Heat Model Research Articles

Mating-Based Manta Ray Foraging Optimization for Fuzzy-Hammerstein Model of an Electric Water Heater

This paper presents an improved variant of the Manta Ray Foraging Optimization (MRFO) algorithm. The optimization method of the original MRFO is a combination of random and spiral strategies. Like other optimization algorithms, MRFO still has a limitation when applied to a complex real-world problem. In this work, mating strategy of a barnacle species is incorporated into the MRFO algorithm. It allows good features of the parent manta ray to be inherited by its offspring thus creating a high-quality population. The proposed algorithm is applied to acquire a dynamic model of an electric water heater. A fuzzy-Hammerstein model is chosen as the candidate model for the water heater considering electrical voltage and water temperature as the input and output responses respectively. The result of the modelling has shown MRFO and the proposed MRFO variant have satisfactorily acquired the dynamic model of the water heater. The improved MRFO variant has tracked the output temperature response more accurately than the original MRFO at costs 425 and 508 respectively.

Model Validation and Real-Time Process Control of a Continuous Flow Ohmic Heater

Ohmic heating is a highly efficient method for rapid fluid heating, with applications in fields such as food processing, pharmaceuticals, and chemical engineering. Prior to its industrial application, thorough analysis and modeling are crucial to ensure safe and efficient operations. Therefore, this research focuses on the development and validation of a transfer function-based model for a continuous flow ohmic heater (CFOH). Validation metrics include root mean square error (RMSE) and mean absolute percentage error (MAPE). The developed model achieves an RMSE of ±1.48 and a MAPE of ±2.58% compared to experimental results, demonstrating its accuracy. Furthermore, the research presents the implementation of robust real-time applications of advanced process controllers, including PID, MPC, and AMPC. These controllers were first simulated using the developed model and subsequently deployed in the pilot plant ohmic heater system to achieve precise temperature control and optimised input voltage. The reliability of this procedure was affirmed through a comparison between simulated results and empirical data obtained from the CFOH pilot plant. The study concludes by suggesting potential applications in fault diagnosis, educational training, system identification, and controller design.

A Blowdown Critical Heat Flux Experimental Vehicle

In the most challenging nuclear power plant accidents, transient critical heat flux (CHF) is a primary phenomenon that drives peak cladding temperature, and ultimately, fuel failure. It has not yet been determined whether the use of steady-state CHF methods can accurately predict transient CHF under the conditions of a blowdown due to a loss-of-coolant accident. There are limited comprehensive experiments at prototypic conditions. To address this deficiency, a quality separate-effects test facility was built to simulate an electrically heated rod under blowdown conditions. Testing reached full pressurized water reactor thermal-hydraulic conditions. With scaled break sizes as large as a double-end cold leg break, CHF was repeatedly measured with depressurization rates ranging from 7 to 17 MPa s−1. These measurements at prototypic conditions acquired in a controlled methodology are novel to the body of knowledge. Several steady-state CHF methods and heater models were evaluated using RELAP5-3D simulations and the Dakota framework. The results showed that many steady-state CHF methods performed inadequately, but that recently developed wide-ranged, look-up table methods had the most acceptable results. Additionally, the results showed no significant correlation between prediction accuracy and the depressurization rates tested.

Data-driven optimal placement of minichannel-based solar water heater using satellite-derived and ground-telemetry weather information

The aluminum minichannel solar collector is a novel technology for solar water heating. Minichannel-based solar collectors have higher thermal efficiency than conventional flat plate collectors and do not suffer from potential loss of vacuum as evacuated-tube collectors. This technology can play a significant role in reducing natural gas consumption that translates into lower greenhouse gas emissions to the atmosphere. However, the performance of solar collectors depends on the geographical location of the installation due to solar resource availability and weather pattern. The potential reduction in natural gas consumption using aluminum minichannel solar collectors is assessed using solar irradiance, ambient temperature, and wind data obtained from ground weather station and satellite-derived data. A data-driven numerical analysis is performed using a validated solar water heater (SWH) model, population, and natural gas consumption data for the entire state of California to assess the best locations to install these systems. The SWH model is validated based on data collected from an actual SWH system installed at a single-family house in Northridge, California. A K-means clustering method is then applied to select the best regions for installation of this technology. Based on performance, population density, and natural gas consumption, the regions of Southern California and the Central Valley are chosen as having the highest potential for reduction of natural gas consumption. The analysis was performed from weather data obtained based on two full years (2020 and 2022), where the effect of COVID-19 (year 2020) is observed as having higher water tank temperatures and higher solar fractions, which could be associated with lower hot water consumption.

