Convective Heat Transfer Problems Research Articles

Research on multi-heat source arrangement optimization based on equivalent heat source method and reconstructed variational autoencoder

The variational autoencoder (VAE) architecture has significant advantages in predictive image generation. This study proposes a novel RFCNN-βVAE model, which combines residual-connected fully connected neural networks with VAE to handle multi-heat source arrangements. By integrating analytical solutions, polynomial fitting, and temperature field superposition, we accurately simulated the temperature rise distribution of a single heat source. We further explored the use of multiple equivalent heat sources to replace adiabatic boundary conditions. This enables the analytical method to effectively solve the two-dimensional conjugate convective heat transfer problem, providing a reliable alternative to traditional numerical solutions. Our results show that the model achieved high predictive accuracy. By adjusting the β parameter, we balanced reconstruction accuracy and latent space generalization. During the stable phase of the multi-heat source optimization iteration, 73.4% of the results outperformed the dense dataset benchmark, indicating that the model successfully optimized heat source coordinates and minimized peak temperature rise. This validates the feasibility and effectiveness of deep learning in thermal management system design. This research lays the groundwork for optimizing complex thermal environments and contributes valuable perspectives on the effective design of systems with multiple thermal sources or for applications like multi-beam lighting equalization.

Exact solution for heat transfer across the Sakiadis boundary layer

We consider the problem of convective heat transfer across the laminar boundary layer induced by an isothermal moving surface in a Newtonian fluid. In a previous work [Barlow et al., “Exact and explicit analytical solution for the Sakiadis boundary layer,” Phys. Fluids 36, 031703 (2024)], an exact power series solution was provided for the hydrodynamic flow, often referred to as the Sakiadis boundary layer. Here, we utilize this expression to develop an exact solution for the associated thermal boundary layer as characterized by the Prandtl number (Pr) and local Reynolds number along the surface. To extract the location-dependent heat transfer coefficient (expressed in dimensionless form as the Nusselt number), the dimensionless temperature gradient at the wall is required; this gradient is solely a function of Pr and is expressed as an integral of the exact boundary layer flow solution. We find that the exact solution for the temperature gradient is computationally unstable at large Pr, and a large Pr expansion for the temperature gradient is obtained using Laplace's method. A composite solution is obtained, which is accurate to O(10−10). Although divergent, the classical power series solution for the Sakiadis boundary layer—expanded about the wall—may be used to obtain all higher-order corrections in the asymptotic expansion. We show that this result is connected to the physics of large Prandtl number flows where the thickness of the hydrodynamic boundary layer is much larger than that of the thermal boundary layer. The present model is valid for all Prandtl numbers and attractive for ease of use.

Mixed convection heat transfer characteristics of nanofluid under magnetic field based on discrete unified gas kinetics scheme

In this paper, we proposed a discrete unified gas kinetic scheme (DUGKS) into the mixed convection issue coupled in a magnetic field and verified the accuracy by comparing with a exist literature. The flow and heat transfer characteristics of Fe3O4-water nanofluid in the mixed convection are investigated using the DUGKS model. The investigation explores the influence of Hartmann number (0.01 ≤ Ha ≤ 100), Rayleigh number (2 × 103 ≤ Ra ≤ 6 × 105), Richardson number (0.5 ≤ Ri ≤ 10), and nanoparticle fraction (0.01≤ϕ ≤ 0.05) on mixed convection heat transfer and flow characteristics. The results reveal that the critical point for the influence of the Hartmann number on the average Nusselt number is 1. When Ha < 1, the variation of Ha has little effect on Nu, but when Ha > 1, the influence of Ha becomes significant. When Ri = 1, the heat convection between the cold wall and the hot wall is strongest, and the Nusselt number at the cold wall reaches its maximum. The changes in velocity and temperature fields under all conditions are effectively captured by the DUGKS method. Therefore, the proposed method exhibits good mesh adaptability and accurately simulates the mixed convection heat transfer problem.

