Three-dimensional Steady-state Heat Research Articles

Insulation performance evaluation of stone-finished exterior insulation systems with insulation frames for green remodeling of concrete exterior walls

This study aimed to evaluate the thermal bridge reduction effect of insulation frames applied to a stone-finished exterior insulation system, which is commonly used in green remodeling projects. The insulation performance of the exterior walls and the energy performance of the building in a baseline case in which an existing steel pipe frame was applied were compared with those in cases alt 1 and alt 2, which included application of double- and single-wired truss-shaped insulation frames, respectively. First, a three-dimensional steady-state heat transfer simulation was conducted for the exterior wall-floor joint of the model building, and the effective U-factor was obtained. Next, mock-ups were constructed and the U-factor was tested to verify the insulation performance of cases alt 1 and alt 2. The heat loss decreased as the effective U-factors of alt 1 and alt 2 decreased by 19.0 % and 19.7 %, respectively, compared to the baseline case, according to the heat transfer simulations. In the mock-up test, the U-factors of alt 1 and alt 2 were similar to design U-factor, indicating almost no heat loss caused by the thermal bridges. Notably, the U-factor of alt 2 was 2.4 % lower than that of alt 1. Finally the energy performance of the entire building was compared through dynamic building energy simulations by reflecting the thermal bridging effect. The annual heating and cooling energy use of alt 1 and alt 2 were 2.5 % and 2.6 % lower than those of the baseline case, respectively, confirming the energy-saving effect of reducing thermal bridges.

A new set of explicit solutions for postbuckling behaviour of anisotropic shear deformable laminated cylindrical shells with general imperfection distribution and thermal loading

Thermal postbuckling analysis is presented for shear-deformable anisotropic laminated cylindrical shell with general imperfection distribution under several typical temperature fields are analyzed, including uniform temperature, tent-like linear distribution, axial and circumferential quadratic parabolic temperature fields over the shell surface and through the shell thickness. On this basis, the general temperature distribution can be obtained based on the three-dimensional steady-state heat transfer equation. At the same time, based on the high order shear deformation theory including anisotropic coupling effect, geometrically nonlinear large deflection displacement-strain relationship, the general initial geometric imperfections obtained by measurement and analytical means are introduced, and the thermal buckling equilibrium differential equation of anisotropic shear deformable laminated cylindrical shell with initial imperfections is established. A two-step perturbation-Galerkin integral method is used to obtain explicit solutions for the path development direction of post-thermal buckling equilibrium. The results of parameter analysis show that the material properties and temperature dependence, temperature distribution, lay-up and geometric parameters such as radius-to-thickness ratio have important effects on the thermal buckling load and postbuckling equilibrium path. The present method provides an effective theoretical prediction and analysis method for the design of the carrying capacity of submarine pipelines.

An inverse problem to estimate simultaneously the heat source strength for multiple integrated circuit chips on a printed circuit board

<abstract> <p>In this three-dimensional steady-state inverse heat transfer problem, we determine the magnitude of the spatially dependent volumetric heat source originating from multiple encapsulated chips mounted on a printed circuit board (PCB). Prior to the estimations, the functional form of the multiple heat sources is treated as unknown, leading to its classification as a function estimation challenge within the realm of inverse problems. The utilization of the conjugate gradient method (CGM) as an optimization tool is rooted in its distinct advantage of not requiring any a priori knowledge regarding the functional form of the unidentified quantities. Furthermore, the CGM empowers the simultaneous correction and estimation of multiple unknowns during each iteration, thereby ensuring the consistent possibility of precise estimates.</p> <p>To affirm the precision of the estimated heat source attributed to multiple chips, a series of numerical experiments were conducted. These experiments encompassed varying inlet air velocities and introduced measurement errors. Notably, the results revealed that meticulous measurements consistently yielded accurate heat generation assessments for the chips, regardless of the prevailing air velocity conditions. The findings underscored that the accuracy of chip heat generation estimates diminished as measurement errors escalated, predominantly due to the ill-posed nature inherent in the inverse problem.</p> </abstract>

