Heat Flux Model Research Articles

The investigation of Darcy-Rayleigh convection with uniform heat flux Model A

The investigation of Darcy-Rayleigh convection with uniform heat flux Model A

Assessment of Turbulence Models over a Curved Hill Flow with Passive Scalar Transport

An incoming canonical spatially developing turbulent boundary layer (SDTBL) over a 2-D curved hill is numerically investigated via the Reynolds-averaged Navier–Stokes (RANS) equations plus two eddy-viscosity models: the K−ω SST (henceforth SST) and the Spalart–Allmaras (henceforth SA) turbulence models. A spatially evolving thermal boundary layer has also been included, assuming temperature as a passive scalar (Pr = 0.71) and a turbulent Prandtl number, Prt, of 0.90 for wall-normal turbulent heat flux modeling. The complex flow with a combined strong adverse/favorable streamline curvature-driven pressure gradient caused by concave/convex surface curvatures has been replicated from wind-tunnel experiments from the literature, and the measured velocity and pressure fields have been used for validation purposes (the thermal field was not experimentally measured). Furthermore, direct numerical simulation (DNS) databases from the literature were also employed for the incoming turbulent flow assessment. Concerning first-order statistics, the SA model demonstrated a better agreement with experiments where the turbulent boundary layer remained attached, for instance, in Cp, Cf, and Us predictions. Conversely, the SST model has shown a slightly better match with experiments over the flow separation zone (in terms of Cp and Cf) and in Us profiles just upstream of the bubble. The Reynolds analogy, based on the St/(Cf/2) ratio, holds in zero-pressure gradient (ZPG) zones; however, it is significantly deteriorated by the presence of streamline curvature-driven pressure gradient, particularly due to concave wall curvature or adverse-pressure gradient (APG). In terms of second-order statistics, the SST model has better captured the positively correlated characteristics of u′ and v′ or positive Reynolds shear stresses (<u′v′> > 0) inside the recirculating zone. Very strong APG induced outer secondary peaks in <u′v′> and turbulence production as well as an evident negative slope on the constant shear layer.

Effects of Soret and Dufour Numbers on the Three-Dimensional MHD Flow of Micropolar Fluid Containing Gyrotactic Microorganisms Over a Bidirectional Stretching Sheet With Cattaneo–Christov Heat and Mass Flux Model

Abstract Stretching flow problems have several real-world applications in engineering, biological, and industrial fields. The real-world applications of the stretching sheet flow problems are continuous cooling of fiber, manufacturing of rubber and plastics sheets, metal-working processes, crystal growth processes, drawing of the filaments through a quiescent fluid, and consideration of the liquid's films and many others. The present problem focuses on the study of heat and mass transmission phenomena of the magnetohydrodynamics flow of three-dimensional micropolar liquid over a bidirectional stretching surface. In the current analysis, the heat and mass transport mechanism are demonstrated by incorporating the Cattaneo–Christov heat and mass flux model. The micro-organisms are only used to stabilize suspended nanoparticles via bioconvection, which is caused by the combination of magnetic field and a buoyancy force. The current model is demonstrated in the system of higher order partial differential equations (PDEs), which are changed into nonlinear ordinary differential equations (ODEs) by the exploitation of appropriate similarity variables. For the analytical solution, the resulting nonlinear ODEs are simulated by employing the homotopy analysis scheme. The physical significance of velocities, microrotation, temperature, concentration, and micro-organism profiles of the fluid via various embedded parameters are calculated and discussed in a graphical form. The Nusselt number, Sherwood number and micro-organism density number are calculated via tables. Some major findings of the current problem are that the Nusselt number is weakened for the boosted estimation of radiation and thermal relaxation time parameter. The bioconvection Lewis number raised the micro-organism density number. The nanofluid microrotation profile is boosted with the augmentation of the microrotation parameter. The temperature of nanoliquid is lower for thermal relaxation time parameter and nanofluid concentration is lower the for solutal relaxation time parameter.