Influence of the cross-sectional geometry of the heat exchanger element on heat flow and pressure drop

This paper examines the influence of the geometry of the heat exchanger element on heat flow, pressure drop, outlet temperature and energy efficiency. By numerical modeling in a two-dimensional formulation, we solved the problem of convective heat transfer when air flows transversely around one and three rows of heated elements of different cross-sections. The following cross-sectional shapes of heated elements are: circle, trefoil, trefoil (mirrored), quatrefoil, cinquefoil and cinquefoil (mirrored). Calculations were carried out using ANSYS Fluent v. 19.2 at the following air flow velocities: 0.01; 0.05; 0.25 and 1.25 m/s. The research results showed that when flowing around one row of elements, the highest energy efficiency is provided by elements with a trefoil shape in cross-section. When flowing around three rows of elements at lower air flow velocities (0.01, 0.05, and 0.25 m/s), trefoil-shaped elements also have the best energy efficiency values, and only at an air flow velocity of 1.25 m/s elements with a trefoil cross-section inferior by 3.67% to elements with a cinquefoil (mirrored) cross-section.

Combination of Karhunen-Loève and intrusive polynomial chaos for uncertainty quantification of thermomagnetic convection problem with stochastic boundary condition

Uncertainty propagation analysis plays a crucial role in understanding the impact of variations in initial condition, boundary condition, and fluid physical properties on simulation results for thermomagnetic convection heat transfer problems. To effectively analyze the uncertainty problem of thermomagnetic convection caused by random temperature fluctuations, a novel and comprehensive computational framework based on intrusive polynomial chaos approach was proposed in this paper. Our proposed approach aims to represent random temperature boundaries using Karhunen-Loève expansion (KLE) and stochastic output response using polynomial chaos expansion (PCE). In addition, we use spectral projection method to transform the stochastic control equation into a group of deterministic control equations. We obtained the uncertainty characteristics of the stochastic output response by solving each polynomial chaos basis. Compared with Monte Carlo simulation (MCS), our approach accurately and efficiently predicts the uncertainty characteristics of thermomagnetic convection problems under stochastic temperature boundary conditions while significantly reducing computational resources.

Mathematical Modeling of Collisional Heat Generation and Convective Heat Transfer Problem for Single Spherical Body in Oscillating Boundaries

The application of high-energy ball milling in the field of advanced materials processing, such as mechanochemical alloying and ammonia synthesis, has been gaining increasing attention beyond its traditional use in material crushing. It is important to recognize the role of thermodynamics in high-energy processes, including heat generation from collisions, as well as ongoing investigations into grinding ball behavior. This study aims to develop a mathematical model for the numerical analysis of a spherical ball in a shaker mill, taking into account its dynamics, contact mechanics, thermodynamics, and heat transfer. The complexity of the problem for mathematical modeling is reduced by limiting the motion to one-dimensional translation and representing the vibration of the vial wall in a shaker mill as rigid boundaries that move in a linear fashion. A nonlinear viscoelastic contact model is employed to construct a heat generation model. An equation of internal energy evolution is derived that incorporates a velocity-dependent heat convection model. In coupled field modeling, equations of motion for high-energy impact phenomena are derived from energy-based Hamiltonian mechanics rather than vector-based Newtonian mechanics. The numerical integration of the governing equations is performed at the system level to analyze the general heating characteristics during collisions and the effect of various operational parameters, such as the oscillation frequency and amplitude of the vial. The results of the numerical analysis provide essential performance metrics, including steady-state temperature and time constant for the characteristics of temperature evolution for a high-energy shaker milling process with a computation accuracy of 0.1%. The novelty of this modeling study is that it is the first to obtain such a high accuracy numerical solution for the temperature evolution associated with a shaker mill process.

Analysis of transient laminar forced convective heat transfer in parallel-plate channels with time-varying thermal boundary conditions of the inlet and wall

The problem of transient laminar forced convective heat transfer in parallel-plate channels with time-varying thermal boundary conditions of the inlet and wall is thoroughly investigated in this study. By employing the methodologies of generalized integral transform technique (GITT) and Duhamel's theorem, we successfully derive an analytical solution for this problem. To validate the accuracy of our analytical findings, a comparison is made with the corresponding numerical solution, demonstrating a remarkable level of agreement between the two approaches. In order to obtain the general patterns of heat transfer, we employ a decoupling technique to separate the thermal response in the case of harmonic temperature boundary conditions of the inlet and wall. This approach enables us to uncover the intricate relationship between the weight coefficient of heat input and the two-dimensional spatial location of the channel, as well as the dimensionless angular frequency of heat input. Furthermore, we present the corresponding dimensionless cut-off angular frequency of heat input at various locations within the channel. To gain further insights, we conduct an in-depth analysis of the effects of integration time or distance on the dimensionless optimum angular frequency corresponding to the dimensionless maximum average heat flux.