A three-dimensional steady-state heat and vapour transport model to assess the risk for interstitial condensation in building enclosures

The article presents a practical 3D heat and vapour model to estimate the risk for interstitial condensation in building enclosures. The model is in fact a three-dimensional implementation of the Glaser method. In the first part of this article the modelling assumptions and solution technique are outlined. Next, the model is validated against an example from the literature. The third part of the article zooms in on the applicability of the proposed model in comparison to more complex hygrothermal models. Both the weaknesses and the strengths of the methodology are discussed. This section reviews the circumstances in which the model can be used safely and when a more detailed analysis is preferable. Finally, the article presents an actual case whereby the applicability of the model is demonstrated by making design decisions for the energetic retrofit of a curtain wall system.

An inverse heat conduction-convection conjugated problem in estimating the unknown volumetric heat generation of an encapsulated chip

A three-dimensional steady-state inverse heat conduction-convection conjugated problem (IHCCCP) is investigated in this work. The goal is to estimate the unknown spatially dependent volumetric heat generation of an encapsulated chip. The functional form of the volumetric heat generation is considered to be unknown prior to the estimation. Therefore, it is known as the category of function estimation in inverse problems. Optimization is performed using the conjugate gradient method (CGM) because this method does not require a priori information regarding the functional form of the unknown functions. Using this method, a large number of unknowns can be corrected and estimated in each iteration, and good estimations can always be obtained. This efficient algorithm has never been applied to the IHCCCP. The results of the inverse estimations are verified using numerical simulations with various inlet air velocities and measurement errors. They reveal that using exact measurements always produces accurate volumetric heat generation and that the regular air velocity does not affect the estimates. The measurement errors and their influence on the estimated heat generation are analyzed. Finally, it is concluded that because the inverse problem is ill-posed, the estimated heat generation becomes less accurate as the measurement error increases.

A steady-state inverse heat conduction-convection conjugated problem in determining unknown spatially dependent surface heat flux

The unknown spatially dependent surface heat flux is estimated for a three-dimensional steady-state inverse heat conduction-convection conjugated problem (IHCCCP) in this study. Air with a specified velocity flows over a flat plate which was subjected to an unknown heat flux on the bottom surface and the simulated temperature measurements on the top surface were used for the estimations. As the functional form of the heat flux is considered to be initially unknown, this inverse problem falls within the category of function estimation. Optimization is performed using the conjugate gradient method (CGM) because this method does not require a priori information regarding the functional form of the unknown functions, enabling a large number of unknowns to be corrected and estimated in each iteration to always yield good estimates. This efficient algorithm has never been applied to the IHCCCP. The results of the inverse solutions are verified using numerical simulations with various inlet air velocities and plate thicknesses. The results show that using exact measurements always produces accurate boundary heat fluxes under thin plate conditions since the maximum error for the estimated heat flux using error measurements was found to be only 6.43%, and the air velocity does not affect the estimates. The measurement errors and their influence on the inverse solutions are analyzed. Finally, it is concluded that because the inverse problem is ill-posed, the estimated heat flux becomes less accurate as the plate thickness increases.

Numerical and experimental investigationg of a turbine guide vane with conjugate heat transfer method

Three-dimensional steady-state conjugate heat transfer numerical method was utilized to study the flow and heat transfer characteristics of a turbine guide vane. In experiment, a real-sized turbine vane model and corresponding test section were designed. We verified the simulation accuracy of different turbulence models, coupling with transition model and limiter factor in conjugate heat transfer method. Compared with the experimental results, the results indicated that the SST model shows better accuracy and economy than other models studied in this paper.

