Solving Heat Transfer Problems Research Articles

Comparison of the Performance of New and Traditional Numerical Methods for Long-Term Simulations of Heat Transfer in Walls with Thermal Bridges

Several previous experiments showed that the leapfrog–hopscotch and the adapted Dufort–Frankel methods are the most efficient among the explicit and stable numerical methods to solve heat transfer problems in building walls. In this paper, we extensively measure the running times of the most successful methods and compare them to the performance of other available solvers, for example, ANSYS transient thermal analysis and the built-in routines of MATLAB, where three different mesh resolutions are used. We show that the running time of our methods changes linearly with mesh size, unlike in the case of other methods. After that, we make a long-term simulation (one full winter month) of two-dimensional space systems to test the two best versions of the methods. The real-life engineering problem we solve is the examination of thermal bridges with different shapes in buildings to increase energy efficiency.

Design, Preparation, and Performance Study of a Miniaturized High-Temperature Thick-Film Heat Flux Sensor

Solving heat transfer problems in high-temperature and temperature-changing environments is critical in a variety of applications, including modern turbines, aerospace, and nuclear power plants. However, most current thin-film-type heat flow sensors operate at approximately 1000 °C. Thus, we fabricated a kind of platinum–platinum/rhodium thick-film thermopile-type heat flux sensor which can work stably at 1200 °C based on an alumina ceramic substrate. The entire electrode layer was prepared by screen printing process. The surface morphology of the Pt electrode and the material in thermal resistance layer at different stages were investigated using scanning electron microscopy. The steady-state characteristics of the sensor were evaluated by using a high-temperature test platform. The experiments show that the peak voltage of the sensor is 1.4126 mV at the temperature of 1200 °C and the heat flow density of 283.3 kW/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Moreover, the repeatability of sensor at 1200 °C and high temperature holding for 4 h experiments were performed, verifying that the sensor has good consistency and durability. Therefore, we infer that the designed sensor can be applied for a long time under high temperature and large heat flow conditions, such as aerospace, mechanical metallurgy and energy construction fields.

Finite element analysis on heat convection effect on air temperature distribution in a heated room

Using the finite element method to solve heat transfer problem in solid medium has been popular since last century, but heat convection effect in fluid medium makes the problem cumbersome to solve efficiently. Thermal transfer calculation of fluid medium is complicated, because solving heat convection and Navier-Stokes equation is hard. By making proper assumptions, intricate equations can be skipped, and it is possible to give rough estimate of heat transfer result through a simple and efficient calculation. Which is significant for design and verifiction of heating system for physicists and engineers. The study aims to solve the temperature distribution of a certain heat system, using finite elment method and with given assumpted air circumfluence. In the calculation, the room domain is subdivided into finite elments, and the boundary condition is given according to the heat influx and emmision, air circumfluence is introduced to simulate the effect of convection. The simplified model illustrated that the finite element method is effective in giving quantitative result of heat transfer calculation. It also qualitatively showcased the significance of heat convection, when the result is compared to calculation without any air flow.

Effect of concentration and temperature on the physical and thermophysical properties of coffee extract

The physical and thermophysical properties (density, freezing temperature, specific heat, enthalpy, and thermal conductivity) of coffee extract were experimentally determined as a function of concentration (10–52 °Brix) and temperature (20 to −40 °C). Some models from the literature were also evaluated for predicting the behavior of these properties. Results indicated that all properties were influenced by the temperature and concentration of the solution due to their relationship with the amount of water/ice in the coffee extract. In general, the evaluated models described well the behavior of the coffee extract properties for a temperature range from 20 to −40 °C, except for the specific heat. Thus, a model for predicting specific heat was obtained using the experimental data through a non-linear regression (R 2 > 0.95). These models can be used to solve heat transfer problems involved in the cooling and freezing process of coffee extract. • Thermophysical properties of coffee extract were determined. • The properties were influenced by temperature and concentration. • Models for the prediction of the thermophysical properties were proposed. • The proposed models can be used to solve heat transfer problems.