Modeling Convective Heat Transfer of Air in a Data Center Using OpenFOAM

Achieving energy and cooling efficiency in data center convective air flow and heat transfer can be a challenging task. Among different numerical methods to work with such issues is the Finite Volume Method in Computational Fluid Dynamics. This work evaluates the performance of two such solvers provided by OpenFOAM® in solving this type of convective heat-transfer problem, namely BuoyantBoussinesqPimpleFOAM and BuoyantPimpleFOAM. This is done for two different flow configurations of significantly different Richardson number. To sufficiently resolve the flow, grid sizing effects are elucidated by way of the kernel density estimate. It determines the volume distribution of the temperature in the data center configuration. For the k-epsilon turbulence model used here, it was found that the compressible solver performs faster and requires less grid resolution for both flow configurations. This is attributed to the nature of the boundary conditions which are set such that the mass flow conservation per server rack and cooling unit is achieved. Transient solutions are found to provide better iterative convergence for cases that involves buoyancy, compressibility and flow separation. This is, in comparison to steady-state solutions where artificial numerical pressure drop is found, to depend on the momentum relaxation factors for the convective case with a higher Richardson number.

PaScaL_TCS: A versatile solver for large-scale turbulent convective heat transfer problems with temperature-dependent fluid properties

PaScaL_TCS is an efficient and scalable solver for large-scale direct numerical simulations of natural convective flow that considers temperature-dependent fluid properties. For increased scalability on a massive-scale distributed memory system, the solver decomposes the computational domain into a cubic sub-domain. The numerical procedure is based on the monolithic projection method with staggered time discretization [1], which is an implicit and non-iterative solver for wall-bounded domains. The PaScaL_TDMA library is used to solve batched tridiagonal systems, which are partitioned according to domain decomposition. For parallel fast Fourier transform in a Fourier Poisson solver for pressure, two transpose schemes with different communicator sizes are proposed and compared according to the number of cores. An explicit intermediate aggregation scheme for MPI-IO is suggested to reduce the number of processes that simultaneously take part in parallel IO. The overall implementation was evaluated using the Nurion cluster system of the Korea Institute of Science and Technology Information with detailed performance profiling. With the efficient communication, the results showed good strong and weak scalability up to 131,072 cores. The file IO performance improved with the suggested MPI-IO scheme using explicit aggregation, especially when many processes are involved in parallel IO. The solver was verified by conducting large-scale differentially heated vertical convection flow simulations under the Oberbeck–Boussinesq (OB) approximation. The capability of the solver to capture and quantitatively describe the non-OB effect was demonstrated via glycerol Rayleigh–Bénard convection flow simulations. Program summaryProgram Title: PaScaL_TCSCPC Library link to program files:https://doi.org/10.17632/3b2bysrcxm.1Developer's repository link:https://github.com/MPMC-LabLicensing provisions: MITProgramming language: Fortran90Nature of problem: Solving the incompressible Navier-Stokes equations for natural convective flow considering the non-Oberbeck–Boussinesq effect, which considers the temperature dependence of fluids properties, in three-dimensional channel domain.Solution method: PaScaL_TCS uses the monolithic projection-based method with staggered time discretization (MPM-STD) [1]. It employs the Crank-Nicolson scheme along with staggered time which evaluates scalar and vector variables at the (n+1/2) and (n+1) time level, respectively. PaScaL_TDMA [2] is used to solve multiple tridiagonal matrix systems for decoupled energy and momentum equations in a distributed memory system. The Poisson equation solver for the pressure-correction scheme is based on Fourier diagonalization. MPI_Alltoallw is used for parallel FFT. PaScaL_TCS supports a single-file-based parallel IO for efficient data generation in large-scale computing.