Insulation Performance Comparison of Curtain Wall Systems with Existing Pipe Frames and Truss-Shaped Insulation Frames

The purpose of this study was to compare insulation performance between a base case that applied the existing steel pipe frame and an alternative case that reduced thermal bridging by applying a truss-shaped insulation frame (TIF) to a back frame type curtain wall. Insulation performance was compared by obtaining the effective U-factor and the lowest indoor surface temperature through a three-dimensional steady-state heat transfer simulation. In addition, mock-up tests were performed to compare the U-factors of the base case and alternative case. The simulation results showed that the effective U-factor of the alternative case was 36% lower than in the base case, a significant heat loss reduction. The lowest indoor surface temperature of the alternative case was 0.5 °C higher than in the base case, showing that the surface condensation risk also decreased. In the mock-up test results, the alternative case U-factor was 33% lower than in the base case, confirming the associated large heat loss reduction. For the base case, both the effective U-factor by simulation and the U-factor by the mock-up test were much higher than the design U-factor according to the Korean Design Standard, which neglects thermal bridging, indicating a significantly increased heat loss caused by this factor. For the alternative case, however, both U-factors were similar to the design U-factor.

Thermal aspect of material selection for substrate board equipped with high heat flux IC chips

This paper investigates the material selection for substrate board equipped with nine silicon heaters that mimic IC chips. This includes computational research on laminar forced convection air cooling of silicon IC chips in electronic components mounted on substrate boards subjected to high uniform heat fluxes in a horizontal channel. Copper clad boards with single and multilayer having thermal conductivities of 8.8, 40.5, and 61.5 W/m K are the substrate materials used in this study. Three-dimensional steady-state conjugate heat transfer with laminar non-isothermal fluid flow module is used from COMSOL Multiphysics 5.4 to study fluid flow and heat transfer. Simulations performed with flowing air velocities of 1.5, 2.5, and 3.5 m/s with very high heat fluxes of 10000, 12500, and 15000 W/m2. It showed that the temperature on subsrate board strongly depends upon placement of heaters, Reynolds number, substrate thermal conductivity. It also found that higher thermal conductivity substrate materials results in heat transfer enhancement and decrease chances of failures of electronic devices. A non-dimensional temperature based correlation is also devised in therms of non-dimensional heat flux, thermal conductivity, Nusselt number, and Reynolds number.

Effects of solid particle thermal conductivity on heat storage performance of heat storage bed

The thermal properties of particles are important parameters that directly affect the heat storage performance of the solid particle heat storage bed. This paper reports the effects of solid particle thermal conductivity on heat storage performance of heat storage bed. A three-dimensional steady-state heat transfer model of heat storage bed with a single vacancy was established using ANSYS 19.0. The effects of thermal conductivity of particles were studied. With the increase in thermal conductivity of particles, the effect of the vacancy on heat storage particle bed heat transfer performance increases, the affected area size increases, so the heat storage and release performance of heat storage bed decreases. With the increase of thermal conductivity of particles from 0.5 W/ (m·K) to 50 W/ (m·K), the size of the affected region increased from 0.61 times of particle size to 1.82 times of particle size in the direction perpendicular to the heat transfer, and the size of the affected region increased from 1.61 times of particle size to 3.91 times of particle size in upstream of the direction parallel to the heat transfer. At the same time, the size of the affected region increased from 1.69 times of particle size to 3.93 times of particle size in downstream of the direction parallel to the heat transfer. It can provide a basis for improving the thermal resistance theory.

Effect of the single vacancy in particle pile on heat transfer performance of particle pile

This paper reports the effect of a single vacancy on heat transfer of particle pile. A three-dimensional steady-state heat transfer model of particle pile with a single vacancy was established. The effects on the temperature distribution, heat transfer mode and heat flux characteristics of the particle pile were studied. In the area close to the vacancy, the particle temperature distribution is significantly affected, and the average temperature line is significantly deformed. The heat conduction between particles along the Y-direction is the dominant heat transfer mode around the vacancy. Compared with a particle pile without vacancy, the total heat flux at the hot wall decreases by 0.63% and the apparent thermal resistance of the particle pile increases by 0.71%. The size of the region affected by a vacancy on heat transfer was determined. At the X-direction, the size of the region affected by a vacancy is 1.79 times of particle size. Upstream position of vacancy at the Y-direction, the size of the region is 4.03 times of particle size. Downstream position of vacancy at the Y-direction, the size of the region is 3.81 times of particle size. The research results can be used to improve the thermal resistance network theory.

