Heat Transfer Problem Research Articles

Numerical investigation on a novel milli-sized heat sink equipped by twisted elliptical tubes

Thermal management in some small chemical reactors is essential to achieve a final high-quality product and heat sinks can play a remarkable role in dissipating heat from such systems. In this regard, this study attends to evaluate the conjugate heat transfer problem in a heat sink equipped by twisted elliptical tubes (TETs). The effects of significant parameters such as Reynolds number (Re = 250, 350, 500, 700 and 950) and twist ratio (TR = 2.5, 5 and 10) on hydrothermal and thermodynamics performance of the novel heat sink are investigated. The swirling flow is the main reason of fluid particles migration from hot surface to cold one and vice versa, leading a better heat transfer occurs at the expense of not significant pressure loss augmentation. The results revealed that the TETs are responsible of more wall temperature uniformity and avoids generating hot spots. Compared with plain elliptical tubes, the presence of TETs inside heat sink improves the heat transfer rate and enlarges the pressure drop by 1.08–2.03 times and by 1.02–1.92 times, respectively. In addition, the TETs decrease the entropy generation rate inside heat sink and the best value of second law efficiency is about 35 %, detected at TR = 2.5 and Re = 250.

The Problem of Heat and Mass Transfer of a Half-Space with an Air Flow with Periodic Changes in Air Temperature

A system of differential equations, boundary and initial conditions for calculating temperature and moisture content fields in a homogeneous halfspace, the boundary of which is blown by an air flow, is formulated. The heat exchange of the boundary with the air medium occurs according to the Newtonian law, and mass transfer — according to the Dalton evaporation law. In the initial state, the air and the material have the same temperature, and water vapor, both near the surface of the material and outside the boundary layer, is in a saturation state, so there is no exchange of heat and moisture between the air and the material. At some point, the air temperature begins to produce small harmonic fluctuations near its initial value. For a mathematical model of heat and mass transfer, in which the movement of moisture to the surface is considered to be caused only by a drop in moisture content, i.e. the phenomenon of thermal diffusion is neglected, an asymptotic time view of the temperature and moisture content fields is obtained. The moisture content field has the form of a damped harmonic wave, and the temperature field is represented by the superposition of two waves of the same type, which have the same frequency, but different attenuation coefficients and phase velocities. The calculation of the basic wave parameters for a material with clay characteristics is carried out, and the results obtained are compared with experimental data. The constructed solution is a generalization of the Fourier formulas known in the literature, which are valid only in a situation when the material does not contain moisture, and according to the harmonic law, not the air temperature changes, but the surface temperature. The results obtained in the article will be used in geocryology as a theoretical tool in the study of seasonal fluctuations in the thermal and physical state of the soil, which is an important task in planning economic activities in the field of the distribution of frozen rocks.

Prediction of heat transfer for a single round jet impingement using the GEKO turbulence model

Two-dimensional Reynolds-Averaged Navier–Stokes simulations are performed to study a single, round impinging jet heat transfer problem, utilizing the generalized k-omega (GEKO) turbulence model as a benchmark. The simulations are performed at a jet Reynolds number of 23,300 and a nozzle-to-plate distance of 2.0 where a second peak in surface Nusselt number is observed. The effects of the three primary (Csep, Cmix and Cnw) and three auxiliary (Cbf,l, Cbf,t and Cnw,sub) GEKO calibration parameters are investigated. The results indicate that Cmix has the most significant impact on the laminar-turbulent transition zone. A deep learning based regression model is developed and trained using the simulation outputs for fast predictions of the heat transfer curve. Using Csep=1.1, Cmix=−0.7, Cnw=2.0, Cnw,sub=2.25 and Cbf,t=3.0 along with laminar-to-turbulent transitional modeling values, provides the best agreement with experimental results from previous studies.

