Heat Flux Model Research Articles

Intelligent Predictive Networks for Cattaneo-Christov Heat and Mass Transfer Dissipated Williamson Fluid Through Double Stratification

This study aims to develop an efficient predictive model for Cattaneo-Christov heat and mass transformation of dissipative Williamson fluid with the effects of double stratification (CCHMT-DWF-DS) using the Levenberg-Marquardt Backpropagation (LMA-BP) algorithm. The under-consideration Williamson fluid flow is magneto-hydro-dynamic, incompressible and two-dimensional through a stretching sheet. The mathematical model of nonlinear partial differential equations for physical phenomena is transformed into ordinary differential equations by means of renowned similarity transformations. The solutions of physical problem are computed by bvp4c technique through MATLAB. The LMA-BP is employed to train a backward neural network capable of accurately predicting velocity, temperature, and concentration profiles under various physical conditions such as changes in the Hartmann number , Prandtl number , Schmidt number , Williamson parameter , the relaxation time of temperature , the relaxation time of concentration , temperature stratification , and concentration stratification for generating a variety of graphical outcomes and statistics. This research is significant for its innovative use of the LMA-BP in analyzing the complex dynamics of non-Newtonian fluids specifically the Williamson fluid, alongside the Cattaneo-Christov heat and mass flux model. The obtaining graphs have been discussed in detail. The thermal and solutal relaxation factors reduce heat and mass flow while fluid motion is delayed by the time-dependent parameter and further reduced by the Hartman number. The Cattaneo-Christov heat flux model enhances simulation accuracy by integrating temporal delays in heat transfer, proving beneficial for sophisticated industrial and scientific endeavors related to non-Newtonian fluids. This analysis offers a powerful predictive tool for applications in thermal management, industrial cooling systems, and biomedical fluid dynamics, advancing machine learning in fluid mechanics.

Natural convection and variable fluid properties of tangent hyperbolic nanofluid flow with Cattaneo-Christov theories and heat generation

The main aim behind this work is that we have to determine the enhancement that happens in thermal conductivity by using the Buongiorno model of nanofluid when the nanofluid particles are added to the tangent hyperbolic base fluid moving above the stretched surface. The viscosity of tangent hyperbolic nanofluid is assumed to be temperature-dependent. The modified form of the Fourier law of heat conduction motivated us; therefore, the Cattaneo-Christov heat and mass flux model is considered to observe its significance for heat and mass transport. The chemical reaction and heat generation are also considered to determine their influence on temperature and concentration gradients. This study is crucial because of its application in industrial manufacturing processes such as the coating of wire, the thinning of copper, the production of paper, photographic films, hot rolling, and the purification of crude oil. In electronic cooling systems, the efficient dissipation of heat in smartphones, computers, and data centers is critical to preventing overheating. Nanofluids, with their enhanced thermal properties, can significantly improve heat transfer rates, ensuring better performance, stability, and energy savings. The partial governing equations arising from fluid flow, mass, and heat transfer are transformed into ordinary differential equations via appropriate similarity variables. The obtained ordinary differential equations are solved numerically by using the Runge-Kutta Fehlberg method in the MATLAB software. The effects of the emerging parameters are represented through graphs. According to the results, the velocity profile upsurges due to the natural convection parameters and curvature parameter, while the power law index declines the velocity profile. As the Brownian motion coefficient rises, the concentration profile diminishes while the temperature profile increases. Both the concentration and temperature profiles increase for larger values of the thermophoresis parameter. The concentration profile declines for larger values of chemical reaction parameters, and enhancement happens in the temperature region.

Viscosity models of tri-hybrid non-Newtonian nanofluid with Cattaneo–Christov heat flux, thermal radiation, Ohmic heating and convective boundary condition

PurposeThis study is to examine the impact of viscous dissipation, thermal radiation and Ohmic heating on the magnetohydrodynamic (MHD) flow with thermal and mass transport over a horizontally stretching surface. Cattaneo–Christov heat flux model on a non-Newtonian viscous fluid along with two viscosity models and convective boundary condition has been employed. Tri-hybrid nanofluid has been used to increase thermal performance.Design/methodology/approachGoverning mathematical model has been transposed into a dimensionless system of ordinary differential equations (ODEs) by applying suitable similarity transformation. Numerical solution has been found by applying the bvp4c shooting method in MATLAB software.FindingsVelocity and thermal profiles of Model-I dominate the profiles of Model-II whereas opposite behavior is noticed for concentration profiles. It is concluded that there is an increase in temperature due to thermal radiation, viscous dissipation and convective boundary condition.Originality/valueThe novelty of presented work is to examine the impact of Ohmic heating, viscous dissipation, thermal radiation, chemical reaction and two models of viscosity on Cattaneo–Christov heat flux model of tri-hybrid non-Newtonian nanofluid with convective boundary constraint. The accuracy and effectiveness of presented model have been compared with already published research.

