Heat Transfer Problem Research Articles

A Modified Enthalpic Lattice Boltzmann Method for Simulating Conjugate Heat Transfer Problems in Non-Homogeneous Media

A Modified Enthalpic Lattice Boltzmann Method for Simulating Conjugate Heat Transfer Problems in Non-Homogeneous Media

Nonlinear coupled multi-physics field analysis of permanent magnet synchronous motor combining finite element analysis with optimized meshless method

Aiming at significant disadvantages of finite element analysis (FEA) performed in coupled multiphysics field calculation, including high computing cost and strong dependency on meshing quality. Taking a high-speed permanent magnet synchronous motor (P MSM) as an example, an approach combining FEA with optimized meshless method is proposed to solve the heat transfer problem. Firstly, electromagnetic losses under rated and 1.2 times overloaded operation conditions are calculated using FEA respectively. Secondly, three-dimensional FEA flow models considering the influence of viscosity varying with temperature are established. Thirdly, convective heat transfer coefficients are calculated as the boundary condition, after which the electromagnetic losses as heat sources are mapped to the threedimensional steady-state temperature field calculations using FEA and conventional meshless method respectively. Applying the above two methods, a singular boundary method (SBM) is employed to replace the temporal derivative term of the transient calculation equation. Finally, to mitigate the illconditioned matrix appearing in the conventional meshless method coupled with FEA, an optimized meshless method is proposed to recalculate the heat transfer equation. After that, the calculation results of the above methods are compared with experimental results. This research is beneficial for the multiphysical coupling analysis of electrical equipment with complex structures considering nonlinear factors.

An experimental and numerical investigation into the sensitivity of Rayleigh–Bénard convection to heat loss through the sidewalls

Thermal buoyancy flows and related heat transfer problems play a crucial role in a variety of fields and industrial applications. The present study is structured around the main objective of systematically investigating the response of fluid convection of the Rayleigh–Bénard type to heat loss taking place through the lateral walls of the considered fluid container. We elucidate, both experimentally and numerically, new aspects which deeply affect the dynamics when the classical assumptions of adiabatic or conducting walls cease to be valid. The emerging spatio-temporal behaviors are examined with respect to several parameters or conditions, including the dimensionality of the system (made accessible by dedicated numerical simulations based on the time-dependent and non-linear governing equations), the average temperature of the liquid, the applied temperature difference, the dependence of fluid properties on temperature and the intensity of heat transfer to the ambient. The results reveal the interesting triadic relationship among the heat exchanged through non-thermally controlled walls, the hierarchy of bifurcations displayed by the flow and the related multiplicity of solutions.

A 3D symmetry-preserving simulation of a concentrated photovoltaic thermal (CPVT) solar collector

In this work, a general collocated and unconditionally stable framework on unstructured meshes for solving Conjugate Heat Transfer (CHT) problems is presented by means of preserving the underlying symmetries of the continuous differential operators, thus not introducing uncontrolled artificial numerical dissipation to our system. Then, this framework is applied to solve a Concentrated PhotoVoltaic Thermal (CPVT) Solar Collector. Furthermore, a new boundary condition is implemented to consider the heat transfer between enclosed elements, including radiation. The model is validated using experimental data.

Application of the localized method of fundamental solutions to heat transfer problems

A localized version of the Method of Fundamental Solutions is applied to the 2D steady heat transfer equation with spatially varying thermal conductivity. Though the corresponding fundamental solution cannot be computed in general, the localization splits the original problem into several subproblems defined on small subdomains; in these subdomains, the subproblems are approximately converted to certain convection-diffusion equations with constant coefficients, so that the Method of Fundamental Solutions is applicable. In each subdomain, the corresponding subproblem is solved separately. This results in an iterative method, which mimics the overlapping (alternating) Schwarz method. Due to its advantageous numerical properties, the technique seems a useful generalization of the Method of Fundamental Solutions. The method is illustrated through numerical examples.