Numerical investigation of thermal soak within engine bay using lattice Boltzmann method

A large amount of heat accumulates in the engine bay for a short time after the engine runs at high load and shuts down, that will lead to thermal damage and thermal fatigue caused by the temperature rise of some heat sensitive components. This paper uses an aero-thermal coupling approach to study the heat transfer problem in the engine bay of an SUV model under thermal soak conditions. Due to the transient characteristics of the heat transfer process, the natural transient CFD software developed based on the LBM method is used to study the engine bay heat transfer during the 400 s key-off soak process. The analysis reveals that convection and radiation are the main heat transfer modes in the early stage of hot immersion (0–120 s), and conduction only makes a significant contribution in contact with high temperature sources. The radiation and convection are the key contributors to heat transfer processes of engine bay during soak, but the efficiency of radiation heat transfer decreases with the increase of time, whereas the efficiency of convection heat transfer is not always reduced, it will increase and then decrease with the increase of time. The coupling method established can predict the thermal state in the engine bay well, and is in good agreement with the experimental results. The results show that the error in the engine coolant temperature is less than 1 °C, and the error in the temperature of the heat-sensitive components is less than 5 °C. Finally, the potential risks of thermal damage and thermal fatigue states were assessed, providing an important reference for the control design of cooling fan running time after key-off.

Local heat transfer measurements of the fin on the blade crown by infrared thermography

Current research on heat transfer of the labyrinth surface mainly focuses on the whole structure made of the same material, but the heat conduction from the tip to the root will affect the measurement of the heat transfer coefficient. To minimize the influence of heat conduction, copper strips are embedded on the surface of the fin made of bakelite. The inverse heat transfer problem is solved using the temperatures collected by an infrared thermal imager to determine the local convective heat transfer coefficient. The error of the lumped parameter method is smaller compared to the differential solution. Constant heat flux experiments are used to validate the experimental results, and numerical analysis is performed to analyze the heat transfer mechanism. The flow field, the Nu number distribution, and fitting correlations of the fins are obtained. By comparing and analyzing the heat transfer coefficients obtained by the three methods, it is found that the lumped parameter method can eliminate the influence of heat conduction on the surface. Taking the lumped parameter method as a reference, the errors of stable heat flow and numerical calculation were 21 % and 4.7 %, respectively. Due to the influence of the vortex direction, the Nu number distribution along the height of the windward surface of the second fin is different from the others. The Nu number distribution along the x-direction on the top surface of the fin is similar to the tip of the windward surface. Along the flow direction, the average Nu number on the top surface of the first fin is 1.2 times that of the second one.

The MEMENTO code for modeling of macroscopic melt motion in fusion devices

The MEMENTO (MEtallic Melt Evolution in Next-step TOkamaks) code is a new numerical implementation of the physics model originally developed for the MEMOS-U code with the objective to self-consistently describe the generation of melt and its subsequent large scale dynamics in fusion devices and to assess the damage of metallic reactor armor under powerful normal and off-normal plasma events. The model has been validated in multiple dedicated EUROfusion experiments. MEMENTO solves the heat and phase transfer problem coupled with the incompressible Navier–Stokes equations in the shallow water approximation for the thin liquid film over the solid metal and with the current propagation equations on a domain that features a time-evolving deforming metal-plasma interface. The code utilizes non-uniform and adaptive meshing along with sub-cycling in time facilitated by the AMReX open-source framework as well as AMReX’s built-in parallelization capabilities.

A hybrid shape functions based temporal finite element method to solve transient heat conduction problems

A novel temporal finite element method is presented to solve Fourier and non-Fourier heat conduction problems. Two kinds of temporal finite element models are developed using Gurtin variational principle and weighted residual technique, respectively. A kind of hybrid shape function with polynomial and trigonometric basis is stressed to give more flexible and appropriate description of temporal behavior of temperature. A recursive algorithm is developed by which the temperature solution at a specific time can be obtained only via a matrix power product with the initial condition, and a criterion of stability analysis is derived, which is can numerically be conducted when the constitution of shape function and time step size are prescribed. The proposed approach is available for Fourier and non-Fourier heat transfer problems, and can conveniently be combined with well-developed numerical algorithms for the boundary value problem, such as FE, SBFEM, etc. Various numerical examples, including those with the nonlinear thermal conductivity, radiative boundary condition, etc. are provided to illustrate the efficiency of proposed approaches, and impacts of the temporal FE model, constitution of shape functions, and step size, etc. are taken into account. Satisfactory results are achieved in comparison with the analytical and the ABAQUS based numerical solutions.

