs during both interface advance and recede, and relating these dissipations to interfacial area changes that occur around the ‘stick–slip’ events.

Prediction of thermal runaway for a lithium-ion battery through multiphysics-informed DeepONet with virtual data

A surrogate model that predicts thermal runaway (TR) of lithium-ion batteries (LIBs) fast and accurately is essential, yet complex phenomena of TR present significant challenges to achieving adequate performance in both aspects, particularly as traditional finite element models (FEMs) incur significant time and cost. This study proposes a multiphysics-informed deep operator network (MPI-DeepONet) with encoders to address these issues. This proposed neural network aims to predict TR under various thermal abuse conditions, offering a fast and accurate TR prediction surrogate model. In this study, MPI-DeepONet with encoders is trained with virtual data from a multiphysics FEM to overcome the scarcity of actual TR data. The architecture of DeepONet solves interpolation and extrapolation problems, allowing predictions across multiple thermal abuse conditions once trained. The neural network is further enhanced by the supervision of energy balance and chemical reaction equations, ensuring accurate and robust predictions despite limited data by effectively capturing the complex phenomena of TR. Quantitative analysis, compared against actual experiments and ablation studies, confirms the effectiveness of the proposed neural network. Notably, MPI-DeepONet achieves a mean RMSE of 13.2°C for temperature predictions in the test set, significantly outperforming the 25.4°C RMSE of purely data-driven DeepONet. This improvement highlights the importance of integrating multiphysics constraints into the neural network. The generality of the proposed neural network is further evidenced by accurate TR prediction in both LFP and NMC cells. The features deployed on the proposed neural network enable real-time quantification of internal temperature distribution and dimensionless concentration of the key components in LIBs, which are challenging to measure directly, achieving speeds at least 10,000 times faster than FEM. The proposed neural network provides comprehensive information for advanced battery management systems to ensure safety and reliability in LIBs, accelerating the digital twin of electric transportation systems through artificial intelligence transformation.

Development of characteristic equations of conical solar still by incorporating N identical concentrator collectors with/without photovoltaic panel: A comparative investigation

This paper focuses on the development of characteristic equations and performance analysis of a conical solar still (CSS) connected to N identical compound parabolic concentrator (CPC) collectors, with or without photovoltaic thermal (PVT) integration. The objective is to achieve sustainable solar distillation in line with the United Nations' sustainability goals. The thermal model is developed by formulating energy balance equations for each part followed by its experimental validation considering N=0and1. A fair agreement between analytical and experimental results is observed having correlation coefficients as 0.996, 0.993, 0.992, and 0.97, 0.98, 0.99 for water temperature, yield, and glass temperature for N = 0 and 1, respectively. The study considers three cases: CSS integrated with N identical partially covered PVTCPCs (case (i)), CSS integrated with N identical fully covered PVTCPCs (case (ii)), and CSS integrated with N identical CPCs (case (iii)). The performance of these cases is compared using climate conditions in New Delhi on a typical day in June. The findings indicate that the mean value of instantaneous efficiency for case (i) is higher by 67.75 % than case (ii), however lower by 22.22 % than case (iii). The study also investigates the influence of variations in mass-flow rate and N on the output of the active CSS.

Process intensification for production of dispersants via integration of reaction and separation in a horizontal thin film evaporator

Process intensification can be achieved in specialty chemicals manufacturing via transition from batch-to-continuous processing. However, the absence of headspace in a continuous tubular reactor limits the ability to remove volatile byproducts from the reacting liquid flow. Previous studies showed that the production of succinimide dispersants follows a two-step amidation-dehydration pathway in which water is formed as a by-product. The inability to remove this water imposed a thermodynamic equilibrium limitation on the dehydration step, and hence necessitated a downstream drying step to obtain a dehydrated dispersant product within commercial specifications. In the present study, the use of an agitated, horizontal thin film evaporator (TFE) was investigated as a continuously operated reactive separator which combines reaction and dehydration into a single operating unit, reducing the overall cost and physical footprint of the process. The continuous TFE unit was first experimentally investigated as a stand-alone, integrated reactor-separator. Using this configuration, the obtained imide yield consistently exceeded the maximum thermodynamic yield at each operating temperature, confirming the efficiency of the integrated reaction and separation steps in the TFE. Next, the unit was modeled by integrating reaction kinetics with mass and energy balance equations, using appropriate correlations for heat and mass transfer from the literature which were verified for the experimental set-up. This model provided insights into the system behavior across different operating conditions, including the role of forward and reverse reactions along the TFE unit length. The model was then used to confirm the feasibility of replacing the two-step tubular reactor-evaporator process with a single TFE unit as an intensified reactive separator, further reducing the physical footprint of the process by enabling compact modular process designs.

The magnetic field does not perform work—or does it?