Analysis of variables in finite element analysis for multi-pass welding in nuclear power plant components, part 1: Comprehensive study with experimental validation using scientific weld specimen

The influence of various parameters in welding simulations using finite element analysis (FEA) was investigated in this study. Welding experiments and finite element simulations were conducted to analyze residual stress and post-welding distortion. It was a specially designed V-groove specimen, filled with bead passes using Gas Tungsten Arc Welding (GTAW), that facilitated the measurement of distorted shapes and residual stress. Advanced measurement techniques, including three-dimensional laser scanning and the contour method, were used to capture detailed data on the welded specimen. Three different heat source models (body heat flux, temperature boundary, and Goldak's double-ellipsoidal model) were employed in the simulations, and their effect on residual stress distributions was analyzed. Additionally, the effects of hardening models, bead deposition methods, bead shape modeling, welding sequences, and lumping of weld passes on simulation were systematically analyzed. The findings suggest that a combined approach using different modeling techniques and careful calibration of parameters can enhance the reliability of simulations in predicting weld residual stress and distortions.

Calculation of in-situ steady-state heat flux on EAST lower divertor

Heat flux is a key issue in tokamak devices. The non-uniform high heat flux on Plasma-Facing Components (PFCs) has led to local severe damage, including cracks and melting, in current tokamaks such as EAST and WEST. To characterize the non-uniform heat flux loading on the divertor surfaces, the parallel incident heat flux q‖, the decay length λq along the radial direction and the Gaussian spreading width S are used. The q‖ can lead to a very high peak heat flux loading on the divertor surfaces, which may cause critical heat flux problems. Additionally, the decay length is a key consideration for future tokamak designs like ITER. Every effort on the present tokamak devices contributes to updating the scaling of the heat flux. In EAST, a calculation method based on a high spatial resolution IR camera is employed to obtain the heat flux and decay length. The main process involves comparing the surface temperature distribution calculated by Fluent simulation with that measured by an infrared camera. Taking a high heating source discharge (#123059 ∼ 10 MW heating source) as an example, the heat flux is as follows: q‖=216-14+19 MW/m2, with λq=6.2-1.1+1 mm, and S=1.2±0.4 mm; it is in line with Langmuir probe data. The infrared-based heat flux calculation method can calculate the peak incident heat flux and the decay length simultaneously, its result can help to update the scaling model of heat flux, thus not only helping to improve the present device but also offering important reference for future tokamaks

Forecasting the flame geometry and ground received radiative heat fluxes of two parallel adjacent fires of hydrocarbon fuel with crosswinds

Radiative heat transfer in fires is a critical parameter and a key aspect of gas storage and fire prevention design. In this study, the flame geometric scale characteristics and ground-received radiative heat fluxes from two parallel adjacent hydrocarbon fuel fires with crosswinds were examined. The separation distance between the two parallel flames, crosswind speed, and heat release rates were considered. The experimental results indicated that the flame tilt angle of the two parallel flames increased with increasing crosswinds. The horizontal flame length scale of the two adjacent parallel flames first increased with the crosswind until a critical point was reached, followed by a fluctuation with a further increase in the wind speed. To further quantify this flame phenomenon, a physical model of the flame interaction between two parallel fires under the effects of crosswinds was proposed. The model analyzed major factors affecting the geometrical parameters of the flame, including the inertial force caused by the crosswind, thermal buoyancy from flame combustion, and the interaction and separation distance between the two fires. Additionally, correlations between the flame tilt angle and the horizontal flame length scale of the two adjacent flames were proposed. It was also demonstrated that the ground-received downstream radiative heat fluxes were the dominant parameters determining flame spread. Based on the assumption of the flame geometry of two adjacent parallel fires, the viewing factor was revised, and the relationship between the position of the radiant point and the horizontal length of the flame was considered in the flame model. Furthermore, based on the updated viewing factor of two parallel adjacent flames, a prediction model of ground-received radiative heat fluxes was proposed, which successfully estimated the variation of ground-received downstream radiative heat flux profiles along the centerline of the two parallel flames under crosswind conditions. This estimation is crucial for future fire research, particularly cross-wind-related experiments.