Sub-minute carbonization of polymer/carbon nanotube films by microwave induction heating for ultrafast preparation of hard carbon anodes for sodium-ion batteries

Hard carbons (HCs) are excellent anode materials for sodium-ion batteries (SIBs). However, the carbonization and granulation of HC powders involve complex processes and require considerable energy. Here, we developed a facile method for manufacturing HC anodes for SIBs via a novel microwave induction heating (MIH) process for polymer/single-walled carbon nanotube (SWCNT) films. Numerical simulations solving electromagnetic field and heat transfer problems revealed the MIH mechanism; the electric current induced by the applied microwave enables direct Joule heating of the SWCNT networks in the composite film. Consequently, the composite films could be heated to the target temperatures (800–1400 °C) and free-standing HC/SWCNT anodes could be prepared by applying MIH for only 30 s. Comparative analyses confirmed that ultrafast MIH is a reliable technique for producing HC anodes and can replace conventional carbonization processes which require a high-temperature furnace. Moreover, the HC/SWCNT anodes prepared by the ultrafast MIH were successfully applied to the SIB full cells. Finally, the feasibility of MIH for scalable roll-to-roll production of HC anodes was verified through local heating tests using a circular sheet larger than a resonator.

Explainable artificial intelligence prediction of defect characterization in composite materials

Non-destructive evaluation (NDE) techniques are integral across diverse applications for void detection within composites. Infrared (IR) thermography (IRT) is a prevalent NDE technique that utilizes reverse heat transfer principles to infer defect characteristics by analyzing temperature distribution. Although the forward heat transfer problem is well-posed, its inverse counterpart lacks uniqueness, posing non-unique solutions. The present study performs simulations using finite element analysis (FEA) in defective (a penny-shaped defect) composites through which the heat transfer flux is modeled. A total of 2100 simulations with various defect positions and sizes (depth, size, and thickness) are executed, and the corresponding surface temperature vs. time and vs. distance diagrams are extracted. The FEA outputs provide ample input data for developing an explainable artificial intelligence (XAI) model to estimate the defect characteristics. A detailed feature engineering task is performed to select the representative information from the diagrams. Explainable decision tree-based machine learning (ML) models with transparent decision paths based on derived features are developed to predict the defect depth, size, and thickness. The ML models’ results suggest superb accuracy (R2 = 0.92 to 0.99) across all three defect characteristics. The provided workflow sets a benchmark applicable to a range of fields, including health monitoring.

Estimation of Multiple Parameters in Semitransparent Mediums Based on an Improved Grey Wolf Optimization Algorithm

This work investigates the inverse coupled radiation–conduction problem for estimating thermophysical parameters and source terms by an improved grey wolf optimization (GWO). The transient coupled radiation–conduction heat transfer problem in participating slab media is solved by the finite volume method. The radiative intensities on both boundaries are adopted as known measurement information in the inverse model. To overcome the disadvantages of the original GWO algorithm, an improved grey wolf algorithm (IGWO) is developed by introducing the weight strategy and nonlinear factors. Three benchmark functions are adopted to prove that the IGWO has a faster convergence speed and higher estimation accuracy than the original one. The IGWO is applied to inverse the thermophysical parameters and source terms based on the coupled radiation–conduction model; the results indicate that the IGWO is accurate and effective for estimating refractive index, absorption coefficient, and source terms.

MULTITHMT: A MATLAB Application for Multidimensional Transient Heat and Mass Transfer Processes

Transient heat conduction and mass transfer have many applications in industry such as heating, cooling, cooking, quenching of steels, freezing, and convective drying of vegetables or fruits. A novel, interactive, and fast MATLAB application, named MULTITHMT, is improved to solve multidimensional transient heat and mass transfer problems. Exact solutions are obtained for infinite rectangular bars, short cylinders, rectangular prisms, and spherical geometries. Instantaneous temperature and moisture content at any location in the objects are obtained and temperature and moisture content at the final time are displayed in two- and three-dimensional graphics. Quenching of steel for rectangle bars and cooking of cylindrical or rectangular prism-shaped meat are represented for transient heat transfer. Cooling of spherical commercial bronze and iron is also investigated. For transient mass transfer, convective drying of rectangular prunes, bananas of short cylinders, and spherical cornelian cherries with different operational conditions is calculated. Drying of cubes with the same shape and different moisture diffusivities is investigated. MULTITHMT is the only program that uses exact solutions to calculate multidimensional heat and mass transfer problems in the available literature. It is also the only application that can calculate the target time with a given temperature or moisture content for any specific location in the studied multidimensional objects. This application can be used for educational purposes in several engineering departments and industrial applications where transient heat and mass transfer processes are needed.