We investigate the question discussed in the literature as to whether the magnetic field can perform work using two models that describe interacting magnetic dipoles. In the first model, the dipoles are realized by rigidly rotating charge clouds, whereas in the second model, one of the two dipoles is described by a real macroscopic spin density. The theoretical foundations of the second model are formulated in a recently published paper. We derive equations of motion and detailed energy balance for both models when the initial magnetic moments are parallel to the connecting line of the initial dipole positions. In this scenario the ‘large’ dipole remains stationary and generates an external magnetic field in which the ‘small’ dipole is accelerated. The answer to the title question depends on the choice of criteria for ‘work of the magnetic field’.

Integration of Energy Conservation Principles Across Mechanical Engineering Curriculum: A Work-in-Progress Project

The conservation of energy, mass, and momentum stands as fundamental laws in physics, resonating deeply within engineering education. This ongoing project, now in its third year of implementation, aims to seamlessly integrate energy conservation principles across the mechanical engineering undergraduate curriculum. Across various courses, including dynamics, fluid dynamics, and thermodynamics, students delve into the diverse forms of mechanical energy. From kinetic and potential energy in dynamics to fluid flow energies and thermodynamic principles in fluid dynamics and thermodynamics courses respectively, the overarching principle remains: energy is neither created nor destroyed but instead transfers between different forms, maintaining a constant total within a fixed domain. The project emphasizes the energy balance equation introduced in the first Thermodynamics course, laying the groundwork for subsequent exploration. Students are guided through the transition from the first law of thermodynamics to Bernoulli's equation in Fluid Mechanics, bridging theoretical concepts with practical applications. This integration continues into Heat Transfer and elective courses such as Industrial Hydraulics and Aerodynamics. To assess student comprehension, direct and indirect assessments are conducted, measuring understanding through principle and practical examples. Feedback and questionnaire responses indicate enhanced understanding of energy conservation principles through the synchronization of energy balance concepts across multiple courses. This presentation showcases the evolution of our work-in-progress project, initially presented at the 2022 and 2023 WVAS meetings. By fostering a holistic understanding of energy conservation principles, our aim is to empower students with a comprehensive foundation to tackle real-world engineering challenges.

Model-based prediction of frost formation inside frozen food packages under temperature fluctuations

Abstract Frozen storage of food products is widely accepted not only in the industry but also by households. Frost formation during long-term storage is recognized as a phenomenon that causes changes in product characteristics and quality losses. However, quantitative prediction and control of frost formation remains a challenge. In this study, a mathematical model was developed to predict frost formation inside frozen food products (i.e., frozen minced meat packed in a polyvinylidene chloride (PVDC) film) under fluctuating temperature conditions in a domestic refrigerator. The proposed model is based on heat transfer and energy balance equations, and the amount of frost formation is estimated from the heat generated by condensation. The heat transfer coefficients were experimentally obtained and applied to the developed model. The interactions between the amplitude and frequency of temperature fluctuations and the corresponding amount of frost formation were visualized using contour plots. Both the amplitude and frequency were found to increase frost formation. For the range of fluctuations tested (temperature amplitudes of 0.5–2.5 K and cooling rates of 0.0125–0.2 K/min when connected to the compressor), the simulation predicted that the amount of frost in the packages varied up to approximately 4.5 times (0.48–2.18 g/month for packages containing 300 g of minced meat) depending on the different temperature fluctuation settings.

Experimental and economic evaluation on the performance improvement of a solar photovoltaic thermal system with skeleton-shaped fins

At elevated ambient temperatures, the production and efficiency of solar panels are degraded due to the overheating of the cells. Cooling photovoltaic cells at elevated ambient temperatures can prevent overheating, extend their life, and enhance overall efficiency, particularly in areas exposed to strong sunlight and elevated temperatures. In this study, an attempt was made experimentally to increase the performance of solar photovoltaic thermal systems with a novel cooling technique. The proposed system has an absorber plate coupled with novel skeleton-shaped fins used to create double-pass ambient air channels below the solar module for natural heat dissipation. Performance of the proposed photovoltaic thermal system with skeleton-shaped fins was designed, evaluated, and evaluated, under different climatic conditions of the southern Algeria city of Ghardaïa from 8:00 am to 6:00 pm. Theoretical analysis was also developed relying on the energy and exergy balance equations for the system components. An economic analysis is also performed by the life cycle cost analysis to evaluate the feasibility, annual performance, and payback period of the proposed solar system compared with that of the conventional system. Results showed that the proposed photovoltaic thermal generates an average daily production of 2.02 kWh, which is 55.1 % more than the conventional system. The energy and exergy efficiency of the proposed system are higher than the conventional system by 8.61 and 8.98 %, respectively. The levelized costs of energy associated with the proposed system (0.17 $/kWh) is lower than that of the conventional system by 11.76 %. The payback period of the proposed system (6.21 years) is lower than that of the conventional solar systems by 34.7 %. This means that the additional power generation obtained by the proposed system with skeleton-shaped fins was sufficient to offset the total life cycle costs.