Consequence of Cattaneo-Christov heat and mass flux models on bioconvective flow of dusty hybrid nanofluid over a Riga plate in the presence of gyrotactic microorganisms and Stephan blowing impacts

This study investigates the impact of the Stephan blowing and Cattaneo-Christov flux model on bioconvective flow of dusty hybrid nanofluid over a Riga plate in the presence of gyrotactic microorganisms and variable dust particles volume friction. Mass and heat phenomena are explored in the context of Stefan blowing impacts. The hybrid nanofluid consists of nanoparticles of MgO and Ag base fluid water. The Cattaneo-Christov mass and heat flux model has a significant impact on the bioconvective flow. The model predicts a slower temperature distribution and a higher concentration gradient than the traditional Fick's law and Fourier's law, respectively. The occurrence of gyrotactic microorganisms enhance the flow characteristics. This model is important for optimizing mass and heat transfer in a variety of engineering systems, including heating and cooling technologies, where effective thermal control is essential. It can be used by employing the regulated migration of microbes. By maximizing the removal of impurities, it helps with the design of sophisticated water purification systems in environmental engineering. The amalgamation of gyrotactic microorganisms and Stefan blowing effects augments the comprehension of intricate fluid dynamics, maybe resulting in advancements in microfluidic apparatuses and bio-inspired technologies. In order to transform the controlling PDEs into nonlinear ODEs, a new set of non-dimensional variables is used. The MATLAB (RKF-45th) technique is then used to resolve the ODEs numerically. As the Stephan blowing parameter (0.1≤Sb≤1.9) increases, the outcomes show that the flow distributions upsurge for both the dust and fluid phases, but the dust and fluid phase thermal distributions drop.

Enhancing thermal field prediction in a jet in cross flow through turbulent heat flux model optimization by using large eddy simulation

High fidelity big data obtained from highly accurate large eddy simulation (LES) was utilized to enhance current models for turbulent heat transfer, boosting the precision of the realizable Reynolds averaged Navier Stokes (RANS) k-ε model in forecasting film cooling thermal field. The LES analysis was conducted on a flat plate with a jet in crossflow, at a primary flow Reynolds number (Re) of around 17382. Post-validation of the LES outcomes, a data analysis, and a numerical optimization (gradient descent algorithm) technique were employed to fine-tune three chosen models for turbulent Prandtl number using data near the coolant wall. In order to demonstrate the effectiveness of these refined models for RANS simulations of various film cooling setups with distinct shapes and flow situations, a series of simulations were executed, encompassing two curved surfaces to simulate flow around leading-edge and over the blade suction side. The optimized models exhibited marked enhancement in forecasting film cooling effectiveness in both averaged lateral and longitudinal directions (achieving reductions in numerical errors of up to 68.0 % and 43.67 % respectively). These fine-tuned models were proven suitable for use across different geometries and flow conditions according to their performance in three analyzed problems.

Entropy optimization in ternary hybrid nanofluid flow over a convectively heated bidirectional stretching sheet with Lorentz forces and viscous dissipation: A Cattaneo–Christov heat flux model