Computational study of micro-polar nanofluid past a spinning disk with non-Fourier's heat and non-Fick's mass flux models

In this study, the flow of micro-polar nanofluid past a spinning disk with non-Fourier's heat and non-Fick's mass flux models has been scrutinized. The flow is considered under the effect of the concentration slip, velocity slip, convective heating, and radial magnetic field. Through boundary layer approximations, the acquired system of partial differential equations from conservations of mass, momentum, energy, and nanoparticles concentration was converted into ordinary differential equations using similarity transformation, and thereafter solved numerically by the bvp4c approach. Plots and tables are used to inspect and analyze the role of physical parameters on flow fields. It is evident from the results that the centrifugal, tangential, and angular velocities significantly deteriorate with an escalation of magnetic field constraints. Also, a declination in the motion of fluid flow along with the centrifugal and tangential surfaces happens with higher micro-rotation constraints. It is discovered from the results that the strengthening in angular velocity is caused by a higher micro-rotation slip parameter. Furthermore, heat relocation can be improved by higher magnetic field constraints, Brownian motion constraints, and thermal Biot number. However, it can be illustrated from the results that an enhancement in thermal relaxation constraint causes a reduction in temperature dissemination. The results also showed that an increment in concentration relaxation and concentration slip parameters causes a reduction in dissemination of concentration. The analysis of skin friction, wall couple stress, heat relocation rate, and mass relocation rate are premeditated via tables. This theoretical and numerical exploration is more helpful in industrial areas and in the field of biological research.

Analysis of CHF characteristics with fuel rods in the natural circulation system under motion conditions

For the floating pressurized water nuclear reactor, CHF is vital to the fulfilment of design and operation criteria for safe performance and the safety of nuclear fuel, and natural circulation is the primary circulation in many designs. However, the traditional method of look-up table or correlations evaluation is no longer applicable to the CHF characteristics because of additional force in the motion conditions, especially in natural circulation system (Gui et al., 2021). In this study, the prediction of CHF under motion conditions is carried out with code development and experimental study. The theory of natural circulation system models, subchannel models, critical heat flux models are coupled together with motion models to establish the prediction model for fuel rod critical heat flux characteristics in the natural circulation system under motion conditions. As rolling motion is studied in the previous study (Huang et al., 2018), inclination and heaving conditions are two motion conditions that are mainly considered in this study. The inclining and heaving conditions are modeled by adding the additional motion force. The code calculated results are validated with experimental data. The calculation results are analyzed with different inclining and heaving conditions, and the regularity of CHF variation characteristics is illustrated.

The Casson Dusty Nanofluid: Significance of Darcy–Forchheimer Law, Magnetic Field, and Non-Fourier Heat Flux Model Subject to Stretch Surface

This work aims to offer a mathematical model for two-phase flow that investigates the interaction of Casson nanofluid and dust particles across a stretching surface. MHD Darcy–Forchheimer porous medium and Fourier’s law through Cattaneo–Christove thermal flux are also considered. The governing equations for the two phases model are partial differential equations later transmuted into ordinary ones via similarity transforms. The Runge–Kutta method with the shooting tool is utilized numerically to solve the boundary layer equations computed in MATLAB to obtain numerical results for various pertinent parameters. The numerical outcomes of momentum, temperature, and concentration distribution are visible for both phases. The results of the skin friction, heat transfer coefficients, and the Sherwood number are also visible in the graphs. Furthermore, by comparing the current findings to the existing literature, the validity of the results is confirmed and found to be in good agreement. The fluid velocity is reduced against increasing strength of Casson fluid parameter, enhanced the fluid phase and dust phase fluid temperature. The temperature declines against the growing values of the relaxation time parameter in both phases. Dusty fluids are used in various engineering and manufacturing sectors, including petroleum transportation, car smoke emissions, power plant pipes, and caustic granules in mining.

Multiphysics Numerical Simulation Model and Hydraulic Model Experiments in the Argon-Stirred Ladle

