Heat Flux Model Research Articles

Predicting Critical Heat Flux in Rectangular Channels: Which Correlation to Trust?

The PALLAS-reactor is an advanced nuclear reactor dedicated to the production of medical isotopes and (medical) nuclear technological research currently under construction in The Netherlands RELAP5 is the primary tool used for modeling the accident scenarios relevant for licensing the PALLAS-reactor. The Groeneveld Look-Up Tables (LUT) are the main Critical Heat Flux (CHF) model of RELAP5. These have been extensively validated against experiments with round tubes. However, literature suggests that the LUT over-predict CHF inside the narrow, rectangular fuel channels of research reactors such as the PALLAS-reactor. As literature abounds with CHF correlations of limited applicability and low degrees of validation and confidence, correlations that can accurately predict CHF in rectangular channels are needed. The goal of this work is twofold. First, it aims at selecting a number of promising CHF correlations and to assess these against experiments representative of the PALLAS-reactor design. Secondly, this work ascertains whether the LUT are indeed optimistic with respect to CHF in rectangular channels. To this purpose, a literature review has short-listed the Sudo-Kaminaga (S-K), the Kim-modified S-K, and the Hall–Mudawar (H-M) correlations. These correlations are implemented in the SPECTRA code developed at NRG and assessed against two experiments in rectangular channels. The Kim-modified S-K correlation fits the experiments better than the original S-K scheme for high mass fluxes, while predicting higher CHF values at low flow rates. Interestingly, the H-M correlation predicts the experiments accurately, although the correlation was developed from round tubes data. At high mass fluxes, the LUT predictions converge towards the experiments, thereby suggesting that the effect of the channel geometry becomes less important at high flow rates. At low mass fluxes, on the other hand, the LUT markedly fail to match the experiments. This work contributes to accurately estimating CHF in narrow rectangular channels, which is crucial for licensing research reactors such as the PALLAS-reactor, thus assisting in the betterment of many people’s lives.

Study on coupled heat transfer model and enhanced heat transfer law of liquid metals and supercritical fluids

ABSTRACT The supercritical carbon dioxide Brayton cycle system is being considered for application in the power conversion system of advanced liquid metal fast reactors. One important research topic is the coupled heat transfer characteristics and enhanced heat transfer laws between liquid metals and supercritical fluids. However, the traditional Reynolds analogy hypothesis with a constant turbulent Prandtl number is difficult to satisfy the numerical conjugate heat transfer research of liquid metals and supercritical fluids. Therefore, based on the open-source computational fluid dynamics program OpenFOAM, a numerical method suitable for the coupled heat transfer calculation of liquid metals and supercritical fluids was developed, which can achieve precise conjugate heat transfer solutions by applying different turbulence models and heat flux models to liquid metals and supercritical fluids. Subsequently, based on this method, the coupled heat transfer behavior of liquid metals and supercritical fluids in the straight channel of a typically printed circuit heat exchanger was studied. The focus was investigating the conjugate heat transfer characteristics of liquid heavy metal lead-bismuth eutectic and liquid metal sodium with supercritical carbon dioxide. Some sensitive results, including the inlet temperature and Reynolds number of liquid metals and supercritical fluids, were qualitatively and quantitatively analyzed.

Characteristics of sodium alginate-based hybrid nanofluid and darcy-forchheimer flow induced by stretching surface with thermal radiation and cattaneo–christov heat flux model