Semidiscrete and Asymptotic Approximations of the Nonstationary Complex Heat Transfer Problem in a System of Grey Square Rods

Semidiscrete and Asymptotic Approximations of the Nonstationary Complex Heat Transfer Problem in a System of Grey Square Rods

The thermal perception of outdoor urban spaces in a hot arid climate: A structural equation modelling (SEM) approach

Human thermal comfort is linked to multi-sensory attributes and psychological cognition besides the influence of prominent meteorological parameters. To date, even the most advanced thermal comfort models like UTCI consider the interaction between human and external surroundings to be a heat transfer problem applying thermodynamic equations in the derivation behind thermal comfort indices. Machine learning (ML) models offer the advantage of improving the accuracy of predictor variable, but they fail to determine the relationship between the independent variables and data-driven prediction models. Structural Equation Modelling (SEM), an advanced modelling technique, can expose all hidden relationships among variables using latent variables while not being data-driven like ML. This study aimed to develop a structural framework which systematically explains these relationships and quantify the effects of 24 variables on outdoor thermal comfort using SEM due to its ability to represents the response of the dependent variable to a unit change in an explanatory variable. The method employed 635 structured interviews, observations, and wide-ranging micrometeorological measurements conducted concurrently in three Pedestrianized urban alleys in Cairo. The model statistically confirmed the hypothesis that overall thermal comfort in urban spaces is significantly influenced by multiple factors. Of these, background microclimatic conditions had the greatest relevance and certain urban features the least. 1 unit increase microclimate leads to a change in thermal comfort by 0.423 and 0.349 in summer and winter, respectively. In terms of thermal perception, the model shows that individuals are willing to tolerate a wider range if certain urban features are present such as shaded seating opportunities. These outcomes may aid to provide important guidance for urban designers to enhance thermal perception in urban streets.

A novel thermal turbulence reconstruction method using proper orthogonal decomposition and compressed sensing coupled based on improved particle swarm optimization for sensor arrangement

With the development of offshore wind turbine single power toward levels beyond 10 MW, the increase in heat loss of components in the nacelle leads to a high local temperature in the nacelle, which seriously affects the performance of the components. Accurate reconstruction and control of thermal turbulence in the nacelle can alleviate this problem. However, the physical environment of thermal turbulence in the nacelle is very complex. Due to the intermittent and fluctuating nature of turbulence, the turbulent thermal environment is highly nonlinear when coupled with the temperature field. This leads to large reconstruction errors in existing reconstruction methods. Therefore, we improve the sparse reconstruction method for compressed sensing (CS) based on the concept of virtual time using proper orthogonal decomposition (POD). The POD-CS method links the turbulent thermal environment reconstruction with matrix decomposition to ensure computational accuracy and computational efficiency. The improved particle swarm optimization (PSO) is used to optimize the sensor arrangement to ensure stability of the reconstruction and to save sensor resources. We apply this novel and improved PSO-POD-CS coupled reconstruction method to the thermal turbulence reconstruction in the nacelle. The effects of different basis vector dimensions and different sensor location arrangements (boundary and interior) on the reconstruction errors are also evaluated separately, and finally, the desired reconstruction accuracy is obtained. The method is of research value for the reconstruction of conjugate heat transfer problems with high turbulence intensity.

A physics-driven and machine learning-based digital twinning approach to transient thermal systems

PurposeIn this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.Design/methodology/approachTo achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.FindingsThe results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.Originality/valueThe present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.

Multi-Objective Topology Optimization of Conjugate Heat Transfer Using Level Sets and Anisotropic Mesh Adaptation

This study proposes a new computational framework for the multi-objective topology optimization of conjugate heat transfer systems using a continuous adjoint approach. It relies on a monolithic solver for the coupled steady-state Navier–Stokes and heat equations, which combines finite elements stabilized by the variational multi-scale method, level set representations of the fluid–solid interfaces and immersed modeling of heterogeneous materials (fluid–solid) to ensure that the proper amount of heat is exchanged to the ambient fluid by solid objects in arbitrary geometry. At each optimization iteration, anisotropic mesh adaptation is applied in near-wall regions automatically captured by the level set. This considerably cuts the computational effort associated with calling the finite element solver, in comparison to traditional topology optimization algorithms operating on isotropic grids with a comparable refinement level. Given that we operate within the constraint of a specified number of nodes in the mesh, this allows not only to improve the accuracy of interface representation and motion but also to retain the high fidelity of the numerical solutions at the grid points just adjacent to the interface. Finally, the remeshing and resolution steps both run within a highly parallel environment, which makes it possible for the proposed algorithm to tackle large-scale problems in three dimensions with several tens of millions of state degrees of freedom. The developed solver is validated first by minimizing dissipation in a flow splitter device, for which the method delivers relevant optimal designs over a wide range of volume constraints and flow rate distributions over the multiple outlet orifices but yields better accuracy compared to reference data from literature obtained using uniform meshes (in the sense that the layouts are more smooth, and the solutions are better resolved). The scheme is then applied to a two-dimensional heat transfer problem, using bi-objective cost functionals combining flow resistance and thermal recoverable power. A comprehensive parametric study reveals a complex arrangement of optimal solutions on the Pareto front, with multiple branches of symmetric and asymmetric designs, some of them previously unreported. Finally, the algorithmic developments are substantiated with several three-dimensional numerical examples tackled under fixed weights for heat transfer and flow resistance, for which we show that the optimal layouts computed at low Reynolds number, that are intrinsically relevant to a broad range of microfluidic application, can also serve as smooth solutions to high-Reynolds-number engineering problems of practical interest.