Topology optimization of simplified convective heat transfer problems using the finite volume method

Topology optimization of simplified convective heat transfer problems using the finite volume method

A simple staggered approach for comprehensive analysis of forced convection heat transfer using the improved element-free Galerkin–reduced integration penalty method to solve the fluid dynamics problem

Forced convection heat transfer problems are successfully solved in this work via a simple staggered approach based on the improved element-free Galerkin (IEFG) formulation, which involves a fluid-dynamic analysis conducted in the framework of Navier–Stokes equations written in terms of velocity via a reduced integration penalty method (RIPM). Subsequently, the velocity field achieved from the solution of the Navier–Stokes equations is used in the IEFG-based solution of the internal energy balance formulated in terms of temperature. The proposed approach is tested in the solution and analysis of forced convection heat transfer problems concerning (i) the simultaneously (thermally and fluid-dynamically) developing flow between parallel plates and, (ii) the confined recirculating flow in non-isothermal lid-driven square cavities (also including viscous dissipation effects). A comprehensive parametric analysis developed in terms of characteristic dimensionless numbers is conducted for both problems, providing reliable benchmark results that will be useful to assess the performance of numerical techniques to model forced convection heat transfer phenomena. The versatility and reliability of the proposed approach are also demonstrated in the solution of a more complex problem with curved geometry, such as the non-isothermal lid-driven semicircular cavity with a circular obstacle. The accuracy and feasibility of solving forced convection heat transfer problems via the mesh-less procedure proposed in this communication are proven by comparison with results achieved via mesh-based techniques, and also with analytical solutions available in the literature. The outcomes demonstrate that the appropriate implementation of such numerical technique allows the achievement of accurate and stable results in a straightforward and remarkably simple manner, even under markedly advection-dominated flow conditions in both thermal and fluid dynamics problems.

A Novel Optimization Strategy for Reducing the Initial Error of a Quasi-Steady Algorithm for Conjugate Heat Transfer

The present study proposes a novel optimization strategy (NOS) for quasi-steady algorithms to optimize the initial error in the fast calculation of conjugate heat transfer (CHT) simulations. In this approach, the change in Nusselt number at the fluid–solid coupling interface is dynamically monitored, and the update of the flow field is turned off according to a given Nusselt variation standard to speed up the solution of the transient temperature field. The NOS has been applied to problems of convective heat transfer in solid parts with internal heat sources. The feasibility of NOS is first verified by using an undisturbed boundary example, and the results show that the optimization strategy reduces the initial error by 92.3% compared with the quasi-steady algorithm, and the calculation time is reduced by 50% compared with the traditional coupling algorithm. The NOS is then combined with the quasi-steady algorithm, and boundary transient disturbances are added to the case. The results indicate that the computational time for NOS and the quasi-steady algorithm is 2.6 and 2.9 times greater than that of traditional algorithms. Nevertheless, NOS significantly optimizes the relative error of the quasi-steady algorithm by 97.3% during the initial computation phase.

A cost‐effective approach to generate accurate correlations via analyzing a minimum number of data points; Case study on the convection heat transfer problem

AbstractIt is very common in the heat transfer area to analyze and design heat equipment using the past available heat correlations. Basically, demanding higher‐accuracy correlations enforces the heat laboratories to test and collect larger banks of laboratory data. However, this conversely affects the laboratory cost. Therefore, it becomes challenging to create new approaches that let the correlation developers use smaller experimental datasets and provide correlations with sufficient accuracies. To surmount this challenge, the present work develops a new approach that benefits from the computational fluid dynamics method as a reliable and cheap tool and adequately enriches the original, insufficient dataset. Then, suitable enhanced correlations are developed using the new enriched experimental‐numerical‐based dataset. In parallel, the artificial neural network (ANN) is used to enrich the original insufficient dataset separately. Using this experimental‐ANN‐based dataset, it provides a totally ANN‐based correlation. It is shown that the results of enhanced correlations are as accurate as those of the ANN‐based correlation. However, the point is that the use of the present approach is about 100 times faster than using the ANN. The typical forced convection heat transfer through a pipe is examined here to show the capabilities of the current approach.