In today's industrial age, one of the most pressing challenges is to find an efficient heat transfer fluid because common fluids don't provide efficient heating and cooling in industries. This paper aims to explore the flow and heat transfer characteristics of (SWCNT-Ag/ Sodium Alginate) and (MWCNT-Cu/ Sodium Alginate) based hybrid nanofluids in the presence of Cattaneo–Christov heat flux model and thermal radiation on a surface. To achieve this, we transform the modeled partial differential equations (PDEs) into ordinary differential equations (ODEs) using suitable similarity variables. These equations are then solved using MATLAB software (bvp4c) to illustrate the influence of important controlling parameters, presented in both tabular and graphical formats. It is noted that raising the Inertia coefficient parameter leads to a drop in the velocity distribution profile of the (SWCNT-Ag/ Sodium Alginate) and (MWCNT-Cu/ Sodium Alginate) based hybrid nanofluid. Enhancing the rotation parameter of (SWCNT-Ag/ Sodium Alginate) and (MWCNT-Cu/ Sodium Alginate) based hybrid nanofluid decreases the velocity distribution profile. The increasing values of the thermal radiation parameter and Biot number increased the thermal distribution profile while the fall down for the enhancing values of the melting parameter. The convergence ranges of emerged flow parameters are listed here(0.1<β<1.4),(0.1<Γ<0.4), (0.1<P<1.3),(0.1<Fr<1.2), (0.01<ϕ1=ϕ2<0.04), (0.4<Me<1.0),(0.1<Bi<2.2),(0.1<Rd<1.2), and (0.4<Ωt<1.0). The key and fascinating aspect of this innovative study is that the heat transfer rate increases for all the parameters involved, aligning with the fundamental goal of utilizing nanofluids in nanotechnology for their promising applications.

Entropy optimization of chemically reactive bioconvective Powell-Eyring nanofluid stratified flow over a Riga plate: A non-Fourier heat and mass flux modeling

This work examines the effects of Riga plate flow in a Powell-Eyring bioconvection Powell-Forchheimer medium. For the Powell-Eyring base fluid, mobile microorganisms are taken into account in addition to nanoparticles. Additionally taken into account are chemical reactions and the effects of linear radiation. The governing PDEs with boundary conditions are transformed into an ODE by using similarity transformation. The resulting equations are solved using the homotopy analysis approach. A detailed description is given of the link between the relevant parameters and the density of dynamic microorganisms, motion, fluid temperature, skin friction rates, local Sherwood and Nusselt numbers, and nanocomposite volume. Gyrotactic microorganism-containing nanoparticles have potential applications in biotechnology, microfluidic devices, microbial fuel cells, and enzyme biosensors. Various features of several physical characteristics are addressed through the use of tables and graphs.

Brownian motion and thermophoresis influence in magnetized Maxwell upper-convected stagnation point fluid flow via a stretching porous surface

This article focuses on the effects of Brownian motion and thermophoresis convection in the stagnation point flow of a Maxwell upper-convected fluid over a non-Darcian porous surface with slip conditions and a magnetic inclination effect. The Maxwell dissipative fluid accounts for Joule heating due to an imposed magnetic field and porous medium resistance. At the same time, the Cattaneo-Christov heat flux model represents thermal relaxation in contrast to the conventional Fourier law. The resulting nonlinear partial differential equations are transformed into ordinary differential equations (ODEs) using similarity variables. The analysis revealed the influence of dimensionless numbers, including Deborah, Eckert, Prandtl, chemical reaction, thermal relaxation, inclination and slip parameters. The findings were presented using graphs and tables. An increase in the thermophoresis parameter notably led to higher concentration and temperature profiles. In contrast, increasing Brownian motion (Nb) decreased the solutal boundary layer thickness but enhanced the thermal boundary layer.

Sensitivity analysis on optimizing heat transfer rate in hybrid nanofluid flow over a permeable surface for the power law heat flux model: Response surface methodology with ANOVA test

&lt;abstract&gt; &lt;p&gt;Joule dissipation has an important role in the conversion of mechanical energy to heat within a fluid due to the internal friction and viscosity. Moreover, Darcy friction is a measure of the resistance to flow in a porous medium. In response to the efficient heat transfer performance, a robust statistical approach was established to optimize the heat transfer rate in a two-dimensional flow of a nanofluid over a permeable surface embedded with a porous matrix. The electrically conducive fluid affected the flow phenomena to include a carbon nanotube nanoparticle in the conventional liquid water for the enhanced heat transfer properties; additionally, the power-law heat flux model was considered. Appropriate transformation rules were adopted to obtain a non-dimensional system that brought a developed model equipped with several factors. The traditional numerical technique (i.e., shooting based Runge-Kutta) was proposed to handle the coupled nonlinear system. Furthermore, the statistical response surface methodology (RSM) was adopted to obtain an efficient optimized model for the heat transportation rate of the considered factors. An analysis of variance (ANOVA) was utilized to validate the result of the regression analysis. However, it was evident that the nanoparticle concentrations were useful to augment the fluid velocity and the temperature distributions; the statistical approach adopted for the heat transfer rate displayed an optimized effect as compared to a conventional effect.&lt;/p&gt; &lt;/abstract&gt;