Optimization of Laminar Boundary Layers in Flow over a Flat Plate Using Recent Metaheuristic Algorithms

Heat transfer is one of the most fundamental engineering subjects and is found in every moment of life. Heat transfer problems, such as heating and cooling, where the transfer of heat between regions is calculated, are problems that can give exact solutions with parametric equations, many of which were obtained by solving differential equations in the past. Today, the fact that heat transfer problems have a more complex structure has led to the emergence of multivariate models, and problems that are very difficult to solve with differential equations have emerged. Optimization techniques, which are also the subject of computer science, are frequently used to solve complex problems. In this study, laminar thermal boundary layers in flow over a flat plate, a sub-problem of heat transfer, is solved with recent metaheuristic algorithms. Teaching learning-based optimization (TLBO), sine cosine optimization (SCO), gray wolf optimization (GWO), whale optimization (WO), salp swarm optimization (SSO), and Harris hawk optimization (HHO) algorithms are used in the study. In the optimization problem, the laminar boundary layer thickness, heat flow, and distance from the leading edge are determined. These three models’ minimum, maximum, and target values are found under the specified design variables and constraints. In the study, 540 optimization models are run, and it is seen that HHO is the most suitable optimization technique for heat transfer problems. Additionally, SSO and WO algorithms gave results close to HHO. Other algorithms also set model targets with an average of less than 0.07% and acceptable error rates. In addition, the average problem solution time of all optimization algorithms and all models was 0.9 s. To conclude, the recent metaheuristic algorithms are found to be powerful and fast in solving heat transfer problems.

Numerical analysis of thermo-fluid problems in 3D domains by means of the RBF-FD meshless method

The use of CAE (Computer Aided Engineering) software, commonly applied to the design and verification of a great variety of manufactured products, is totally reliant on accurate numerical simulations. Classic mesh-based methods, e.g., Finite Element (FEM) and Finite Volume (FVM), are usually employed for such simulations, where the role of the mesh is crucial for both accuracy and time consumption issues. This is especially true for complex 3D domains which are typically encountered in most practical problems. Meshless, or meshfree, methods have been recently introduced in order to replace the usual mesh with much simpler node distributions, thus purifying the data structures of any additional geometric information. Radial Basis Function-Finite Difference (RBF-FD) meshless methods have been shown to be able to easily solve problems of engineering relevance over complex-shaped domains with great accuracy, with particular reference to fluid flow and heat transfer problems. In this paper the RBF-FD method is employed to solve heat transfer problems with incompressible, steady-state laminar flow over 3D complex-shaped domains. The required node distributions are automatically generated by using a meshless node generation algorithm, which has been specifically developed to produce high quality node arrangements over arbitrary 3D geometries. The presented strategy represents therefore a fully-meshless approach for the accurate and automatic simulation of thermo-fluid problems over 3D domains of practical interest.

Quasi-analytical solution to the problem of heat transfer by vortex flow based on self-similarity

Highly efficient vortex flow increases fluid flow and simultaneously enhances heat transfer. An accurate vortex flow model is of great importance to analyzing and solving heat transfer problems. The general form of the solution to the vortex flow problem was derived from the self-similarity properties of vortex flow along the radius direction, and its correctness was validated. The temperature distribution function of vortex flow was determined, and the relative thermal conductivity was obtained. A dimensionless number (ρCpvθ′Rk) was defined to characterize the temperature distribution of vortex flow. The rate of heat transfer was also determined. The results indicated that the dimensionless number represents the ratio of convection to thermal conduction, and can be used to accurately describe the temperature distribution of vortex flow. When the temperature at the vortex flow center is close to the average temperature, the difference in temperature phase is significant, and convection plays a dominant role in the heat transfer process. The temperature can be defined by sine function when the radius of vortex is decreased to a certain extent. The results can be applied to the analysis of large-scale vortex flow heat transfer, the optimization design of small-scale vortex flow heat transfer, and the development of vortex flow and temperature sensors.

Investigation on thermal characteristics of walking reheating furnace for beam blank

Beam blank reheating is a key process in the production of high-quality H-beam. To gain better insight into the heat transfer process of the beam blank in reheating furnace, a heat transfer model considering radiative heat transfer of furnace gas and conductive heat transfer in beam blank simultaneously is established. The main variable-correction method and zonal method are adopted to solve heat transfer problems in reheating furnace. The best productivity point (BPP) and optimal productivity range (OPR) of the reheating furnace based on the relationship between the specific heat consumption and furnace efficiency are firstly proposed to guide the production process. Then, the effects of the length of soaking zone and preheating temperature of air and fuel on thermal characteristics of walking reheating furnace for beam blank are analyzed. The results show that the reasonable length of soaking zone can obtain high reheating quality of the beam blank, reasonable temperature of furnace gas and exhaust gas. The preheating air has a more influence than preheating fuel on the reheating process of reheating furnace for beam blank. This work can provide valuable reference for the determination to make thermal schedule of beam blank and on-line supervisory control of the production process.