A fast fluid–solid coupled heat transfer algorithm based on dividing the development stages of the flow field

In this study, a fast numerical method for solving the forced convection conjugate heat transfer problem was developed. The method first proposes a new dimensionless number (Fs) that represents the degree of influence of convection on the temperature field in the flow field. It delineates the stage of development of the flow field by monitoring the change in Fs to determine the moment when the flow field suspends updating and improve the computational efficiency of the transient temperature field. The accuracy of the algorithm is verified by taking the fluid–solid conjugate heat transfer under forced convection conditions as an example, which can accurately capture the changes of the flow field for a given monitoring step number of 100, and classify the flow field into E3, E4 and E5 development stages according to the judgment criteria. The results show that the higher development stages correspond to smaller levels of root mean square error (RMSE) of monitoring point temperatures within 3600 s of physical simulation time, and stages E3, E4, and E5 can reach the levels of E-2, E-3, and E-4, which are 3.4, 3.3, and 3.1 times faster than the traditional coupled calculations, respectively. The algorithm is still applicable at variable time steps, but it will require a higher number of determinations compared to a fixed step. The initial error of the quasi-steady algorithm can be reduced from the E-1 level to E-4 by choosing a higher stage of development. Finally the algorithm is tested under a variety of conditions by varying the inlet temperature and flow rate and is found to be robust to both device warming and cooling.

A-priori evaluation of data-driven models for large-eddy simulations in Rayleigh–Bénard convection

Natural convection is a commonly occurring heat-transfer problem in many industrial flows and its prediction with conventional large eddy simulations (LES) at higher Rayleigh numbers using progressively coarser grids leads to increasingly inaccurate estimates of important performance indicators, such as Nusselt number (Nu). Thus, to improve the heat transfer predictions, we utilize Gene Expression Programming (GEP) to develop sub-grid scale (SGS) stress and SGS heat-flux models simultaneously for LES. The models’ development is performed using reference direct numerical simulation data of a typical natural convection case, i.e. the Rayleigh–Bénard convection (RBC). The training frameworks are built by using alignment as the evaluation metrics of the basis functions when comparing to the Gaussian-filtered SGS stress and SGS heat-flux. The trained models in isotropic form, by utilizing the L2 norm of the grid cell ΔL2 as the length scale, demonstrate good performance in the bulk region, but less improved performance in the near wall region. It is shown, that for LES of wall-bounded flow, the GEP models in anisotropic form, i.e. using different grid length scale for the different spatial directions, are required to obtain generalized models suitable for different regions. Consequently, the a-priori results demonstrate a significant improvement in the prediction of both instantaneous and mean quantities for a wide range of filter widths.

Heat transfer model analysis of fractional Jeffery-type hybrid nanofluid dripping through a poured microchannel

This study investigates the impact of coupled heat and mass transfer on the peristaltic migration of a magnetohydrodynamic (MHD) stress-strain Jeffery-type hybrid nanofluid flowing through an inclined asymmetric micro-channel with a porous medium. The fundamental two-dimensional momentum and energy transport equations are simplified under the assumptions of long wavelength and low Reynolds number. To solve the momentum and heat transfer problems, two advanced fractional derivative approaches are employed: the fractal integral and the Prabhakar fractional derivative. The pressure difference is determined using numerical integration techniques, such as the Stehfest and Tzou's algorithms. The results are presented through graphs and tables, which illustrate the effects of various parameters on the velocity, heat transfer, and trapping phenomena. As a result, we concluded that, pressure gradients grow with higher Reynolds numbers and channel-inclined angles. The heat transfer rate is observed to decrease as the Darcy number and the orientation of the electromagnetic field increase. When comparing the fractional derivative approaches, the fractal operator exhibits a more significant impact on the momentum profiles compared to the Prabhakar fractional operator. This difference is attributed to the distinct characteristics of the integral kernels associated with each fractional derivative definition. Furthermore, when comparing hybrid nanofluids, water-based (H2O + Ag + TiO2) hybrid fluids have a somewhat more significant effect than (C6H9NaO7 + Ag + TiO2) hybrid nanofluids.