Numerical study of bioconvection and Cattaneo-Christov heat flux model in MHD Maxwell nanofluid flow over a variable thickness elastic surface

Numerical study of bioconvection and Cattaneo-Christov heat flux model in MHD Maxwell nanofluid flow over a variable thickness elastic surface

Thermal convection with a Cattaneo heat flux model

The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to a Cattaneo–Christov theory, and the results for linear instability theory are in agreement with those for a material derivative. It is further shown that none of the theories allow a standard nonlinear, energy stability analysis. A further heat flux due to P.M. Mariano is added and then an analysis is performed for stationary convection, oscillatory convection, and fully nonlinear theory. For the material derivative case, the analysis proceeds and global nonlinear stability is achieved. For Cattaneo–Christov theory, it appears necessary to add a regularization term in the equation for the heat flux, and even then the analysis only works in two space dimensions, and is conditional upon the size of the initial data. For the three-dimensional situation, it is shown how a nonlinear stability analysis may be achieved with a Navier–Stokes–Voigt fluid rather than a Navier–Stokes one.

Time-independent three-dimensional flow of a water-based hybrid nanofluid past a Riga plate with slips and convective conditions: A homotopic solution

Abstract In the present analysis, we have analyzed the three-dimensional flow of an electromagnetohydrodynamic copper–aluminum/water hybrid nanofluid flow on a Riga plate. The heat and mass flux model proposed by Cattaneo-Christov is deliberated here. Thermal radiation, thermophoretic diffusion, Brownian motion, and chemical reaction phenomena are considered in analyzing the flow problem. Thermal convective, mass convective, and velocity slip conditions are adapted in this analysis. Suitable resemblance variables are implemented for the conversion of the model equations to dimension-free form. The homotopy analysis method is adopted to solve the modeled equations. The obtained results show that the velocity profiles are reduced with an increasing estimation of the slip factors. Additionally, the nanoparticles’ concentration and the temperature of the hybrid nanofluid increase with higher values of thermal and solutal Biot numbers. The Nusselt number is increased with an increase in the radiation factor and thermal Biot number.

Experimental study on the thermal performance of building external window greenery in a subtropical climate

Previous research has found that building greenery systems can cool both buildings and their surrounding environments during the summer. However, the window greenery system, which is a widely adopted form of building greenery, has received limited attention. This study analyzed the thermal performance of window greenery systems in general and the building-integrated window gardens in specific, based on in-situ measurements in a subtropical city. The results show that the cooling effects of the window garden on the envelope were significant near the bottom region. During the air-conditioning period, the heat flux through the bottom wall and windowpane interior surfaces was decreased by 29.0 % and 25.8 %, respectively. A regression model for heat flux through the bottom windowpane was proposed, which estimated that the reduction in radiative heat transfer by plants was 88.0 %. The equivalent heat transfer coefficient for the walls adjacent to the window garden was calculated. Window gardens also improved the outdoor microclimate, reduced the average air temperature over planting troughs by 1.0 °C, and increased the average relative air humidity by around 10.0 % throughout the day. Given that window gardens’ cooling effects strongly depend on water evaporation, a win–win strategy for energy and water saving by harvesting the air conditioning condensate for irrigation is proposed. Based on an estimation, the condensate could fully meet the daily requirements of window greenery, confirming the feasibility of the win–win strategy.

Darcy-Forchheimer flow with viscoelastic Cattaneo-Christov heat flux model and nonlinear thermal radiation: A numerical investigation