Optimization of single and double pass solar air heater-phase change material (SAH-PCM) system based on thickness to length ratio

This paper presents a two-dimensional transient model for a solar air heater with phase change material (SAH-PCM), focusing on the thickness-to-length ratio (t/L) of the PCM container. Verified through experiments, the model considers single (SP) and double pass (DP) flow configurations, assessing liquid fraction, dead length, outlet temperature, energy, exergy, and system efficiency during PCM charging and discharging. Increasing the t/L ratio improves peak liquid fraction, reduces dead length, and delays PCM discharge in both configurations, enhancing system energy and exergy efficiencies. In a SP flow system, optimizing t/L at 0.042 yields a peak liquid fraction of 0.928, a 92.28% dead length reduction, and a 2 h and 22 min delay for PCM discharge (base-case t/L ratio: 0.0182), achieving a highest discharging efficiency of 39.1%. For a DP flow system, the optimized t/L ratio of 0.058 results in a peak liquid fraction of 0.976 and a 1 hour and 34 min delay for PCM discharge, attaining the highest discharging efficiency of 63.34%. Moreover, an improvement in the energy payback time (EPBT) is observed for both SP and DP flow as the t/L is increased. For the DP flow, a minimum EPBT of 0.68 years (energy basis) and 6.55 years (exergy basis) is observed at a t/L ratio of 0.058. In terms of energy cost, SP flow reaches a minimum of Rs. 20.824 Rs/kWh at a t/L ratio of 0.042. For DP flow, the minimum energy cost is 13.033 Rs/kWh at a t/L ratio of 0.058, representing a noTable 37.42% improvement compared to SP flow. These findings underscore the critical role of optimizing system parameters, specifically the t/L ratio, for enhanced energy and exergy performance, and economic viability of SAH-PCM.

Thermal Rectification across an Asymmetric Layer Carbon Nanotube van der Waals Heterostructure.

The exceptional thermal conductivity and strength of carbon nanotubes (CNTs) position them as outstanding materials for thermal conduction. The intriguing properties introduced by van der Waals (vdW) heterojunctions have also captured the interest of researchers. However, further refinement of the research concerning the integration of these two elements is required. In our study, a vdW heterostructure with asymmetric layer nesting of multiwalled CNTs (ALCNTs) is devised, with a specific focus on the model's heat flux and thermal rectification (TR) properties, which are analyzed using nonequilibrium molecular dynamics (NEMD). Notably, the greatest TR ratio is observed in the connection of three-layer and single-layer ALCNTs. Moreover, multilayer variable-length nested models exhibit a sluggish TR ratio. An examination of the interface thermal resistance (ITR) reveals that the maximum ITR in the multilayer nested model resides at the rightmost interface. However, it is essential to highlight that the determinant of the TR ratio and heat flux in the multilayer nested model is not the maximum ITR of the rightmost interface but rather the ITR of the outermost layer on the left. Additionally, the impacts of the defect density, length, temperature difference, and hydrogenation on the model's heat flux and TR are explored, yielding noteworthy conclusions. For instance, defects in the outer CNT have a minimal influence on the heat flux and TR compared with those in the inner CNT. As the length increases, the heat flux initially decreases and then increases. Hydrogenation significantly enhances the model's heat flux but does not favor the TR. Our study contributes to advancing the understanding of CNT vdW heterojunctions and offers valuable insights for their practical applications.