Accurate Temperature Reconstruction in Radiofrequency Ablation for Atherosclerotic Plaques Based on Inverse Heat Transfer Analysis.

Radio frequency ablation has emerged as a widely accepted treatment for atherosclerotic plaques. However, monitoring the temperature field distribution in the blood vessel wall during this procedure presents challenges. This limitation increases the risk of endothelial cell damage and inflammatory responses, potentially leading to lumen restenosis. The aim of this study is to accurately reconstruct the transient temperature distribution by solving a stochastic heat transfer model with uncertain parameters using an inverse heat transfer algorithm and temperature measurement data. The nonlinear least squares optimization method, Levenberg-Marquardt (LM), was employed to solve the inverse heat transfer problem for parameter estimation. Then, to improve the convergence of the algorithm and reduce the computational resources, a method of parameter sensitivity analysis was proposed to select parameters mainly affecting the temperature field. Furthermore, the robustness and accuracy of the algorithm were verified by introducing random noise to the temperature measurements. Despite the high level of temperature measurement noise (ξ = 5%) and larger initial guess deviation, the parameter estimation results remained closely aligned with the actual values, with an overall ERMS consistently below 0.05. The absolute errors between the reconstruction temperature at the measurement points TC1, TC2, and TC3, and the actual temperature, remained within 0.33 °C, 2.4 °C, and 1.17 °C, respectively. The Levenberg-Marquardt algorithm employed in this study proficiently tackled the ill-posed issue of inversion process and obtained a strong consistency between the reconstructed temperature the actual temperature.

A fast Bayesian parallel solution framework for large-scale parameter estimation of 3D inverse heat transfer problems

The inverse heat transfer problems (IHTP) have a wide range of applications in the engineering field. Bayesian methods using Markov Chain Monte Carlo (MCMC) have long been considered as a robust and effective method for solving inverse problems. However, the discretization of the problem domain by the spatio-temporal Galerkin skill, i.e., the finite element interpolation also includes the time dimension, making the scale of the unknown parameters extremely difficult for Bayesian calculations. In this paper, a fast Bayesian parallel sampling (FBPS) framework is proposed for large-scale parameter estimation of benchmark three-dimensional inverse heat transfer problems (3D-IHTP). The FBPS we developed achieves a parameter computation scale of 105 magnitude within minutes, through dimensionality reduction of the space-time dependent problem domain. The Hamiltonian Monte Carlo (HMC) sampler, which is proven to be more efficient for high-dimensional parameter estimation, is employed. Through several simulation tests of IHTP, it was confirmed that the solving efficiency of FBPS surpasses that of the traditional Bayesian strategy significantly. Finally, FBPS is successfully developed to estimate the unknown heat flux on the chip heat sink and pack interface effectively, given some simulated high resolution measurement data. The reliability and efficiency show that FBPS has the potential to support efficient prediction techniques for a class of IHTPs in engineering applications.

Thermal analysis for SWCNTs and MWCTs due to coaxially stretchable disks with applications of viscous dissipation and thermal radiation: Artificial neural network analysis

Owing to exclusive thermal prospective of nanoparticles, diverse applications of such materials have been reported in heat transfer systems. The carbon nanotube (CNTs) is the modified class of nanoparticles which is preserve more stable thermal properties. The decomposition of CNTs with base materials offer special applications in enhancing thermal efficiency of energy systems, nuclear processes, sensors, diagnostic imaging etc. Following to such motivations in mind, the objective of current work is to present artificial neural network analysis for heat transfer problem due to suspension of carbon nanotubes-based nanofluid. Both single-walled and multi-walled carbon nanotubes are utilized to analyse the thermal impact of water base fluid. The source of flow is coaxially stretchable disks. The applications of porous medium phenomenon are reported to inspect the inertial effects. The problem is further updated by utilizing the radiative phenomenon, external heat generation and dissipation and slip constraints. The transport system is expressed via coupled nonlinear equations which are tackled via numerical computations.