Convective boundary integral equation: the case of a non-axisymmetric dendrite with a forced viscous flow

Abstract The paper is devoted to obtaining an integral solution to the problem of convective heat transfer in the vicinity of the tip of a stationary growing non-axisymmetric dendrite. The boundary integral equation for an elliptical paraboloid growing in a viscous forced flow is solved using the Green function technique. The total undercooling at the dendrite tip is found for single-component and binary melts, which is a function of the Péclet, Reynolds, and Prandtl numbers as well as the ellipticity parameter. Also, we demonstrate that these parameters substantially influence the total undercooling. We show that the increase of fluid flow and ellipticity of the crystal tip allows it to grow faster at fixed undercooling and average tip diameter. The 3D non-axisymmetric theory under consideration is verified with previous solutions constructed by Ananth and Gill (1989 J. Fluid Mech. 208 575–593) for elliptic paraboloid and Alexandrov and Galenko (2021 Phil. Trans. R. Soc. A 379 20200325) for a paraboloid of revolution and a parabolic cylinder with a forced flow. The method developed can be used for the stationary growth of arbitrary patterns in the presence of convective flow.

Numerical investigation on a thermoelectric generator in an exhaust automotive line with convergent metal foam

In the present paper, a 2-D steady state convective heat transfer problem in a convergent channel partially filled with aluminum foam with an external thermoelectric generator (TEG) component is numerically solved. The channel is characterized by a length equal to 272 mm and by a height of 60 mm. The TEG has the dimensions equal to 65 mm and 8.5 mm. The investigation is executed considering the Darcy-Forchheimer-Brinkman assumption and the local thermal equilibrium (LTE) hypothesis for modelling the metal foam. The exhaust gas is considered to have the same properties of the air in corresponding to the assigned temperature of the upper surface of the thermoelectric generator. The thermophysical properties are temperature independent and the thermoelectric generator is studied as a solid with an internal energy generation. The governing equations for gas, porous media and thermoelectric generator are solved by finite volume method using the Ansys-Fluent code. Different configurations of convergent metal foam are analyzed. The aluminum foams are characterized by 5 PPI and porosity equal to 0.905, 0.946 and 0.971. Results are presented in terms of temperature distributions, thermoelectric efficiency, power density, and the Energy Performance Ratio (EPR) for different gas flow rates and aluminum foam configurations. Furthermore, a comparison with the use of the same foam samples characterized by a constant section is showed for the same system. From the comparison, it is possible to deduce how the configuration with convergent channel has a more uniform temperature profile than the geometry with constant section.

N-Side Cell-Based Smoothed Finite Element Method for Incompressible Flow with Heat Transfer Problems

In this paper, an n-sided cell-based smoothed finite element method (nCS-FEM) is presented to solve the convective heat transfer in incompressible viscous fluid flow. The Characteristic-based-split (CBS) scheme is used to stabilize the spatial and pressure oscillations of CS-FEM that occur during the process of solving incompressible Navier-Stokes equations. Meanwhile, the characteristic-Galerkin method in CBS is adopted as the convective stabilization in the heat transfer equation. In order to verify the proposed method, typical numerical examples are used to test the computational accuracy of CS-FEM. Meanwhile, the investigation of the robustness of highly distorted element is conducted in a natural convection test case. The calculation results of numerical examples show that CS-FEM is qualified to solve the steady and unsteady convective heat transfer problems for incompressible laminar flow with high reliability. The flow across tube banks with complex geometry in the heat sinks is also simulated to prove the capabilities of the proposed method. Well agreed comparison with the results of CFD software, Fluent, proves that the present method can effectively simulate realistic and complex flow with heat transfer problems.