Bidirectional stretching sheet models can represent surfaces in heat exchangers where fluids flow under continuous deformation. Ternary hybrid nanofluids could be employed in these systems to increase heat transfer rates between fluids in heat exchangers and improve the efficiency of energy conversion processes. In this work, we explore the novel application of a ternary hybrid nanofluid (water with titanium dioxide, cobalt ferrite, and magnesium oxide nanoparticles) for enhanced heat transfer in heat exchangers modeled by a bidirectional stretching sheet. This approach offers a potential advancement over traditional nanofluids (with one or two nanoparticles). Furthermore, we present a comprehensive analysis that incorporates ohmic heating, Cattaneo–Christov heat flux, thermal radiation, viscous dissipation, and irreversibility. The governing equations are transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations and then solved using the bvp4c solver, a MATLAB built-in function. This study's findings reveal that the Eckert number and radiation parameter increase fluid temperature, while the thermal relaxation parameter leads to a reduction in the temperature of the fluid. It is detected that an increase in magnetic field parameter and volume fraction of [Formula: see text] results in a decline of the skin friction factors in both directions. It is revealed that there is a reduction in the Nusselt number with the rise in Eckert number ([Formula: see text]), and the same number declines at a rate of 0.8252 when [Formula: see text]. It is noticed that the skin friction coefficient declines at a rate of 0.62179204 (in case of x-direction) and 0.621791816 (in case of y-direction), respectively, when the values of magnetic field parameter lie between 0 and 3.5. Furthermore, it is noticed that an upsurge in thermal relaxation parameter results in a fall in the temperature of the fluid.

Effect of Cattaneo–Christov heat flux model and elastic deformation on Walters'B viscoelastic fluid flow with porosity

In the current work, flow of 2-D MHD Walters'B viscoelastic fluid is discussed in the existence of elastic deformation, Cattaneo–Christov Heat Flux Model (CCHFM), heat source, Newtonian heating, viscous dissipation and porous medium. Dimensionless equations that are in charge of the problem's analysis are produced by using the suitable similarity transformation, and Optimal Auxiliary Functions Method (OAFM) is employed to solve them. In the ongoing investigation, the main results are decreasing behavior of temperature profile for the thermal relaxation parameter and elastic deformation parameter, while the reverse effect is noticed while increasing the Weissenberg number and porosity parameter. Our findings reveal significant insights into the fluid dynamics and heat transfer characteristics. Integrating the Cattaneo–Christov heat flux model and elastic deformation analysis in Walters'B viscoelastic fluid flow having its importance in polymer processing, aerospace engineering and waste treatment systems.

Influence of Cattaneo-Christov Heat Flux Model Rotating Maxwell Nanofluid with MHD and Double Stratification Across a Bidirectional Stretching Surface

Influence of Cattaneo-Christov Heat Flux Model Rotating Maxwell Nanofluid with MHD and Double Stratification Across a Bidirectional Stretching Surface

Non-similar analysis of two-phase hybrid nano-fluid flow with Cattaneo-Christov heat flux model: a computational study

The purpose of this research elaborates the behaviour of the two-phase hybrid nano-fluid flow of viscous fluid through the stretching sheet. Impacts of heat transfer, for MHD two-dimensional steady flow over stretching surface with Cattaneo-Christov (CC) model are discussed. Bio-convective, thermal radiation and convective conditions are considered. Porous surface and velocity slip effects are also considered. Darcy-Forchheimer relation characterizes porous medium. The governing equations are solved through MATLAB. Plots of temperature and velocity fields are discussed via various estimations of emerging variables. Results findings shows the velocity profile decreases in case of both simple and hybrid nano-fluids for higher estimations of magnetic parameter and local inertia coefficient parameter. Fluid temperature reduces for maximum thermal relaxation parameter and possess higher values against radiation parameter. Microorganism profile reduces bio-convection Lewis number but increases for the magnetic parameter. Prominent results from this study include determining the effective parameters to enhance heat transfer efficiency and defining the circumstances in which the nano-fluid performs better than traditional fluids. These discoveries offer significant perspectives on the utilization of Cattaneo-Christov model with hybrid nano-fluid flow in comprehensive thermal management systems and establish a basis for subsequent practical and theoretical investigations within the domain.

A modified algebraic turbulent heat flux model for non-equilibrium and rotating flow and its application in film cooling simulation of a rotating turbine blade