Jeffrey fluids have found vast applications in industries and engineering along with their rheological properties. This article investigates the heat and fluid flow within the frame of the nonlinear thermal radiation and non-Fourier heat flux model on Jeffrey nanofluid over an inclined permeable stretched cylinder through saturated porous medium. In addition, non-uniform heat generation/absorption, nonlinear thermal radiation, thermal stratification, and homogeneous/heterogeneous reactions are accounted. Porous medium is characterized through nonlinear Darcy-Forchheimer relation. Shooting method is employed in conjunction with Runge-Kutta-Fehlberg method to solve nonlinear ODEs. The effects of flow variables involved in velocity, temperature and concentration profiles are deliberated through graphs. It is evident from obtained results that the temperature field rises with thermal radiation parameter and space dependent heat generation/absorption parameter. Local Nusselt number has same enhancing attitude towards the thermal relaxation time (0.7443≤−Nˆuz(Rez)−12≤0.7857 for0.2≤δe≤0.6) and thermal stratification parameter (0.7239≤−Nˆuz(Rez)−12≤0.7689for0.2≤S1≤0.6). The exactness of the solution and F′(ξ) variation is verified by comparison with already published literature. The computed results are of great interest in cooling of nuclear reactors. Viscoelastic stuff are generally employed in mats, car shields, computer hard drives and other protective paddings. Synthetic materials can work as the lubricant for an osteoarthritic joint.

Nuclear Meltdown Relocation and Core Catcher Analysis

Nuclear meltdown with the potential human and environmental harm is one of the major accident hazard (MAH) faced by nuclear power plants. Limiting (or entirely avoiding) criticality events are the main design strategies for reactors of generations 3½ and 4 (Gen3½ and Gen4). These include ensuring negative void and negative temperature coefficients (for both moderator and fuel) regardless of operational conditions, which provide a self-regulating mechanism that helps preventing accidents occurrence (i.e., to address safety and reliability aspects of Gen4’s goals). However, in severe accident scenarios (e.g. during loss-of-coolant, LOCA, events) where failure to extract heat from the reactor may lead to core degradation, strategies to mitigate reactor meltdown and relocation are critical in the design of safety protocols. This work aims to numerically investigate core relocation as an integrated multi-fluid and heat dynamics problem in which flow of melted materials (UO2, Zircaloy and graphite) are modelled through interface capturing/tracking methods. Two interface tracking/capturing methods were compared, the level-set volume of fluid method (VOF) in Ansys Fluent, and the compressive advection method (CAM) in Fluidity/ICFERST. Both methods are in good agreement for the core relocation simulation. An in-vessel core catcher (IVCC) of tungsten alloy was also proposed to demonstrate core degradation control strategy through cooling of the melted multi-materials. The IVCC was simulated with a multifluid model in Ansys Fluent, in a specified applied heat flux model. The thickness of the IVCC is 0.20 m and the heat flux used is 600 kW m-2. The tungsten material used was able to withstand both thermal and mechanical loads on the lower plenum by extracting decay heat from the corium.

Two-phase analysis on radiative solar pump applications using MHD Eyring–Powell hybrid nanofluid flow with the non-Fourier heat flux model

Two-phase analysis on radiative solar pump applications using MHD Eyring–Powell hybrid nanofluid flow with the non-Fourier heat flux model

Lubricated stagnation point flow of Walters-B nanofluid with Cattaneo-Christov heat flux model: Hybrid homotopy analysis simulations

Thermal mechanism of non-Newtonian nanofluid coated by lubricated power law material has been theoretically worked out. The slip interaction constraints has been proposed for inspecting the thermal transport. The modelling of heat transfer is processed via updated Cattaneo-Christov (CC) expressions. The rheological constraints of nonlinear model are observed by Walter B fluid. The flow phenomenon is governed by stagnation point flow. The differential system is associated to interaction of similarity variables. The solution technique is based on new developed hybrid homotopy analysis scheme. The hybrid homotopy algorithm is developed by combining the shooting technique and traditional HAM. The accuracy regarding the developed scheme is carefully inspected after making comparison of results with earlier claimed studies. The different physical aspect of transport phenomenon is attributed in view of parameters.

Flow and thermal fields modeling in jet impingement configurations using a Reynolds stress turbulence closure within the RANS and Sensitized-RANS framework