The argon-stirred ladle is a standard piece of steelmaking refining equipment. The molten steel quality will improve when a good argon-stirred process is applied. In this paper, a Multiphysics model that contained fluid flow, bubble transport, alloy transport, bubble heat flux, alloy heat flux, alloy melting, and an alloy concentration species transport model was established. The fluid model and bubble transport model that were used to calculate the fluid velocity were verified by the hydraulic model of the ladle that was combined with particle image velocimetry measurement results. The numerical simulation results of the temperature fields and steel–slag interface shape were verified by a ladle that contained 25 t of molten steel in a steel plant. The velocity difference between the hydraulic model and numerical model decreased when the CL (integral time-scale constant) increased from 0 to 0.3; then, the difference increased when the CL increased from 0.3 to 0.45. The results showed that a CL of 0.3 approached the experiment results more. The bubble heat flux model was examined by the industrial practice, and the temperature decrease rate was 0.0144 K/s. The simulation results of the temperature decrease rate increased when the initial bubble temperature decreased. When the initial bubble temperature was 800 °C, the numerical simulation results showed that the temperature decrease rate was 0.0147 K/s, and the initial bubble temperature set at 800 °C was more appropriate. The average melting time of the alloy was 12.49 s and 12.71 s, and the mixture time was approximately the same when the alloy was added to two slag eyes individually. The alloy concentration had fewer changes after the alloy was added in the ladle after 100 s.

Numerical simulation of entropy generation for nanofluid with the consequences of thermal radiation and Cattaneo-Christov heat flux model

Nanofluids have attracted a lot of attention as a result of their various manufacturing, technical, and medical purposes. The current investigation looks at the usage of Casson nanofluid in a permeable solar collector flow on an indefinite surface. Copper oxide-water (CuO − H2O), titanium dioxide-water (TiO − H2O), and disulfide molybdenum-water (MoS4 − H2O) nanofluids outcomes were all evaluated and expounded on as well. Copper oxide (CuO) nanoparticles have more elevated heat conductivity than titanium dioxide (TiO) nanoparticles, the Copper oxide-water (CuO − H2O) nanofluid demonstrated better heat transport capability than titanium dioxide-water (TiO2 − H2O) nanofluid. As the values of various parameters improve, the velocity, temperature, and entropy profiles of specified fluids grow and decrease, as shown in the graphical depictions. Using appropriate similarity adjustments, the governing partial differential equations were converted into nonlinear ordinary differential equations. The shooting technique is used in conjunction with the MATLAB software included with the bvp4c to compute a highly nonlinear system of equations. Graphs show the effects of key factors on velocity and temperature concentration. The temperature profile rises as shape factors rise. The temperature panel is decreasing as the Cattaneo-Christov component increases. By increasing the influence of the Biot number, both temperature and entropy profiles are rising. The conclusions for Casson nanofluid are analyzed using the parameterized development of the Cattaneo-Christov component. These findings are helpful for the thermic control of heat transmission in upcoming technologies. Finally, the dynamics of fluid flow are investigated using streamlines.

A Study on Heat Flux Characteristics of Tubular Quartz Lamp for Thermal Load Design of High Temperature Structural Test

Development of supersonic flying vehicle is one of the most latest issue in modern military technology. Specifically, structural integrity of supersonic flying vehicle can be verified by high temperature structural test. High temperature structural test is required to consider thermal load caused by aerodynamic heating while applying structural load simultaneously. Tubular quartz lamps are generally used to generate thermal load by emitting infrared radiation. In this study, modified heat flux model of tubular quartz lamp is proposed based on existing model. Parameters of the proposed model are optimized upon measured heat flux in three dimensions. Finally, thermal load of plate specimen is designed by the heat flux model. In conclusion, it is possible to predict heat flux applied on plate specimen and desired thermal load of high temperature structural test can be obtained.

Galerkin finite element analysis for the augmentation in thermal transport of ternary-hybrid nanoparticles by engaging non-Fourier’s law

Boosting of thermal transportation is the demand of current era. Several techniques have been used to do so. One of an important way is the mixing of nanoparticles to boost thermal performance. Current investigation has been prepared to study the inclusion of tri hybrid nanoparticles in Prandtl fluid model past over a stretched heated sheet. Modelling of consider problem has been done due to consideration of movement in flow in Cartesian coordinates which results coupled partial differential equation system thermal transport in presented by considering generalized heat flux model and heat generation/absorption. The derived coupled complex partial differential equations (PDEs) system is simplified by engaging boundary layer theory. Such developed model is used in coolants regarding automobiles, dynamics in fuel and production of solar energy, fuel cells, optical chemical sensors, automotive parts, dental products, cancer therapy, electrical insulators and dental products. Handling of complex PDEs for the solution is a challenging task. Due to complexity in computational work these PDEs have been transformed into ordinary differential equations (ODEs) after applying similarity transformation afterwards converted ODEs have been approximated via finite element algorithm coded in MAPLE 18.0 symbolic computational package. Comparative study has been presented for the validity of code and authenticity of obtained result. It is observed that fluid velocity for tri-hybrid nanoparticles is higher than fluidic motion for pure fluid, nanofluid and hybrid nanomaterial.