Studies on acceleration algorithms for numerical simulations of hypersonic conjugate heat transfer problems

This research proposes acceleration algorithms for the coupled numerical simulation of the long-time hypersonic conjugate heat transfer problem from two perspectives. First, the newly developed disturbance region update method (DRUM) is introduced to enhance the convergence speed of the steady flow field. The numerical investigations reveal that, in the context of hypersonic CHT issues, the disturbance prompted by variations in wall temperature remains confined post the detached shock wave. The implementation of DRUM has been shown to substantially diminish the computational demand per iteration and the total iterations required for convergence. DRUM could reduce the time needed to calculate the flow field by over 60 % for a typical CHT case. Second, a new aerodynamic heat flux estimate method is introduced based on the local wall temperature within a coupled time step to increase the coupled time step. Combining this method with the adaptive coupled time step method, a long-time CHT problem with a total time of 1100s requires only 25 coupled time steps, much less than the 220 steps needed for the existing method. Meanwhile, the average error of the obtained solid temperature field, when compared to the temperature obtained from an accurate simulation with a fixed small coupled time step, is maintained below 0.22 %.

Simulation of heat transfer in Poiseuille pipe flow via generalized finite difference method with a space stepping algorithm

The aim of this paper is to propose an efficient numerical scheme to deal with heat transfer problems in pipe flow with a large length/diameter ratio. The generalized finite difference method (GFDM) is combined with a space stepping algorithm (SSA) for the solution. The SSA divides the solution domain into a number of overlapping sections in the length direction of the pipe. Due to the large Peclet number, the heat transport process is dominated by advection, which allows an approximate boundary condition to be applied at the downstream cross section. The problem is then solved section by section. Using the uniform distributed points, the solution matrix for each section does not change, and only the right hand side needs to be refreshed for the changing boundary conditions. This leads to a highly efficient scheme for problems with a large pipe length. To show the accuracy of the numerical scheme, a problem with available analytical solution is studied. Then the method is applied to problems of single pipe with different pipe wall temperature and flow Reynolds number, and concentric annular pipe. Numerical results confirm the stability and efficiency of the GFDM-SSA. The method can be applied to many real world transient heat transfer problems in which the pipe is heated or cooled along its length with arbitrary wall temperature for heat exchange and other purposes.

Thermo-mechanical coupled peridynamics simulation of concrete failure under fire scenarios

A coupled thermo-mechanical bond-based peridynamical (PD) method is developed to simulate thermal cracking processes in concrete. Based on the bond-based PD heat conduction and motion equations, the PD differential operator (PDDO) is used to express the classical computational fluid dynamics basic equations in a non-local integral form, establishing a PD model for the thermo-mechanical coupling problems. In this model, concrete is considered a heterogeneous material composed of aggregates and mortar, with material parameters assumed to be temperature-dependent. The multi-rate explicit time integration scheme is proposed to overcome the multi-scale time problem in coupled thermo-mechanical systems. The model is applied to simulate the transient heat transfer problem of a homogeneous plate. The results show good agreement with the analytical solution, providing evidence for the correctness and accuracy of the proposed coupled numerical method. The damage behavior of the borehole heated concrete plate is analyzed, followed by the simulation of the damage to the concrete plate under a fire scenario. The numerical results accurately predict the temperature distribution within the heterogeneous concrete and the resulting material damage. This study provides new theoretical basis for the fire resistance design and high-temperature performance improvement of concrete materials and structures.

Application of the adaptive method to determine the process noise in the extended Kalman filter to estimate the parameters of the two dimensional inverse heat transfer problem

To deal with inverse nonlinear heat transfer problems in a two-dimensional heat conduction problem, this paper presents a hybrid approach combining fuzzy logic and the extended Kalman filter (EKF). The proposed algorithm has been applied to the real-time reconstruction of the temperature field, time-varying convective heat transfer coefficient, and time-varying boundary heat flux using temperature data from a set of sensors. The effects of the covariance of the initial estimation error, the time step of data acquisition by the sensors, and the number of installed sensors on the precision and stability of the estimation results has been investigated by numerical experiments. To compare and validate the results, all these parameters were investigated using the EKF method. The results show that the adaptive fuzzy extended Kalman filter (FEKF) method for estimating temperature, convection coefficient, and heat flux at the boundaries is precise and stable. The comparison shows that the performance of the FEKF method in parameter estimation is better than the EKF method, and the highest increase in precision and stability of the results is related to the convective heat transfer coefficient.