A non-field analytical method for heat transfer problems through a moving boundary

This paper presents an extension of the non-field analytical method—known as the method of Kulish—to solving heat transfer problems in domains with a moving boundary. This is an important type of problems with various applications in different areas of science. Among these are heat transfer due to chemical reactions, ignition and explosions, combustion, and many others. The general form of the non-field solution has been obtained for the case of an arbitrarily moving boundary. After that some particular cases of the solution are considered. Among them are such cases as the boundary speed changing linearly, parabolically, exponentially, and polynomially. Whenever possible, the solutions thus obtained have been compared with known solutions. The final part of the paper is devoted to determination of the front propagation law in Stefan-type problems at large times. Asymptotic solutions have been found for several important cases of the front propagation.

Exact method to solve of linear heat transfer problems

When approximating multidimensional partial differential equations, the values of the grid functions from neighboring layers are taken from the previous time layer or approximation. As a result, along with the approximation discrepancy, an additional discrepancy of the numerical solution is formed. To reduce this discrepancy when solving a stationary elliptic equation, parabolization is carried out, and the resulting equation is solved by the method of successive approximations. This discrepancy is eliminated in the approximate analytical method proposed below for solving two-dimensional equations of parabolic and elliptic types, and an exact solution of the system of finite difference equations for a fixed time is obtained. To solve problems with a boundary condition of the first kind on the first coordinate and arbitrary combinations of the first, second and third kinds of boundary conditions on the second coordinate, it is proposed to use the method of straight lines on the first coordinate and ordinary sweep method on the second coordinate. Approximating the equations on the first coordinate, a matrix equation is built relative to the grid functions. Using eigenvalues and vectors of the three-diagonal transition matrix, linear combinations of grid functions are compiled, where the coefficients are the elements of the eigenvectors of the three-diagonal transition matrix. Boundary conditions, and for a parabolic equation, initial conditions are formed for a given combination of grid functions. The resulting one-dimensional differential-difference equations are solved by the ordinary sweep method. From the resulting solution, proceed to the initial grid functions. The method provides a second order of approximation accuracy on coordinates. And the approximation accuracy in time when solving the parabolic equation can be increased to the second order using the central difference in time. The method is used to solve heat transfer problems when the boundary conditions are expressed by smooth and discontinuous functions of a stationary and non-stationary nature, and the right-hand side of the equation represents a moving source or outflow of heat.

Analysis of Algorithm Efficiency for Heat Diffusion at Nanoscale Based on a MEMS Structure Investigation

This paper presents an analysis of the time complexity of algorithms prepared for solving heat transfer problems at nanoscale. The first algorithm uses the classic Dual-Phase-Lag model, whereas the second algorithm employs a reduced version of the model obtained using a Krylov subspace method. This manuscript includes a description of the finite difference method approximation prepared for analysis of the real microelectromechanical system (MEMS) structure manufactured by the Polish Institute of Electron Technology. In addition, an approximation scheme of the model, as well as the Krylov subspace-based model order reduction technique are also described. The paper considers simulation results obtained using both investigated versions of the Dual-Phase-Lag model. Moreover, the relative error generated by the reduced model, as well as the computational complexity of both algorithms, and a convergence of the proposed approach are analyzed. Finally, all analyses are discussed in detail.