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective grey low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. The ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

Assessment of the energy production of a hybrid PV/T collector based on different fluids for Agadir climate

The aim of this paper is to evaluate the electrical and thermal energies produced by a hybrid PV/T collector for Agadir city climatic conditions. To achieve the goal a theoretical model based on energy balance equations applied on each collector component is developed. The discretization of the equations is done using the finite difference method and solved numerically by TDMA matrix algorithm. The validity of the model is examined by the comparison of the our simulation findings with the available literature results. The thermal and electrical powers outputted by the glazed and unglazed hybrid collector are evaluated over the course of a typical day for Agadir region climate (Morocco), using various heat transfer fluids (water, water-EG mixture and Cu−water nanofluid). It is abtained that the employ of the nanofluid Cu−water improves the energy production of the hybrid collector in comparaison to other working fluids. In fact, the high daily thermal and electrical energies are obtained using the nanofluid by approximately 5.548 kWh and 1.273 kWh respectively. The results showed that the produced thermal energy of the solar collector with glass is 37.4% higher than unglazed one. However, the supplied electrical energy by the glazing collector is lower than the unglazed system by almost 11.5%. In Agadir region, we recommend choosing the unglazed PV/T to benefit from the weather conditions and the solar potential of this region.

ASSESSMENT OF HEAT BALANCE IN THE FSRU REGASIFICATION CYCLE ALIGNS WITH IMO’S DECARBONISATION STRATEGY

In 2023, the International Maritime Organization revised its greenhouse gas strategy, striving to reduce annual emissions from international shipping by at least 70% by 2040. The Mediterranean Sea will become an emission control area for sulphur oxides and particulate matter from May 2025, and the EU will include shipping in its Emission Trading System from 2024. Liquid natural gas is expected to become a cleaner marine fuel, but it alone cannot meet emission reduction goals. The cryogenic carbon capture process can separate CO2 from exhaust gases, compress it, and store it in a liquid state with high density. This study aims to integrate an energy balance equation model to analyse the energy exchange in the regasification process and identify potential areas for improvement and targeted solutions to enhance performance and comply with IMO emission regulations. Based on a mathematical model, the energy balances are calculated and yield the following results: steam heater (26,999 kW), R-290 preheater (5,837 kW), trim heater (3,290 kW), R-290 evaporator (13,322 kW), and LNG vaporiser (23,118 kW). A report also determined that within a temperature range between -56.6℃ and 31℃ and a pressure range of greater than 5.2 bar (absolute) and less than 74 bar (absolute), the CO2 is in a liquid phase. Due to CO2 density which fluctuates in liquid at 1032 kg/m3 and in solid phase at 1562 kg/m3 the physical condition is compatible with the storage stage of capture emission.

Pressure-Driven Switching of Photoelectron Impact Ionization-Chemical Ionization/Penning Ionization in Vacuum Ultraviolet Photoionization Mass Spectrometry.

Vacuum ultraviolet photoionization (VUV-PI) is a soft ionization technique that operates under pressures ranging from vacuum to ambient pressure. VUV-PI has played an essential role in direct sampling mass spectrometry. In this study, new ionization processes initiated by photoelectrons have been studied through the inclusion of a radio frequency (RF) electric field at different pressures. After deducting the contribution of single photoionization (SPI), the signal intensity of 1 ppmv toluene (C7H8+) in Ar was approximately 5-fold higher than that in N2. Mixed gases with different ionization energies (IEs) and excitation energies (EEs) were further investigated to reveal that metastable species were involved in the enhancement process. Reactant ions were produced by photoelectron impact ionization (PEI), which further triggered ion-molecule reactions, i.e., chemical ionization (CI). Metastable species were produced by photoelectron impact excitation (PEE), which further triggered Penning ionization (PenI). Analytes with IEs above 10.6 eV, such as CO2 (IE = 13.78 eV) and CHCl3 (IE = 11.37 eV), could be sensitively ionized by PenI with a sensitivity comparable to SPI. Except for the contribution of SPI, the dominant ionization process was switched from PEI-CI to PenI when the pressure was elevated from 50 to 500 Pa, as the electron energy gradually decreased and was only able to produce metastable states based on the kinetic energy balance equation of electrons. The conversion processes and conditions from PEI-CI to PenI will provide novel insights to develop new selective and sensitive VUV-PI sources and understand the ionization mechanism in other discharge ionization sources.