Thermal fields and cooling flows over rotating turbine blades are usually a non-equilibrium anisotropic flow, and most turbulence models in RANS simulations do not provide acceptable accuracy. A modified model is proposed and assessed here. This is based on an explicit algebraic heat flux model that is a low-Reynolds-number version of the higher order generalized gradient diffusion hypothesis turbulent heat flux model. The presented model, called “Non-equilibrium and Sensible to Rotation Algebraic Heat Flux Model” or “NSR-AHFM” includes additional production terms added to the second moment closure of turbulent heat flux transport equation that considers system rotation and non-equilibrium effects in velocity field, while maintaining the frame invariance during transformation to a rotating coordinate system. The model was initially tested through a-priori analysis, comparing the model to corresponding quantities obtained from Direct Numerical Simulations, allowing for the identification of suitable model parameters. Subsequently, the proposed modified model was implemented in a CFD code to a representative configuration (i.e., rotating turbine blade) and results were compared against available experimental data from literature. The present model was undergone a comparative analysis with other similar models in both stationary and rotating channel flow scenarios. Also, the present model was applied to a film cooling simulation of a rotating turbine blade in different rotational speeds. The findings indicate that the present model exhibits superior performance when compared to other models. Moreover, its behavior aligns consistently with the underlying physics governing the flow dynamics of the rotating channel.

Thermal Performance of Cattaneo-Christov Heat Flux Model on 3D Micropolar Fluid with Motile Microbes Across a Permeable Surface

Thermal Performance of Cattaneo-Christov Heat Flux Model on 3D Micropolar Fluid with Motile Microbes Across a Permeable Surface

Impact of chemical reaction on the Cattaneo–Christov heat flux model for viscoelastic flow over an exponentially stretching sheet

In this article, the numerical solutions for the heat transfer flow of an upper-convected Maxwell fluid across an exponentially stretched sheet with a chemical reaction on the Cattaneo–Christov heat flux model have been investigated. Using similarity transformation, the controlling system of nonlinear partial differential equations was transformed into a system of ordinary differential equations. The resulting converted equations were solved numerically by a successive linearization method with the help of MATLAB software. A graphic representation was created to analyze the physical insights of the relevant flow characteristics. The findings were presented in the form of velocity, temperature, and concentration profiles. As the relaxation time parameter varied, the local Nusselt number increased. The thermal relaxation time was shown to have an inverse relationship with fluid temperature. Furthermore, the concentration boundary layer becomes thinner as the levels of the reaction rate parameter increase. The results of this model can be applicable in biological fluids and industrial situations. Excellent agreement exists between the analysis's findings and those of the previous studies.

Numerical modeling of heat flux in ultrasonic-assisted grinding of difficult-to-cut materials with a pressurized lubrication system

The temperature measurement during grinding process is difficult due to work–wheel interactions and nearby coolant layers. Surface integrity also gets affected by the grinding burns caused due to high heat generation. Therefore, the theoretical temperature estimation could provide prior detection of grinding burns. This article presents an analytical model to predict the heat flux in pressurized lubricated ultrasonic-assisted surface grinding of Nimonic 80 A using Cubic Boron Nitride (cBN) grinding wheel (vitrified grinding bond, grit 80/100, concentration 100%). In this process, the high frequency of ultrasonic vibration and low amplitude is employed to vibrate the workpiece. In the current modeling approach, the motion analysis of grains has been estimated initially, which provided the effective grinding force. This effective grinding force was then utilized to obtain the analytical model of heat flux. Finally, the model was formulated by considering the effect of heat conducted into the material and heat released due to the lubrication system. The established model comprised the effects of lubricating and machining parameters such as dynamic viscosity of cutting fluid, pressure, diameter and length of cutting fluid pipes, width of cut, frequency, speed of table, amplitude, depth of cut and speed of the wheel. This numerical model revealed affirmative results substantiated by experimentally procured data. This developed model can add to the direction of sustainable grinding approach.

Spatial substrate heterogeneity limits microbial growth as revealed by the joint experimental quantification and modeling of carbon and heat fluxes

Spatial heterogeneity is a pervasive feature of soils, affecting the distribution of carbon sources as well as their microbial consumers. Heterogeneous addition of substrates typically results in delayed microbial growth compared to homogeneous addition, and this effect has frequently been attributed to spatial separation of microorganisms from their food. We investigated the importance of two other potential causes of this effect, the availability of nutrients and oxygen, by measuring heat and CO2 release along with O2 consumption from soil samples after homogeneous or heterogeneous addition of glucose as well as with or without further addition of a nutrient solution. We then employed a microbial-explicit model to quantitatively interpret our observations. The results revealed that delayed growth after spatially heterogeneous substrate addition was primarily caused by nutrient limitation. While sufficient co-location of all entities - substrate, microorganisms, and nutrients - is required for optimal growth, spatial separation of glucose and microorganisms only played a minor role in our experiment. Model simulations captured the dynamics based on aerobic growth and maintenance, utilizing a simple formulation of nutrient limitation coupled with dynamic transition of microbes between activity and dormancy. The model predicted an overall lower microbial activity over the course of the incubation in treatments with heterogeneous substrate addition. Despite reduced rates, neither the experimental carbon and energy balances nor modeling showed an effect of heterogeneity on the growth efficiency after 50 h of incubation. In all treatments, energy use efficiency exceeded carbon use efficiency by 9–21%. We found no evidence of anaerobiosis. The application of a bioenergetic framework facilitated the interpretation of complex experimental data and quantitatively captured the mechanisms underlying the effects of spatial heterogeneity.