Application of Genetic Algorithm for Optimization of Heat-Transfer Parameters

Nowadays, new materials are developed with the aim to reduce heat transfer and energy loss. Thus, energy can be reduced and heat energy can be transferred efficiently. Many researches on the field of heat transfer have been made in the literature. However, there are few studies on the determination of insulation material thickness using heuristic algorithms and there is no study on finding the thermal boundary layer thickness using heuristic algorithms. One of the heuristic algorithms used in the field of computer science is Genetic Algorithm (GA), which is frequently applied in optimization problems. We propose that GA could be used to solve heat transfer problems of insulation material selection and laminar thermal boundary layer thickness determination. The goal of the proposal is to estimate the optimal parameters using a GA. In the first case, the thickness of insulation material selection and the maximum amount of heat loss that can be caused by different thicknesses of the insulating material under the boundary conditions and assumptions are calculated using GAs. It is shown that, using the heat-transfer coefficient and unit length cylinder, GAs can be used in everyday problems, such as determining the thickness of the insulating material or the outer temperature of the insulating material. In the second case, the boundary layer thickness is determined using GA for air flow with a laminar flow, where its characteristics are constant, irradiation is neglected, and plate and air temperatures are constant in the continuous regime on the plate. For both cases, the GA results are repeated 5 times and it is observed that the results are very close to each other. The experimental results demonstrate that, for both cases GA gives optimal target, minimum and maximum values, thus, GAs are applicable in heat-transfer problems that require optimization.

Computationally efficient thermal network model and its application in optimization of battery thermal management system with phase change materials and long-term performance assessment

This paper presents a simple 2D thermal network model for a battery thermal management system with phase change materials (PCMs). An equivalent electric circuit model is developed to solve heat transfer problems that include the processes of battery heat generation and PCM thermal storage. This thermal network model is compact and accurate. The simulation time is saved by 99% compared with a conventional numerical model, whereas the average prediction error of battery temperature is lower than 1 °C. This model is applied for the rapid optimization of the PCM properties to warm up a battery pack rapidly during cold starts. The results demonstrate that the PCM suitable for thermal management under low temperatures should have a melting point of approximately 40 °C, high thermal conductivity of over 5.4 W/m K, and a low latent heat storage density of less than 0.0145 kJ/m3. Utilizing its high computation efficiency and resolution for capturing the temperature distribution in 2D, the model can quantitatively assess the long-term effect of the thermal management system on the life of a battery module during a 10,000-hour charge–discharge cycle. A lifespan model that integrates a battery capacity fade model into the thermal network is developed and the simulation results verify that a lower temperature and temperature difference reduce the capacity loss in a multi-cell module. The thermal network model is efficient to design and optimize the thermal management system for a real-size battery pack, based on the assessment of its long-term impacts on battery performance.

Экспериментальное определение теплопроводности композиционных материалов в широком диапазоне значений при комнатной температуре

In developing new composite materials and solving heat transfer problems, the thermal conductivity is an important characteristic that must be reliably determined. This often requires samples of the smallest dimensions, which is relevant for the production of pilot batches of material, as well as if they are taken directly from the product, when the amount of material is very limited. Most common methods for determining thermal conductivity require samples of relatively large sizes. To measure thermal conductivity on small-sized samples, an upgraded benchtop instrument is introduced. The instrument uses the relative method of longitudinal heat flux, which consists in a comparative measurement of a sample located between the heater and the standard in a stationary thermal mode. This paper presents the instrument design details, the requirements for the samples, explains the calibration features and the measurement procedure. The measurement results in a number of composite materials, as well as in materials with well-studied properties are analyzed. Findings show that the error of determining the thermal conductivity on a modernized instrument does not exceed several percent.

A trust region approach for numerical modeling of non-isothermal phase change

An efficient enthalpy-based numerical approach is introduced for solving heat transfer problems with non-isothermal phase change. The goal of this model is to simulate permafrost thaw rates, understand the significant effects of climate change on permafrost, and assess the reciprocal effects of permafrost thaw on climate. In order to simulate permafrost over time spans of several years, a robust and efficient model is required. In the present setting, the heat transfer problem is converted to a minimization problem, in which we minimize a potential function that characterizes the governing heat transfer PDE within a time discrete framework. The use of the trust region minimization algorithm proves desirable due to the highly non-linear energy functional which also involves non-convex terms induced by phase change. Results obtained show satisfactory agreement with existing analytical solutions. Moreover, the grid and time step convergence studies conducted to examine the dependence of the solution on mesh and time step sizes indicate robust convergence rates. This is the first application of trust region energy minimization algorithm in permafrost simulation.