Development of Digital Twins to Support the Functioning of Cyber-physical Systems

The peculiarities of developing a digital twin for cyberphysical systems using an analytical model of the investigated process are considered. The proposed approach takes into account the conceptual uncertainty of the analytical model parameters with the subsequent passive identification by adapting the analytical model to the dynamic characteristics of the real physical process. In the article, the digital twin development is carried out on the analytical model air heating process example with the help of an electric calorifier. The analytical model uncertain parameters of the electric heater are analyzed and an integral quality index is proposed to evaluate the dynamic model adequacy in the process of air heating. For electric heater model adaptation, the passive identification algorithm of uncertain parameters is developed, in which deviations of the mathematical model uncertain coefficients are minimized. A numerical study of the considered approach has been carried out. It is shown that uncertain parameters’ passive identification of the model belongs to the problem of single-extremal optimization. The considered modeling examples confirmed the effectiveness of the proposed approach to digital twins’ development for cyber-physical systems.

Optimizations of Double Titanium Nitride Thermo-Optic Phase-Shifter Heaters Using SOI Technology.

A commercial thermo-optic phase shifter (TOPS) is an efficient solution to the imbalance problem in the fabrication process of Mach-Zehnder modulator (MZM) arms. The TOPS consumes electrical power and transforms it into thermal energy, which changes the real part of the effective refractive index at the waveguide and adjusts the MZM transfer function to work in the linear region. The common model being used today is constructed with only one heater; however, this solution requires more electrical power, which can increase the transmitter system cost. To reduce the system energy cost, we propose a pioneering optimal double titanium nitride heater model under forward biasing at 1550 nm wavelength using the standard silicon-on-insulator technology. Numerical investigations were carried out on the key relative geometrical parameters, heat distribution at the silicon layer, thermal crosstalk, and laser wavelength drift. Results show that the optimal TOPS design can function with a low electrical power of 19.1 mW to achieve a π-phase shift, with a low thermal crosstalk of 0.404 and very low optical losses over 1 mm length. Thus, the proposed device can be used for improving the imbalance problem in MZMs with low electrical power consumption and low losses. This functionality can be utilized to obtain better performances in transmitter systems for data centers and long-range optical communication system applications.

Numerical Study on Enhanced Heat Transfer of Downhole Slotted-Type Heaters for In Situ Oil Shale Exploitation.

In order to improve the flow state of the heater shell side and enhance the performance evaluation of the heater, this paper proposes a perforated plate-type heater model. Based on Fluent, numerical studies are conducted on the heat transfer performance and shell-side fluid flow characteristics of a perforated plate-type heater. The variations of the heat transfer factor Nu, friction factor f, and evaluation parameter Nu/f1/3 are analyzed for different helix angles β and ratios of the long and short semiaxes of the circular holes on the heating plate under different Reynolds numbers Re. The results reveal that under the same shell-side Reynolds number Re, the heat transfer factor Nu shows an increasing trend with the increase in the proportion of the helix angle β. The heat transfer factor Nu for the heating plate with the hole shape ratio a/b = 1 does not exhibit significant improvement compared to hole shape ratios a/b = 0.8 and a/b = 0.6, but it increases by 4.87 to 7.07% compared to the hole shape ratio a/b = 0.4 in the perforated plate-type heater. On the other hand, the friction factor f decreases as the helix angle β and the ratio of hole shapes on the heating plate increase. The lowest friction factor f is observed for the helix angle β of 25° and the hole shape ratio a/b = 1 in the perforated plate-type heater. When the helix angle β is 25° and the hole shape ratio is a/b = 1, the evaluation parameter Nu/f1/3 reaches its highest value, indicating the optimal overall performance of the perforated plate-type heater.

Integration of a malt kilning model and a solar air heater model for its use as a viability estimation tool

The current work deals with a model of malt kilning, coupled to the design equation of a solar air heater, to use it as a tool for the estimation of the energy saved through its operation. The kilning model was previously validated by previous works, while the design equation for the solar air heater was obtained by a published characterization of a solar air collector manufactured in Mexico, to use it as a platform to evaluate its behavior in the solar conditions with a known equation. The kilning model was obtained previously by other works, where the malt was characterized, and its drying parameters were obtained, this model was modified to improve its convergence. This coupled model will be used to do experiments on the thermal behavior of the process, being able to predict the behavior of the process and being capable of modifying the heating schemes and reflux fractions, and verifying if the solar heating of the process is viable.