The flow and thermal field characteristics underlying turbulent convective heat transfer in two reference configurations, representing a jet exiting a planar slot and a circular tube and impinging on a heated wall, are studied computationally. The performance of a conventional Reynolds Stress Model (RSM) and its scale-resolving variant, employed in the context of a time-accurate Reynolds-Averaged Navier–Stokes (RANS) simulation, is investigated in conjunction with different modeling approaches for the turbulent heat flux uj′θ′¯, whose gradient represents the turbulence-induced heat source in the temperature transport equation. In this so-called Sensitized-RANS modeling strategy, employing an improved eddy-resolving instability-sensitive Reynolds Stress Model (IISRSM, Jakirlić and Maduta (2015)), the unresolved ‘sub-scale’ turbulent correlations represent the solutions of a set of corresponding transport equations for the entire stress tensor ui′uj′¯. The turbulent scalar-flux models follow from the classical gradient-diffusion approach with the diffusion-like coefficients formulated as a function of both the scalar eddy-viscosity and the anisotropic Reynolds stress tensor. The latter model expressions also take into account various non-linear relationships in terms of turbulent stress components. The computational results of the fully-developed channel flow, featured only by the mean shear and constant wall heat flux, representing a preliminary investigated flow configuration, agree very well with the corresponding DNS (Direct Numerical Simulation) database for both RSM versions in conjunction with all the turbulent heat flux models adopted. However, the study of the two flow impingement cases with the different structure of the impinging jet and nozzle-to-wall distance variations, characterized by a much more complex flow straining, using the considered conventional Reynolds stress model shows significantly different results for the Reynolds stress and thermal fields compared to the available DNS data, especially in the immediate impact region manifested by a significant overprediction of the turbulence intensity. In contrast, the IISRSM-relevant results for the mean flow and temperature fields, the associated integral characteristics, and the corresponding turbulence quantities are in very good agreement with the reference DNS data, due to the much higher predictive capabilities of this eddy-resolving turbulence model compared to its baseline counterpart.

A critical heat flux model for IVR-ERVC application based on the experimental observation

It is essential to conduct theoretical and experimental research on the heat transfer limit for External Reactor Vessel Cooling (ERVC), which aims to implement In-Vessel Retention (IVR) severe accident mitigation strategy successfully. In this paper, a theoretical model for IVR-ERVC condition is proposed to predict the critical heat flux (CHF) based on the experimental observation. According to the experimental observation on the one-dimensional full height IVR-ERVC experimental facility, it is found that there is a thin liquid film between the heating surface and the vapor slug. And this film is evaporated completely when CHF occurs. In addition, a large number of bubble condensation collapses were observed under subcooling condition. According to these experimental observations, a CHF model based on the mechanism of liquid film dryout is developed. The CHF trigger mechanism of this model is that the supply of fresh liquid into the liquid film is not sufficient to prevent depletion of the liquid film due to the boiling. The influence of heating surface geometry and the heat flux shape are considered in this model. The predicted values of the model are compared with the CHF experimental result from different test facilities with different conditions, and the comparison result shows that the relative errors are basically within 20 %. The analysis results of the model indicate the increasing of coolant subcooled degree is conductive to the improvement of CHF. When the coolant subcooled degree increases by 15 ℃, more than 30 % maximum increase in CHF is obtained. In addition, this model can reflect the “exit phenomena” to a certain extent.

Heat and mass transport aspect on magnetised Jeffery fluid flow over a stretching cylinder with the Cattaneo–Christov heat flux model

This study offers the impacts of MHD Jeffery fluid research on a stretching cylinder. The Cattaneo–Christov heat model is acquired instead of the Fourier law of heat conduction to construct the energy equation. The order analysis of a fluid model is performed using the boundary layer theory. On differential equations, appropriate similarity transformations are used to attain the differential equations. The following nonlinear equations were then mathematically solved utilising the shooting method. The visual inspection of the conclusions of the velocity, thermal and concentration profiles is completed for several important thermophysical parameters. For numerous thermos physical variables, the numerical variation in the valuations of the mass transport rate, coefficient of skin friction and heat rate transfer has been assessed and provided in a table. The main conclusions of the study show that temperature, concentration distribution and flow speed all decrease as the curvature parameter increases. It has also been deduced in this investigation that the higher values of the Lewis number higher the mass transfer rate and lower the heat flux at the surface of the cylinder. These results exhibit a more favourable agreement across all findings when compared to previous findings.