A 2D discrete heat transfer model considering the thermal resistance effect of fractures for simulating the thermal cracking of brittle materials

A concise, two-dimensional discrete heat transfer model is presented, which considers the thermal resistance effects of cracks. The discrete heat transfer model discretizes the continuum into individual triangular elements, and the adjacent triangular elements transfer heat through corresponding joint elements. Then, the principle of selecting the heat exchange coefficient of the joint element is determined through a parameter sensitivity analysis. Moreover, the 2D discrete heat transfer model is combined with the finite discrete element method to build a thermomechanical coupled model for simulating brittle material thermal cracking. The thermal stress and thermal shock problems are studied by using the thermomechanical coupled model, and the numerical results are compared with either the analytical solution or experimental results to validate the 2D discrete heat transfer model and thermomechanical coupled model. The discrete heat transfer model and thermomechanical coupled model provide a powerful tool for solving heat transfer problems in discontinuous media as well as the thermal cracking problem in brittle materials.

Temperature dependence of thermal conductivity of Al-Si-1%Fe alloys under heating up to 150 °C

We have studied the temperature dependence of the thermal conductivity of a series of experimentally obtained aluminum-silicon alloys with different silicon addition and additional iron content of 1 % by weight. The article shows how the change in the silicon content affects the thermal properties of the experimentally obtained alloys at room temperature. Also, the article describes the character of the change in thermal conductivity when the samples are heated up to 150 °C. Based on the obtained data, we con clude that the alloy containing 4 % silicon by weight is the most prospective for usage as a material for solving heat transfer problems.

Study of Multiple Interfaces of Contact Using the Lattice Boltzmann Method

The Lattice Boltzmann Method is a very successful numerical modeling method that has proved its effectiveness in many areas of study and especially in the field of fluid flow and thermo-hydrodynamic problems. In this paper, authors study heat transfer problems with thermal contact resistance (TCR) using the Lattice Boltzmann Method (LBM) and more specifically using the Particle Image model (PI) which is a numerical model for solving heat transfer problems. In this study, we show a brief presentation of thermal Lattice Boltzmann Method and its main steps for the two dimensional model. and we introduce our new study of heat transfer involving two contacting media along multiple interfaces of contact. To do so, we detail the Particle Image model and the whole methodology for treating this new study and provide a case of study and numerical results to support this new configuration. The obtained numerical results of temperature gap between the two media show an agreement between this model and the theoretical solution for different values of the thermal contact resistance.

Prediction of oscillatory heat transfer coefficient for a thermoacoustic heat exchanger through artificial neural network technique

Heat exchangers under oscillatory flow condition in thermoacoustic devices are quite different with the traditional ones in heat transfer and flow behavior of thermo-viscous fluid. As a result, one cannot directly apply the heat transfer correlations for the steady flow to design thermoacoustic heat exchangers, otherwise, significant deviation will arise. However, some correlations of heat transfer for the oscillatory flow have not been well established yet. This study involves the application of artificial neural network (ANN) as a new approach to predict oscillatory heat transfer coefficient of one thermoacoustic heat exchanger under some operating conditions. One ANN model for the oscillatory heat exchanger used in one standing wave thermoacoustic refrigerator has been developed based on the published experimental data. This proposed ANN model has three layers with the configuration of 2-10-1, namely one input layer with two neurons representing two operating parameters, oscillating frequency and mean pressure, one hidden layer with optimal ten hidden neurons and one output layer with one neuron representing the oscillatory heat transfer coefficient as response. Moreover, a statistical analysis has been provided for studying the influence strength of these two input parameters on the oscillatory heat transfer coefficient. This ANN model had been proven to be desirable in accuracy for predicting oscillatory heat transfer coefficient by comparing ANN model results with both experimental results and calculated results by several other correlations from the published literature at the same operating conditions. This research work provides a new and accurate modeling approach based on ANN technique for the research of thermoacoustic heat exchangers and solving heat transfer problems related with oscillatory flow condition.

An element decomposition method for heat transfer analysis

In this work, an element decomposition method (EDM) is formulated to deal with heat transfer analysis. For this method, the quadrilateral elements are first divided into sub-triangular cells and the local temperature gradient in each sub-triangular cell is obtained using linear interpolation function. Then, the temperature gradient of whole quadrilateral can be calculated by averaging the local gradient in each sub-domain. As only one integration point is utilized for each element, the computational cost of presented method is much less and no mapping or coordinate transformation is involved. Several numerical examples are given to fully test the validity of this method and it is found that the EDM is very accurate, stable and can achieve high level of convergence when solving heat transfer problems.