Adaptive observer design for uncertain hyperbolic PDEs coupled with uncertain LTV ODEs; Application to refrigeration systems

The problem of estimating the temperatures and the heat transfer coefficient of a concentric tube heat exchanger coupled with a heater is considered in this work. Measurements collected from the extremities of the exchanger tube are used to estimate the heat distribution over the length of the exchanger, which induces a boundary estimation problem. This system, which is part of any standard cooling plant, is particularly challenging due to the distributed nature of its variables. It is modeled by a system of (2 × 2) hyperbolic PDEs, coupled with an ODE at the boundary. To solve the estimation problem, we consider a general class of systems consisting of a (2 × 2) hyperbolic system coupled with a set of nX linear time-varying (LTV) ODEs at the boundary. Both the PDE and the ODEs have uncertain parameters to be estimated. The objective is to estimate the PDE states, the ODE states, and the parameters simultaneously with no assumption on the ODEs stability. We design a Luenberger state observer, and our method is mainly based on the decoupling of the PDE estimation error states from that of the ODEs via swapping design. We then derive the observer gains from the Lyapunov analysis of the decoupled system after proving the boundedness of the swapping filters. We give sufficient conditions of the exponential convergence of the adaptive observer through differential Lyapunov inequalities (DLIs). Finally, we apply the developed theory on the coupled heat exchanger–heater model to evaluate the performance of the observer in numerical simulations.

Electro-magnetic radiative flowing of Williamson-dusty nanofluid along elongating sheet: Nanotechnology application

The flowing of nanomolecules in Williamson nanoliquids via a stretched sheet has a significant influence, and its demand in the manufacturing, therapeutic disciplines, medication, and cooking supplies is enormous and frequently reported. However, 2-dimensional (2-D) combined convective flowing of Williamson-dusty nanofluid (WDNF) via a stretchable sheet in the presence of a magneto force and the porous medium remains unidentified. Hence, this report inspects the combined influence of Brownian and thermophoretic diffusion preserved in magneto WDNF modeling in the occurrence of radiative flowing. The Runge-Kutta Fehlberg approach (RKFA) is used to numerically study the problem of an ordinary differential system employing shooting techniques. The table also addresses the frictional force factor, heat, and mass transmission rate, as well as validates the current findings with earlier available results in the scheduled manner. The acquired outcomes demonstrate that a larger magnetic field decreases the rapidity and thickening of the impetus boundary layer of nanofluids. The momentum dust parameter and the fluid interaction parameter are shown to enhance the heat transmission rate. The rapidity and temperature fields of the liquid and dusty phases improved as the radiation parameter was raised on the contrary of magnetism force which causes dwindling in two phases. Consequently, the examined model's heat transference is reduced in the opposite direction of the Weissenberg number by the magnetic force. Additionally, it is found that higher thermophoresis parameters show an increasing trend in temperature for both phases.

An Installed Hybrid Direct Expansion Solar Assisted Heat Pump Water Heater to Monitor and Modeled the Energy Factor of a University Students’ Accommodation

This paper focused on the performance monitoring and modeling of a 6.0 kW, 2000 L hybrid direct expansion solar assisted heat pump (DX-SAHP) water heater used for the production of hot water in a university students’ accommodation with 123 females. The data of total electrical energy consumed, volume of hot water consumed, ambient temperature, relative humidity, and solar irradiance were obtained from the data acquisition systems and analyzed in conjunction with the energy factor (EF) of the system. A multiple linear regression model was developed to predict the EF. The EF of the hybrid DX-SAHP water heater was determined from the summation of the coefficient of performance (COP) of the heat pump unit and the solar fraction (SF) of the solar collectors. The operations of the hybrid energy system were analyzed based on three phases (first phase from 00:00–08:00, second phase from 08:30–18:30, and third phase from 19:00–23:30) over 24 h for the entire monitoring period. The average EF of the hybrid energy system per day during the second phase of operation was 4.38, while the SF and COP were 0.697 and 3.683, respectively. The developed multiple linear regression model for the hybrid DX-SAHP water heater accurately predicted the determined EF.