Entropy Generation Optimization in an Unsteady Hybrid Nanofluid Flow Over a Flat Plate with Variable Viscosity: A Cattaneo-Christov Heat Flux Model

Nanofluids are a novel and intriguing class of heat transmission fluids that can be used in place of more conventional options. They have several applications, including fuel cells, heat exchangers, and the pharmaceutical industry. When it comes to heat transport, hybrid nanofluids much outperform their mono-fluid counterparts. These are being put to use in a wide variety of areas, from solar power to air conditioning. Unsteady flow characteristics of a hybrid nanofluid (Ethylene Glycol + ZnO + TiO2) over a flat plate at varied Lorentz forces, volume fraction of nanoparticles, and thermal radiation are unknown when variable viscosity is taken into account. Paper’s novelty is addressing this gap, which is to examine the impact of variable viscosity on the hybrid nanofluid flow by a flat plate under convective boundary condition when thermal radiation and magnetic field are significant. Cattaneo and Christov’s heat flux model is used to analyse the phenomenon of heat transfer. This paper also includes an analysis of irreversibility. The equations required to represent the problem have been turned into a system, and this system has been solved using the bvp4c solver. Validated the results (of engineering parameters including friction coefficient) obtained using the bar graphs by using Multiple linear regression. It has been observed that the thermal relaxation parameter (Γ) and the unsteady parameters (S) both have similar effects on the heat transmission rate. It is found that there is an increment of 0.001278 (when 0 ≤ Γ ≤ 0.6) and 0.103865 (when 0.4 ≤ S ≤ 1) in the Nusselt number. It is clear from a closer inspection that as magnetic field parameter (Mg) and viscosity parameters (δ) are raised, the friction factor declines. It is observed that, at 0 ≤ Mg ≤ 1.8, friction factor declines at a proportion of 0.08974. It is detected that higher Brinkman number values lead to a greater rate of entropy generation and an upsurge in the (temperature-dependent) viscosity parameter contributes to a decline in the same. As the viscosity parameter is amplified, it is also seen that the fluid’s velocity declines.

Rapid identification of boiling crisis with event-based visual streaming analysis

The formation of a stable vapor layer during boiling processes triggers the boiling crisis that can damage the entire system. While there have been efforts to build a predictive model for critical heat flux on live images, unfortunately, images from conventional frame-cameras show limitations for performing real-time digital inference as they contain significant unnecessary information. A new type of imaging technique, neuromorphic event imaging, captures individual pixel-wise brightness changes, thereby recording motion-based phenomena in a sparse and efficient manner. In this study, we develop neural network models capable of predicting the onset of boiling crisis by utilizing neuromorphic-simulated event data. We reveal that event-based models demonstrate their proficiency and time efficiency in learning patterns of the boiling process from relatively small datasets. The event-based models also prove the generalizability to unseen surfaces by showing the potential for transfer learning. The results suggest that an extension of this work may prove effective in developing forecasting models that detect the incipient boiling crisis before it damages boiling surfaces. These findings highlight that event data can be effectively applied to real-time, motion-dependent contexts.

A comparative study on the rheological properties of upper convected Maxwell fluid along a permeable stretched sheet

The objective of this paper is to examine the flow of a non-Newtonian Maxwell fluid induced by a permeable stretching sheet in motion within a porous medium. The research incorporates the Cattaneo-Christov heat flux model to study the heat transfer process. The utilization of the Cattaneo-Christov heat flux approach becomes relevant in scenarios involving materials with high thermal conductivity or during short time intervals. Consequently, the current investigation holds significant importance. It is assumed that the viscosity of the Maxwell fluid changes exponentially as the temperature changes. The modeling of the physical phenomena being investigated takes into account the effects of a magnetic field, thermal radiation, velocity, and thermal slip conditions. In this study, the viscous dissipation phenomenon is taken into account because it can have notable impacts on the temperature and viscosity of the fluid, and is known to play a crucial role in fluid flow phenomena. The equations developed to model fluid flow are transformed into nonlinear ordinary differential equations through the use of appropriate similarity transformations. The focus of the research revolves around investigating the numerical solution of ordinary differential equations accompanied by boundary conditions using the shooting technique. The findings are then showcased via tables and graphs and scrutinized in order to arrive at conclusions. Furthermore, the precision of the present findings was evaluated by contrasting the heat transfer rate with outcomes that were previously published. Based on the obtained outcomes, it can be concluded that both the Eckert number and thermal radiation have a comparable enhancing influence, whereas the thermal relaxation parameter and thermal slip parameter exhibit opposing effects.