Validation and application of numerical modeling for in-vessel melt retention in corium pools

In a hypothetical severe accident scenario in light water reactors (LWR), after the loss of primary coolant, the melted core moves to the lower plenum of the reactor pressure vessel and accumulate there. The melted core cautiously releases the decay heat which forms a pool of melted core, called corium, and turbulent natural convection starts. The decay heat transferred by the corium to the vessel may result in vessel failure due to the focusing effect in the absence of an effective cooling system. A numerical analysis is carried out using STAR-CCM+ commercial software to investigate the ability of the existing turbulence models and Algebraic Heat Flux Model (AHFM) to simulate the natural convective heat transfer phenomena in the corium pools. Efforts have been made to predict the BALI experimental results which are designed to simulate the heat transfer in corium pools, in the framework of severe accident studies. For BALI experiments various test campaigns are run varying the internal Rayleigh number, the viscosity of the simulant fluid, and test facility height. Various such experimental cases are verified and compared with numerical simulations. Temperature profiles along a vertical line, surface heat flux along the curved surface, average Nusselt number on the top, and curved surfaces are estimated. The effect of wall boundary conditions on heat transfer is analyzed. The numerical analysis is extended to Pressurized Water Reactor (PWR) and Boiling Water Reactor (BWR) geometries. The CFD analysis predicts the stratified zone and upper mixing zone very well, and the temperature profiles and average heat transfer values are in agreement with the experiments.

A heat-flux upper boundary for modeling temperature of soils under an embankment in permafrost region

Building roads in permafrost region is challenged because permafrost is sensitive to temperature increase. As an embankment gains/drains heat mostly at the upper surface, accurately modeling the heat transfer in the upper surface is crucial to understand the thermal stability of the road. Popular methods treat the upper boundary as a temperature-controlled model (TCM), where temperature of the upper surface is set as a sinusoidal function. This simple function, however, fails to identify the influences of solar irradiance, heat convection, and thermal irradiance on the heat transfer on the ground surface. Here we introduce a heat-flux model (HFM) to calculate the heat fluxes at the embankment upper surface and at the adjacent ground surface. HFM-predicted temperature under an embankment is compared against the observed temperature to validate the model, and is compared to the TCM-predicted temperature. While TCM-predicted temperatures and HFM-predicted ones are similar in trend and in pattern, the HFM-predicted temperatures are far more coincident with the observed ones. The pros and cons of both HFM and TCM are discussed. Further studies are expected to use HFM to understand the heat flux components such as solar absorption, heat convection, and thermal irradiance on the temperature of permafrost under embankments.

Numerical investigation of double diffusion heat flux model in Williamson nanofluid over an exponentially stretching surface with variable thermal conductivity

This investigation examines the Williamson nanofluid flow over an exponentially stretched surface with variable thickness. Cattaneo-Christov double diffusion (CCDD) heat flux model is applied while examining two cases of heat transfer, i.e., prescribed exponential surface temperature (PEST) and prescribed exponential heat flux (PEHF). A mathematical model of the problem based on momentum, mass, and energy conservation. The governing non-linear partial differential equation (PDEs) are converted into non-linear ordinary differential equations (ODEs) via similarity transformations. The velocity, temperature, and concentration profiles are obtained numerically. Additionally, the impacts of numerous physical parameters of engineering significance are visually depicted through graphs and tables. It is noted that by raising the thermal relaxation parameter γ 1 , the temperature profile decreases. When the concentration relaxation parameter γ 2 rises, then the concentration distribution also decays. When the magnetic parameter M increases, then the velocity profile decreases. For the selected numeric values of the Prandtl number Pr , the temperature profile decreases for both PEST and PEHF cases.