THREE TEMPERATURE MODEL FOR HEAT AND MASS TRANSFER IN NON-NEWTONIAN Cu-EG NANOFLUIDS EMBEDDED WITH PERMEABLE MEDIUM

In the current study, the impacts of local thermal non-equilibrium model and Cu-EG Oldroyd-B nanofluid layer on natural convective heat and mass transfer in a permeable medium are investigated. The transport equations are framed using modified Buongiorno two-phase Darcy model with different temperature profiles for fluid, particle, and porous-matrix phases. The thermophysical properties of the considered nanofluid are calculated using available experimental data. In the current situation, weak, non-linear analysis has been performed to find the Nusselt number and Sherwood number by solving finite amplitude equations using NDSolve in Mathematica 12.0. Influence of different parameters including viscoelastic parameters, LTNE parameters, thermal Rayleigh number, and nanoparticle volume fraction on heat and mass transfer mechanisms are explained graphically. An increase in the Nusselt number with the rising values of volume fraction of nanoparticles is registered and reach its maximum value at φ = 0.05 due to enhanced thermal conductivity. The significant findings for Oldroyd-B nanofluids are that the stress relaxation parameter declines heat transfer while strain retardation parameter promotes it. This study improves the theoretical understanding of heat transfer in porous media and facilitates the use of such theoretical models in practical applications.

Regularity for a non-local diffusion equation with Riemann-Liouville derivative

Our main goal in this paper is to investigate the regularity of the mild solution fractional diffusion equation which can be used in the modelling of heat transfer with memory effects. Under some various assumptions of the input data, we obtain two main results. We also provide the upper bound and lower bound of the source function. The main tool is to use complex evaluations involving the Wright function.

Utilizing ARMA Models for System Identification in Stirred Tank Heater: Different Approaches

Since system identification is a substantial part of many control algorithms, attaining a suitable model is necessary. In this paper, as a novelty, six standard identification methods are used so as to identify the linear ARMA forms of the proposed, widely used model of stirred tank heater. We have chosen these six methods because these methods fit to our desire for the parameter estimation of the ARMA model and they are new and applicable for modeling of all fields of engineering and systems. Beyond that, the mathematics of these methods are so easy to apply and they provide enough data for identifying a wide variation of systems. Furthermore, these algorithms are brought up in a simple and concise manner and easy to implement. In addition, the mathematical form of the suggested stirred tank heater is presented. Furthermore, identification methods are compared in terms of some measures, such as rate of convergence and produced error. Finally, the effectiveness of the six presented identification methods for estimating the stirred tank heater model is illustrated.

Recursive training based physics-inspired neural network for electric water heater modeling

Aggregating flexibility from residential electric water heaters (EWHs) is fast gaining commercial interest. Flexibility modeling of an EWH involves highly precise and quick simulation of EWH water temperature using the EWH thermal dynamics model for various flexibility control actions. Since EWH tank water temperature data is usually unavailable or costly to obtain, developing an accurate and computationally inexpensive EWH thermal dynamics model with limited sensor data is essential for devising advanced control strategies for EWH flexibility aggregation. In this paper, we present a novel recursive training-based unsupervised physics-informed neural network (PINN) model for predicting tank water temperature which requires only historical EWH power consumption data to train the model. PINN models enable the integration of domain knowledge from traditional physical processes and methods into neural network (NN) models. Single-zone thermal grey-box differential equation model (DEM) is used as the basis to develop and demonstrate proof-of-concept of the proposed approach. Physics from the single-zone model is encoded into the PINN loss function to incorporate domain knowledge and the PINN architecture is structured to mimic the single-zone DEM. The recursive training approach enables the use of previous-step water temperature as an input to the simulation model. Two separate models for EWH ON- and OFF-states are developed and trained with real-world EWH power consumption data. Water temperature prediction results indicate that the proposed approach has similar performance as the traditional single-zone DEM model, thereby demonstrating the ability of the proposed model to learn the underlying physics behind the single-zone model without water temperature data. The proposed model has high accuracy and performs well outside the control set point temperatures indicating its suitability for simulating load shifting and other DR events. Additionally, EWH simulation results for two different scenarios with different water demand compositions are presented to study the effects of propagation errors on temperature prediction. The proposed approach paves the way for developing advanced EWH flexibility modeling tools for the aggregator to precisely control a large portfolio of EWHs considering user comfort and rebound effects.