A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

AbstractIn this article, we propose a simple, consistent, and robust Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics (EL‐WCSPH) for the simulation of hydrodynamics and convection heat transfer problems. First, the basic governing equation is formulated using the ALE‐SPH framework. The universal formulation is similar to the standard WCSPH, but the degree of Eulerian and Lagrangian schemes can be controlled by inserting a pre‐defined arbitrary parameter . To alleviate potential numerical errors and inconsistency, particle mass correction is proposed along with particle disorder correction. Then, an algorithm is introduced, in which only a slight modification is necessary compared to the standard WCSPH. Finally, extensive benchmark simulations are conducted to validate the proposed method. As a result, the proposed method is found to perform well in hydrodynamics problems with various flow conditions (pipe flow, lid‐driven problem, Taylor–Green vortex, vortex shedding problem, and water sloshing) and thermal‐hydraulics problems (natural convection in a square cavity).

Topology optimization of convective heat transfer by the lattice Boltzmann method

AbstractTopology optimization (TO) is a dependable approach to obtain innovative designs with improved performance. This study presents a TO method based on the adjoint lattice Boltzmann method (ALBM) and the level set method which is developed for both one‐way coupled and two‐way coupled convective heat transfer problems. The adjoint lattice Boltzmann model for fully coupled natural convection system is derived, and the coupled solution strategy is applied in the ALBM. The forward model is validated by the finite element simulation, while the adjoint model and the sensitivity expression is validated by a finite difference check, and the whole TO method is validated by a typical pure fluid flow optimization problem given in the literature. The validated TO method is then applied to enhance the heat transfer of forced convection in a two‐dimensional open chamber, and the Pareto frontier of the bi‐objective optimization is further presented and the effects of the blockages at the inlet and outlet on the overall performance are revealed. Finally, the two‐dimensional natural convection process in a closed cavity is optimized, in which the effective heat transfer coefficient can be increased to 3.96 ∼ 6.11 times of that without the optimized design when the Grashof number ranges from 1.7 to 4.2 × 105. Moreover, effects of Grashof number, porosity limitation and solid thermal diffusivity on the optimization results are analyzed in detail. Physically reasonable designs are obtained for both forced convection and natural convection systems under various parameter settings, demonstrating the effectiveness and robustness of the presented TO method.

NATURAL CONVECTION ON CORRUGATED PLATES: A NUMERICAL CASE STUDY ABOUT MESHES, BOUNDARY CONDITIONS AND PHYSICAL DOMAIN DETERMINATION

The transfer of heat and mass by natural convection is present in the most diverse physical and chemical phenomena of nature and engineering equipment. In the last decades, the number of research on natural convection has grown dramatically, highlighting studies in physical-mathematical modeling and numerical solutions, experimental analysis and design and optimization techniques for fluid-thermal systems. This case study analyzed the influence of several numerical parameters in physical-mathematical modeling and numerical solution of natural convection heat transfer problems on isothermal plates with square waves in turbulent conditions of high Rayleigh number. The numerical parameters analyzed were the mesh refinement degree, wall boundary conditions (with or without wall functions implemented in the turbulent parameters) and computational physical domain influence. Free and open-source computational numerical tools were exclusively used in the construction of this work. Meshes with wall functions implemented in turbulent parameters presented greater accuracy and required less computational effort and simulation time, besides enabling the use of a lower degree of mesh refinement. The best numerical configuration of the physical model for the situation problem studied were defined from the criteria of accuracy, computational effort demanded, and stability and numerical convergence of the solution.

Solving the Problem of Liquid Metal Convective Heat Transfer in the Helical Coordinate System

We show a way to solve the problems of hydrodynamics and heat transfer in helical medium flow channels in the helical coordinate system. Specifically, such problems are solved for the buoyant liquid metal flow in a heated helical fin ring-shaped channel. The problems are related to heat transfer in the flow process over the fuel pin located within the fuel bundle finned in the liquid metal nuclear reactor core. The article shows the tensor analysis derivation of the mass-, momentum-, and energy-conservation equations as applied to a liquid metal medium in the helical coordinate system. We assume as the basis the well-known equations for a cylindrical system proposed to be added, with extra terms arising in the process of transition to the helical coordinate system. In line with the proposed technique, numerical computation of the velocity, pressure, and temperature profiles in the process of turbulent liquid flow in a helical fin ring-shaped channel was performed. Two computation cases are compared: with straight and twisted (helical) fins. Examples of the computation data show the measurable effect of a twisted fin upon flow and heat transfer parameters. The available gap between the fin and the external tube enhances the vorticity effect.