Comparative analysis of hybrid nanofluids with Cattaneo-Christov heat flux model: A thermal case study

The hybrid nanofluids have higher heat transfer efficiency than nanofluids, which has expanded their applications to include electronic cooling, production, automobile, heat transfer, solar energy, heating elements, and biomedical. The current research aims to investigate the effects of Powell-Eyring hybrid nanofluid with slip boundary conditions, and the Cattaneo-Christov heat flux model over a moving surface. By applying the appropriate transformations, the governing boundary layer system is transformed into a dimensionless non-linear ODEs. These non-linear ODEs are computed numerically by using the Keller-Box method via computational tool MATLAB. Physical flow performance and numerical results of physical parameters are obtained by using the MATLAB tool. The researchers noted that hybrid nanofluid have a higher heat transfer rate than nanofluid. The consequences reveal that the velocity profile diminishes with an augmentation in a volumetric fraction of nanoparticles parameter, slip parameter, and porous medium parameter. Furthermore, an increase in thermal radiation parameter, volumetric fraction of nanoparticle parameter, Biot number, and thermal relaxation parameter enhance the temperature layer thickness. To the researchers' knowledge, no one has previously attempted to investigate the current challenge using a mass-based hybrid nanofluid framework. Furthermore, the problem's solution is novel. Indeed, the findings of this research are unique, and the numerical results have never been reported before. Furthermore, the researchers assumed that the findings of this study will be valuable in the development of a hot-wire anemometer or a shielded thermocouple for monitoring wind velocity, among other applications.

Mass Transfer of a Thermally Radiative MHD Cattaneo-Christov Nanofluid between Two Stretchable Spinning Disks

The investigation on the impacts of magnetic field, thermal radiation, generation of heat and mass transfer in a porous-medium-embedded homogenous nanofluid flow between two stretchable spinning disks is crucial since spinning disks are prevalent in many engineering and technological applications. The objective of this research was to analyze the influences of these parameters using the Cattaneo-Christov heat flux model against the flow’s temperature, velocity and concentration profiles. Temperature profile is a decreasing function of thermal relaxation time parameter due to the particles require a longer period to transfer heat to the next particles. The rates of heat transfer at both spinning disks decrease as values of heat generation, Eckert number, Prandtl number, Brownian diffusion, thermophoresis diffusion and rotation ratio increase. The disks’ rates of mass transfer decrease with more thermophoresis diffusion, heat generation, heat transfer dissipation, and momentum diffusivity, but they increase with thermal radiation parameter. The current work attempts to include the transport profile of a Buongiorno’s nanofluid embedded in a Darcian porous medium between dual spinning disks with magnetic field, thermal radiation and generation of heat using the heat flux model of Cattaneo-Christov’s. Von Karman transformations are utilized to transform the nonlinear partial differential equations of fluid dynamics into coupled nonlinear ordinary differential equations (ODEs). These coupled ODEs are later solved by employing a shooting method with MATLAB bvp4c algorithm. All numerical evidences from this investigation are conferred through tables and figures after validation of present computations.

Assessment of turbulent heat flux models for URANS simulations of turbulent buoyant flows in ROCOM tests

Turbulent mixing in buoyant flows is an essential mechanism involved in many scenarios related to nuclear safety in nuclear power plants. Comprehensive understanding and accurate predictions of turbulent buoyant flows in the reactor are of crucial importance, due to the function of mitigating the potential detrimental consequences during postulated accidents. The present study uses URANS methodology to investigate the buoyancy-influenced flows in the reactor pressure vessel under the main steam line break accident scenarios. With a particular focus on the influence of turbulent heat flux closure models, various combinations of two turbulence models and three turbulent heat flux models are utilized for the numerical simulations of three ROCOM tests which have different characteristic features in terms of the flow rate and fluid density difference between loops. The simulation results are compared with experimental measurements of the so-called mixing scalar in the downcomer and at the core inlet. The study shows that the anisotropic turbulent heat flux models are able to improve the accuracy of the predictions under conditions of strong buoyancy whilst in the weak buoyancy case, a major role is played by the selected turbulence models with essentially a negligible influence of the turbulent heat flux closure models.