A comparison of steady-state and transient modelling approaches for the performance prediction of solar air heaters

• A transient solar air heater model using high resolution weather data is developed. • Transient model is compared to stationary model using hourly averaged weather data. • Steady approach results in large deviations, especially under variable cloud cover. • Large differences between approaches in useful energy above threshold temperatures. • Potential implications for latent heat storage, solar drying and other processes. Due to the nature of solar energy, the operation of solar air heaters is fundamentally transient, but most mathematical modelling published to describe their behavior has used stationary models coupled with hourly-averaged weather data. Little attention has been paid to the transient behavior of solar air heaters under real, highly variable weather conditions. In this study, the common modelling approach using a steady-state description of solar air heaters is compared to predictions of using a transient model to which minute resolution weather data is given as input. The steady-state approach was found satisfactory, although not optimal, only under clear sky conditions, with relatively small outlet air temperature errors compared to the results obtained with the transient model. Under less favorable conditions with partial cloud cover, the outlet air temperature with the transient model presented large variations due to the sudden changes in solar radiation not captured in the steady-state approach. With the solar air heater parameters employed, instantaneous deviations of almost 15 °C were found, as well as errors in the predicted useful energy above threshold temperature levels. These results support the use of transient models of solar air heaters and high resolution weather data for accurate, short-term modelling of solar drying, latent heat storage and other highly temperature dependent processes.

Plume Model for Buoyancy-Induced Flow and Heat Transfer in Closed Rotating Cavities

Abstract The radial clearance between the rotating blades and stationary casing of a gas-turbine compressor depends on the radial growth of the rotating discs to which the blades are attached, and this growth depends on the buoyancy-induced flow and heat transfer in the air-filled cavities between adjacent discs. In some engines, the cavities are sealed, which creates a closed rotating cavity. A theoretical model has been developed to calculate the radial distribution of the temperature of the disc in a closed rotating cavity. The principal assumptions are that the convective heat transfer from the hot shroud to the cold hub of the cavity is via plumes of fluid in which the cold fluid moves radially outward, and the hot fluid inward, inside an inviscid quasi-axisymmetric core of rotating fluid. The fluid core is surrounded by boundary layers on all rotating surfaces, with free-convection layers on the surfaces of the shroud and hub and laminar Ekman layers on the surface of the discs. In addition to the convection, heat is transferred by one-dimensional radial conduction in the rotating discs. Using the model, equations have been derived to calculate the radial distribution of temperature in the discs and fluid core. These equations reveal that the non-dimensional temperatures for the disc and core, θd and θc, are controlled by three non-dimensional parameters: Reϕ, βΔT, and χ, the rotational Reynolds number, the buoyancy parameter, and the compressibility parameter, respectively. The compressibility parameter is defined as χ=defMa2/βΔT where Ma is a Mach number, and χ is shown to strongly affect the radial distribution of the core temperatures. There will be a critical value of χ at which the core temperature equals that of the heated shroud. For a closed cavity with adiabatic discs and xa = 0.5, the critical value is 6.7. Above this critical value, stratification is expected to occur and heat transfer from the shroud to the core will be by conduction rather than by convection. The theoretical model predicts radial distributions of temperatures in the discs and fluid core that are in good agreement with the experimentally derived values in a companion paper.

Intermittent Sensor Faults Detection Based on Fractional-Order Transient Chaotic System

Safety and reliability are the most important issues for modern automation systems, fast, precise, and reliable fault detection (FD) is a feasible and easy-implemented method for preventing property loss and casualties. Considering the importance of sensors in modern systems and the characteristics of intermittent faults, the problem of intermittent sensor FD under unknown disturbance and strong noise is the focus of this article. Oriented by the problem, a kind of intermittent sensor faults detection scheme is proposed. The fractional-order transient chaotic system is adopted for the processing of the residual signal and the calculating of the detection threshold. A continuous stirred tank heater (CSTH) model is adopted for the simulation experiment, a simplified F-16 aircraft vertical dynamic model is used for the comparison experiment, and a real-world liquefied natural gas (LNG) filling process is provided for actual experiment. The experiment results show that the proposed intermittent faults detection (IFD) scheme can achieve the purpose of IFD under unknown disturbance and strong noise and performs well. The detectability of the intermittent sensor faults within the proposed IFD scheme is explored.