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.

Transient Radiation Heat Transfer of Thermally Compact Bodies: an Explicit Solution

Abstract An explicit, analytical solution is offered to the problem of transient radiation heat transfer of thermally compact bodies. This solution is readily implemented as a calculator on a simple spreadsheet software, allowing prediction of transient radiation that can aid didactics, design, test, and operations. It is shown that transient radiation heat transfer has a few similarities, and many differences, in comparison to linear forms of transient heat transfer such as conduction and convection. Both linear and radiation forms of transient heat transfer asymptotically approach their steady state conditions. Differences of note are that transient radiation heat transfer is non-self-similar, it depends upon two nondimensional variables, transient radiative heating is generally faster than transient radiative cooling, and externally applied heat sources substantially delay transient radiation heat transfer relative to internally applied heat sources.

Application of meshless generalized finite difference method (GFDM) in single-phase coupled heat and mass transfer problem in three-dimensional porous media

This paper achieves effective and precise meshless modeling of three-dimensional (3D) single-phase coupled heat and mass transfer problems based on the generalized finite difference method (GFDM). It utilizes the Taylor formula and the weighted least squares method in the node influence domains to derive a generalized finite difference scheme for spatial derivatives of pressure and temperature. Consequently, a sequential coupled discrete scheme for the pressure diffusion equation and heat convection–conduction equation is formulated, resulting in the determination of pressure and temperature. An example conducts sensitivity analysis with different schemes of node collocation and different radius of influence domains. The calculation results demonstrate that this method exhibits good convergence. Two 3D model examples with regular and irregular boundaries illustrate the advantages of the GFDM in handling complex geometric problems within the computational domain, showcasing its superior flexibility and simplicity. This paper demonstrates the significant potential of GFDM in addressing complex geometric multi-physics field coupling challenges, offering innovative ideas for geothermal resource development, groundwater management, and thermal recovery in oil and gas reservoirs.

Методология матричного моделирования многокомпонентных многопоточных многоступенчатых энергетических комплексов

Traditionally, heat transfer problems are solved in relation to two-flow systems in which heat exchange is carried out between hot and cold coolants. However, along with two-flow systems, there are often multiflow systems in which the number of coolant flows is three or more. In addition, each energy carrier stream may consist of several components, and the installation may include several stages. Thus, the development of universal approaches and methods for modeling, calculation, and optimization of multi-component multiflow multistage energy complexes within the framework of a unified methodology is an urgent scientific and practical task. A methodology of matrix formalization of modeling heat and mass transfer processes is based on methods and approaches of matrix description of heat and mass transfer systems in energy complexes. The approaches and methods of modeling energy power installations are summarized. Within the framework of the matrix description methodology, the rules and approaches to the development of models of heat and mass transfer processes are formulated in relation to multicomponent multiflow multistage energy complexes. The authors have proposed a solution to the inverse problems with and without considering a phase transition in coolants. Analysis of formulated and solved problems within the framework of the proposed methodology allows us to recommend the use of methods and approaches of matrix modeling of equipment to solve direct and inverse problems for multicomponent multiflow multistage energy complexes for various purposes.

An improved sequential quadratic programming method for identifying the total heat exchange factor of reheating furnace

Accurate identification of the total heat exchange factor (THEF), which serves as the foundation for online control data in the reheating furnace, holds significant importance for enhancing the digitization and intelligence level of the furnace, mitigating environmental pollution, and improving the economic performance of enterprises. For this purpose, based on the theory of inverse heat transfer problem, a solver combining Sequential Quadratic Programming and Broyden Combined Method (SQPBC) was developed to accurately identify high-dimensional and strongly nonlinear THEF in the reheating furnace. Integrating the efficient Broyden Combined Method (BCM) into Sequential Quadratic Programming (SQP) enables the rapid and accurate estimation of the Jacobian matrix to effectively enhance computational speed without compromising accuracy. Experimental data has been employed to validate the accuracy of the inversion results. The performance of SQPBC has been comprehensively analyzed through a series of numerical experiments, with a particular focus on investigating the impact of sampling frequency and sensor location on the inversion results. The findings reveal that after reducing the sampling period to 2 min, further decreasing the sampling period has a minor effect on the average relative error of the identification results; the closer the measurement points are to the surface of the slab, the more accurate the identification of THEF on the slab's surface.