A novel boundary-type meshfree method for solving three-dimensional single-domain steady-state heat conduction problem

The virtual boundary meshfree Galerkin method (VBMGM) is further developed to compute three-dimensional single-domain steady-state heat conduction problem. Using VBMGM, three-dimensional problem is reduced into two-dimensional boundary, whose element information can be obtained by the meshing software, namely ANSYS software. It greatly facilitates the programing implementation of the proposed method that ANSYS Parametric Design Language (APDL) is demonstrated for the element information acquisition of the curved surface. The virtual source function on the virtual boundary element method (VBEM) is interpolated by the radial basis function interpolation (RBFI) of the meshfree method. The calculation equation of three-dimensional single-domain steady-state heat conduction problem by VBMGM is constructed by the Galerkin method of the weighted residual method. Therefore, it has the advantages of the VBEM, the meshfree method and the Galerkin method that the proposed method is employed to computed three-dimensional single-domain steady-state heat conduction problem. It is beneficial to further popularize the proposed method to solve other three-dimensional heat conduction problems that the detailed numerical discrete formula of the proposed method for three-dimensional single-domain steady-state heat conduction problem is obtained. The numerical results of two numerical examples are computed and compared with the other numerical method and the extract solutions. The accuracy and stability of VBMGM for three-dimensional single-domain steady-state heat conduction problem are verified.

A Hamiltonian-based analytical approach for three-dimensional heat conduction of cylinders with specific mixed boundary conditions

A novel analytical symplectic method is introduced to investigate the three-dimensional steady-state heat conduction of cylinders with specific mixed boundary conditions (partial temperature and partial heat flux density). By defining the temperature and heat flux density as the mutually dual variables, the Hamiltonian form of governing equations are established. The original problem is reduced into a symplectic eigenproblem which can be solved by the method of separation of variables and a symplectic sub-system. Exact analytical solution is obtained and expressed in terms of symplectic eigensolutions. Comparison studies demonstrate the accuracy of the proposed method. Some new results are given also.

An improved implementation of triple reciprocity boundary element method for three-dimensional steady state heat conduction problems

The domain integrals caused by heat generation appearing in the boundary integral equation (BIE) of steady state heat conduction problems can be converted into boundary integrals by triple reciprocity method (TRM). However, the current triple reciprocity approximation (TRA) of domain functions is time-consuming and its accuracy is not stable in different geometric models, due to the need to solve a combination equation, whose degree of freedom is twice the number of boundary nodes plus the number of domain interpolation points. Therefore, a new formula of TRA is proposed in the current study to save computing time and storage space and improve accuracy. In the new proposed TRA formula, the combination equation is transferred into three equations that are solved in sequence. Four numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. Results show that although the new TRA formulation is equivalent to the original one, the approximation results are quite different, especially for non-thin structures. Particularly, the improved formula of TRA can save computing time and storage space, and get better accuracy. The improved triple reciprocity BEM is a useful approach to analyze the three-dimensional steady heat conduction problems more efficiently and accurately.

A novel interface integral formulation for 3D steady state thermal conduction problem for a medium with non-homogenous inclusions

A novel regularized interface integral equation for three-dimensional steady state heat conduction problems with non-homogeneous inclusions is developed. The proposed formulation only contains the fundamental solution of isotropic matrix. As a result, the fundamental solution of non-homogeneous inclusion, usually very difficult to obtain, is avoided. Domain integrals caused by the contrast of heat conductivities between the inclusions and the matrix are converted into equivalent interface integrals using the radial integration method by expressing the temperature gradient as a series of radial basis functions. Therefore, a pure interface integral equation is obtained and there is no need to discretize the inclusion into finite elements to evaluate the domain integral. For the determination of the flux and temperature, collocation points are distributed inside the inclusion to form a system of linear equations. To eliminate the geometrical errors and study the inclusions with arbitrary geometry, bivariate Non-Uniform Rational B-Splines basis functions are used to depict the boundaries of the inclusions. Numerical results are compared with available analytical solutions or finite element solutions.