Thermal analysis in Darcy-Forchheimer hybrid nanofluid through a Riga plate: An ANN optimization

In the present study, a double-hybrid nanofluid's Darcy-Forchheimer flow behavior over a Riga plate with the presence of radiation and heat source impacts is examined. Two distinct nanoparticles as Silicon Carbide (SIC), and Graphite (C) with a base fluid of Ethylene glycol (C2H6O2) are taken into consideration. The model of Cattaneo-Christov heat flux is discussed in the energy and mass equation. The symmetry variables are utilized to remodel the boundary conditions and governing flow models into non-linear ordinary differential equations. The redesigned ordinary differential equations are numerically computed using bvp4c in MATLAB. Graphical representations are used to study how distinct parameters create variations in the concentration, temperature, and velocity profile. The present study shows that the velocity profile decreases with an upsurge in the Hartmann number. The current analysis determined that the fluid velocity declines and the Forchhiemer number (Fr) increases. The fluid concentration increases when temperature temperature-dependent coefficient (B) rises. The significance of emerging parameters on skin friction, Nusselt number, and Sherwood number are computed in tabular shape. Artificial neural networking (ANN) is applied to optimize physical quantities of data, by training, validation, and testing, to check the accuracy of the data.

Radiating heat effect on Powell–Eyring blood-based hybrid nanofluid over a Riga plate with thermal stratification CattaneoChristov heat flux model

The contemporary investigation deliberate the influence of radiating heat on the flow of Powell-Eyring fluid over a Riga plate subjected to thermal stratification, utilizing the CattaneoChristov heat flux model. Additionally, the insertion of heat sources along with thermal radiation energies the study significantly. The basic equations that correspond to conservation principles of mass, momentum, energy are formulated for Powell-Eyring fluid. The CattaneoChristov heat flux model is incorporated for the non-Fourier effects arising due to thermal relaxation phenomena are also taken into account. The resulting nonlinear partial differential equations are transmuted into ordinary equations and numerically solved using the Runge-Kutta method combined with shooting approach, which is a reliable numerical methodology. The impacts of pertinent factors on the momentum and temperature profiles are scrutinized systematically. Additionally, the imposition of these factors on shear rate and Nusselt number are deployed, which are crucial for practical applications and heat transfer enhancement strategies. As a novelty, the optimization of share rate together with heat transmission rate are obtained by employing a innovative statistical procedure of response surface methodology followed by analysis of variance, a hypothetical test. The outcomes of this study of heat transmission processes in Powell–Eyring fluids under thermal radiation over a Riga plate involving thermal stratification have potential applications in various engineering and industrial processes including thermal management, materials processing, and energy conversion devices.

Development and application of turbulent heat flux model for lead-bismuth eutectic based on deep learning

Existing turbulent heat flux (THF) closure models in Reynolds-averaged Navier–Stokes simulation of scalar transport are insufficient on accuracy for fluids with a low Prandtl number (Pr), such as lead–bismuth eutectic (LBE), especially under complex operating conditions like in heat exchangers of nuclear reactors. This paper aims to propose a THF model suitable for such conditions. Firstly, we established a high-fidelity database of forced convection flow past two tandem cylinders under a Reynolds number (Re) of 1 × 105 and various low Pr conditions by hybrid large eddy simulation and direct numerical simulation algorithm. Based on the database, a deep learning architecture was then built and trained to predict dimensionless THF. Finally, a posteriori test proved that the proposed THF model helps to improve the prediction performance for temperature fields and also performs well when extrapolated to cases of LBE past the tube bundles, especially under the case with large Peclet numbers.