A study on integrated HTR-PM driven hydrogen production using thermochemical cycles

This present study aims to design a nuclear-based hydrogen production system by using the three- and four-step magnesium-chloride cycles, and compares the three-step magnesium-chloride cycle integrated nuclear-based system and the four-step magnesium-chloride cycle integrated nuclear-based system. Within the scope of this study, four units of high-temperature gas-cooled-pebble bed modular nuclear reactor are employed, where a total of 1 GW thermal energy (heat) is secured from these four reactors. All of the heat generated by the reactors is used to drive the power generation and hydrogen production cycles. The proposed system, along with its cycles and processes, are examined by using mass, energy, entropy, and exergy balance equations. The modeling and simulations for the three- and four-step magnesium-chloride cycles are carried out via the Aspen Plus software package. The results are compared for two hydrogen production methods, and sensitivity analysis is assessed for various steam/MgCl2 ratios, as well as different reactor temperatures and pressures for each reaction in the cycles. While the three-step magnesium-chloride cycle integrated nuclear-based system produces 2.43 kg/s hydrogen, 2.13 kg/s hydrogen is produced by the four-step magnesium-chloride cycle integrated nuclear-based system. As a consequence of this present study, energy and exergy efficiencies are calculated as 54.2% and 60.9% for the three-step magnesium-chloride cycle, while these values are 48.0% and 54.0% for the four-step magnesium-chloride cycle. Additionally, while the energy and exergy efficiencies of the three-step magnesium-chloride cycle integrated overall system are 29.2% and 40.3%, these values are 25.6% and 35.2% for the four-step magnesium-chloride cycle integrated system, respectively.

Analysis of the exergy performances of a glazed and unglazed PV/T collector under different conditions

The exergy performances of the hybrid PV/T solar collector using different heat transfer fluids was numerically investigated. The mathematical model is based on the energy balance equations applied to each collector element as well as exergy balance founded on the second law of thermodynamics. The governing equations are discretized and solved using Finite difference method based on alternating directions implicit scheme. A comparative study of the exergy performances of the hybrid collector with and without glass cover using nanofluid Cu−water, distilled water and water-EG mixture as transfer fluids is conducted. The results showed that Cu−water nanofluid enhances the total exergy of the collector by 1.6% and 2.7% highest than water and water-EG respectively. However, regarding the thermal exergy, water-EG mixture is the best fluid which allows to improve the collector production by 17% and 28.5% than water and Cu−water respectively. The maximum energy and exergy efficiencies reached over the day are around 70% and 15% respectively. In addition, it is found that the overall exergy produced by the unglazed system is 6.45% higher than the collector with glass cover. While, the total energy yield of this latter is 26% higher than the system without cover. The effect of operating parameters on the collector exergy effectiveness is analyzed and discussed in this work.

Pulsating non-Newtonian heat and fluid flow in a concentric annular duct: An analysis using perturbation series method

In the current study, an analytical analysis is conducted to examine laminar pulsating flow and heat transfer of power-law fluid in a concentric annular channel that is uniformly heated. The momentum and energy balance equations are solved analytically using the perturbation series method under the assumption that fully developed hydrodynamic and thermal conditions exist. Nondimensional frequency and amplitude effects on periodic and period-averaged friction factor and Nusselt number are obtained for various power-law index values, representing pseudoplastic, Newtonian, and dilatant fluids. The results from the present study are compared to those from the literature for some specific cases, and an excellent agreement is observed.

Dynamic performance analysis of a photovoltaic thermal (PVT) collector with an extruded absorber using python optimization modeling object (Pyomo)

Solar photovoltaic thermal (PVT) integrates photovoltaic panels and solar thermal collectors in one system for simultaneous electricity and heat production in a reduced area. The absorber type used for heat extraction significantly affects PVT performance. This work examines the performance of an extruded absorber PVT under varying solar irradiance, ambient temperature, and wind speed. A detailed dynamic mathematical model is developed from energy balance equations and heat transfer correlations for each layer of the PVT collector. Using orthogonal collocation on the finite difference method, the system of differential equations is discretized and solved numerically with Pyomo, a Python optimization modeling tool. Following validation against literature data, the model is used to predict the temperature of each layer and the thermal and electrical output of the PVT collector. The effect of cooling fluid mass flow rate, solar irradiance intensity, ambient temperature, and wind speed on PVT performance is analyzed. This design provides a maximum electrical efficiency of 15.47 % at a wind velocity of 3 m/s, regardless of the cooling fluid flow rate. Peak electrical power of 212.26 W is achieved at the highest flow rate (14.14 kg/hr) and with the highest wind velocity (3 m/s), while the peak thermal power of 348.03 W occurs at a wind velocity of 1 m/s and a flow rate of 11.31 kg/hr. Compared to the conventional sheet-and-tube design at 1 m/s wind speed and 5.65 kg/hr cooling fluid flow rate, the extruded absorber PVT delivers 203.18 W electrical and 189.27 W thermal power, outperforming the 207.46 W electrical and 128.9 W thermal power of the conventional design, demonstrating the potential of the extruded absorber design for enhancing heat generation.