Performance-based numerical appraisal of hybrid and nanofluid flows with Cattaneo-Christov heat flux model in a rotating frame with thermal stratification

Performance-based numerical appraisal of hybrid and nanofluid flows with Cattaneo-Christov heat flux model in a rotating frame with thermal stratification

Near wall effects on the premixed head-on hydrogen/air flame

The paper focuses on laminar and turbulent premixed head-on hydrogen/air flames interacting with inert, non-reacting walls. Both adiabatic and isothermal (450K) walls are considered in a counterflow-like, statistically stationary configuration. In the laminar condition, the flame-wall distance and isothermal-wall heat flux are studied under different strain rates. In the turbulent condition, interactions between turbulent, thermal and chemical effects are analyzed via direct numerical simulations. Influences on the flame dynamics due to near wall effects are characterized by conditional statistics on the flame fronts, such as the flame front temperature, thickness and the heat release rate. Compared with the single-step chemistry results, the detailed chemical reaction mechanism brings new and more complicated physics. Because of the differential diffusion between heat and mass, the flame front topology associated with major species changes with the wall boundaries. Accounting for contributions from various reacting species, a newly defined mean flame displacement speed has been proposed to quantify the movement of the turbulent flame zone. Interestingly, the wall heat flux model developed from the single-step chemistry remains applicable even for the detailed chemistry case with good predictability for both laminar and turbulent flames.

An axisymmetric flow analysis by means of tangent hyperbolic fluid with Cattaneo-Christov heat and mass flux model

In present analysis three dimensional steady, axisymmetric, incompressible, non-Newtonian tangent hyperbolic flow of nanofluid due to rotating disk is investigated. A rotating disc is a phenomena in which a disc rotates around an axis at a constant angular velocity and each point on the disc follows a circle's arc. The force necessary to move the disc to overcome frictional resistance is determined by the shear stress between the disc and the rotating fluid and the heat transfer is affected by the local flow field. The heat and mass transfer field is explored in the existence of chemical reaction and Cattaneo-Christov heat and mass flux model. By using similarities transformations, the supreme partial differential equations of the problem are turned into typical differential equations respectively. The determining differential equations are solved on MATLAB software by using bvp4c method that has been cracked through shooting technique. The deviation of velocity, temperature and mass profiles for different inputs of power-law index, Prandtl number, Brownian motion parameter, Schmidt number, thermophoretic parameter, heat and mass relaxation time parameters and chemical reaction parameter are displayed via graphs. The increment happens in radial velocity field whereas tangential and axial velocity fields reduces due to power index parameter n. The results show that for Cattaneo-Christov model, the temperature and concentration profiles exhibit reducing behaviour than that of Fourier's classical model. The concentration within fluid declined due to chemical reaction.

Modeling the thermal conduction in the solar atmosphere with the code MANCHA3D

Context. Thermal conductivity is one of the important mechanisms of heat transfer in the solar corona. In the limit of strongly magnetized plasma, it is typically modeled by Spitzer’s expression where the heat flux is aligned with the magnetic field. Aims. This paper describes the implementation of the heat conduction into the code MANCHA3D with an aim of extending single-fluid MHD simulations from the upper convection zone into the solar corona. Methods. Two different schemes to model heat conduction are implemented: (1) a standard scheme where a parabolic term is added to the energy equation, and (2) a scheme where the hyperbolic heat flux equation is solved. Results. The first scheme limits the time step due to the explicit integration of a parabolic term, which makes the simulations computationally expensive. The second scheme solves the limitations on the time step by artificially limiting the heat conduction speed to computationally manageable values. The validation of both schemes is carried out with standard tests in one, two, and three spatial dimensions. Furthermore, we implement the model for heat flux derived by Braginskii (1965, Reviews of Plasma Physics, 205) in its most general form, when the expression for the heat flux depends on the ratio of the collisional to cyclotron frequencies of the plasma, and, therefore on the magnetic field strength. Additionally, our implementation takes into account the heat conduction in parallel, perpendicular, and transverse directions, and provides the contributions from ions and electrons separately. The model recovers Spitzer’s expression for parallel thermal conductivity in the strongly magnetized limit but also transitions smoothly between field-aligned conductivity and isotropic conductivity for regions with a low or null magnetic field. We describe the details of the implementation of Braginskii’s thermal conductivity using a combination of the first scheme for the perpendicular and transverse directions and the second scheme for the parallel component. We estimate thermal conductivities in a quiet-Sun model. In this model, we find that the perpendicular and transverse components for electrons and ions and the parallel component for ions might have some significance below the transition region. Above the transition region only the parallel component for ions might be important. Finally, we present a two-dimensional test for heat conduction using realistic values of the solar atmosphere where we prove the robustness of the two schemes implemented and show that our adaptation of the hyperbolic treatment offers a great advantage over the computational cost of the simulations.