Sensitivity analysis of the Cercignani - Lampis accommodation coefficients in prototype rarefied gas flow and heat transfer problems via the Monte Carlo method

In rarefied gas dynamics, the Cercignani-Lampis (CL) scattering kernel, containing two accommodation coefficients (ACs), namely the tangential momentum and normal energy ones, is widely employed to characterize gas-surface interaction, particularly in non-isothermal setups, where both momentum and energy may simultaneously be exchanged. Here, a formal and detailed sensitivity analysis of the effect of the CL ACs on the main output quantities of several prototype problems, namely the cylindrical Poiseuille, thermal creep and thermomolecular pressure difference (TPD) flows, as well as the plane Couette flow and heat transfer (Fourier flow), is performed. In each problem, some uncertainties are randomly introduced in the ACs (input parameters) and via a Monte Carlo propagation analysis, the deduced uncertainty of the corresponding main output quantity is computed. The output uncertainties are compared to each other to determine the flow configuration and the gas rarefaction range, where a high sensitivity of the output quantities with respect to the CL ACs is observed. The flow setups and rarefaction regimes with high sensitivities are the most suitable ones for the estimations of the ACs, since larger modeling and experimental errors may be acceptable. In the Poiseuille and Couette flows, the uncertainties of the flow rate and shear stress respectively are several times larger than the input uncertainty in the tangential momentum AC and much smaller than the uncertainty in the normal energy AC in a wide range of gas rarefaction. In the thermal creep flow, the uncertainty of the flow rate depends on the input ones of both ACs, but, in general, it remains smaller than the input uncertainties. A similar behavior with the thermal creep flow is obtained in the TPD flow. On the contrary, in the Fourier flow, the uncertainty of the heat flux may be about the same or even larger than the input ones of both ACs in a wide range of gas rarefaction. It is deduced that in order to characterize the gas-surface interaction via the CL ACs by matching computations with measurements, it is more suitable to combine the Poiseuille (or Couette) and Fourier configurations, rather than, as it is commonly done, the Poiseuille and thermal creep ones. For example, in order to estimate the normal energy AC within an accuracy of 10 %, experimental uncertainties should be less than 4 % in the thermal creep or TPD flows, while may be about 10 % in the Fourier flow.

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.

BEM performance with the addition of polynomials solving stationary thermal problems with functional gradation

This work presents the formulation and numerical results of the Dual Reciprocity Boundary Element Method (DRBEM), adapted to include the procedure known as the addition of polynomial functions. This technique is used to improve the interpolation scheme’s accuracy using radial basis functions. This idea works quite effectively in simple interpolation procedures, especially when the field profile to be approximated has similarities with added polynomials. Although applied as a supplementary resource in some works, the efficiency and restrictions of the procedure were not discussed in detail as necessary. In this article, the addition of functions is applied to solve non-homogeneous stationary heat transfer problems. The main objective is to analyze its capability, especially in reducing the demand for internal interpolation points. The three simulations show that although introducing polynomials can improve the results, other characteristics are mandatory for achieving suitable accuracy. Three examples of numerical simulation are solved and show that its effectivity is relative, mainly limited by the type of application.

Hydrogen peroxide droplet gasification and decomposition: Classic evaporation model vs. conjugate model

The purpose of the present study is to investigate the evaporation of hydrogen peroxide droplet and the impacts of gas phase thermal decomposition on this process. Two different flow solvers are developed for analysis where one uses the classic evaporation model, and the other solves the conjugate heat transfer problem considering temperature distribution within both gas and liquid phases accurately. The finite volume method is utilized to solve the governing equations of the reacting two-phase flow. Single droplet evaporation in the hot open surrounding is analyzed first to illustrate the effect of gas phase decomposition on droplet regression rate. It is shown that the decomposition changes the temperature distribution around droplet that leads to higher regression rate by increasing the heat transfer from the gas phase into the liquid phase. This cannot be captured using the classic model and must be studied by conjugate model. In addition, the effects of droplet radius, ambient pressure, and ambient temperature on the regression rate augmentation due to decomposition are investigated for single droplet. Finally, evaporation and decomposition of hydrogen peroxide droplet cloud in a closed vessel is simulated and it is demonstrated that conjugate model has more accurate prediction than the classic model and must be used in practical studies especially when the transient processes are drastic.