Semi-analytic solution of three-dimensional temperature distribution in multilayered materials based on explicit frequency response functions

Multilayer coatings have been widely using in a wide range of applications, including industrial, biological and electrical areas, and the thermal distribution in a multilayered material is of great interest. In present paper, the frequency response functions (FRFs) of temperature field under unit point heat flux are derived through thermal conduction equation. The unknown coefficients in the FRFs are assembled in a linear system of matrix equations according to the heat input and continuity condition of heat flux and temperature at each interface; then the coefficients are solved and expressed recursively. Based on the closed-form solution of FRFs, a fast semi-analytical method (SAM) is developed to solve the three-dimensional steady state heat conduction in arbitrary multilayered materials, and there are no limits on the number or the thickness of layers. The temperature fields under different kinds of heat flux in multilayered coatings are studied. Moving heat flux and convection on the surface are also considered.

Probing torque, traverse force and tool durability in friction stir welding of aluminum alloys

A coupled theoretical and experimental study was undertaken to examine the impact of plate thickness, alloy strength and processing conditions on the susceptibility of tool failure in friction stir welding of AA7075 and AA7039. A three-dimensional steady-state heat transfer model was used to compute the temperature field in tool and workpiece alloy. The torque and traverse force, and the mechanical stresses on the tool were estimated analytically and validated with the corresponding experimentally measured results for a range of processing conditions. The propensity of the tool to failure was assessed by a durability factor, which was estimated as a ratio of tool material strength at the computed peak temperature and the resultant mechanical stress on the tool probe. The results showed that rise in welding speed, alloy strength and plate thickness could lead to increased mechanical stresses on tool probe, reduced durability factor and enhanced susceptibility of tool failure. The overall methodology was used successfully to provide the underlying basis for two reported practical examples of tool failures in friction stir welding.

3-D numerical study of the effect of Reynolds number and baffle angle on heat transfer and pressure drop of turbulent flow of air through rectangular duct of very small height

Summary Present article illustrates a computational study of three-dimensional steady state heat transfer and high turbulent flow characteristics through a rectangular duct with constant heat fluxed upper wall and single rectangular cross-sectioned baffle insertion at different angles. RNG k–ɛ model along with standard wall function based computations has been accomplished applying the finite volume method, and SIMPLE algorithm has been executed for solving the governing equations. For a Reynolds number, Re of 10,000 to 50,000, Prandtl Number, Pr of 0.707 and baffle angle, α of 30°, 60°, 90°, 120°, 150°, computational studies are executed, centred onto the hydraulic diameter, D h , test section and hydrodynamic entry length of the duct. Flow field has been solved using Ansys Fluent 14.0 software. Study exposes that baffled rectangular duct has a higher average Nusselt number, Nu and Darcy friction factor, f compared to a smooth rectangular duct. Nu as well as f are found to be maximum at 90° baffle angle. Results illustrate that both α and Re play a significant role in heat transfer as well as flow characteristics and also effects TEF. The correctness of the results attained in this study is corroborated by comparing the results with those existing in the literature for smooth rectangular duct within a precision of ±2% for f and ±4% for Nu .

Influence of Thermal Bridges on the Insulation Performance of Curtain Wall Panel Systems

AbstrctThermal insulation plays a key role in saving energy consumed by buildings. To obtain a high level of insulation performance, repeated thermal bridges should be minimized. These bridges may cause a substantial heat loss through the building envelope. Recently, the application of curtain walls has been rapidly increasing. However, thermal bridges frequently occur in the non-vision panel system in which the insulation materials are installed because of the numerous metal members passing through the insulation layer. The aim of this study was to analyze the influence of thermal bridges on the insulation performance of curtain wall panels in terms of the energy performance and internal surface condensation risk. A three-dimensional steady state heat transfer simulation was performed for four types of panel systems: insulation-joined metal sheet, insulation-separated metal sheet, bracket-fixed metal panel and screw-fixed metal panel. The heat loss, effective U-value, lowest internal surface temperature and lowest temperature factor of each panel system with and without thermal bridges were calculated and compared.

Numerical Simulation of the Flow and Heat Transfer of Fractal Tree-Like Minichannel Heat Exchanger

A three-dimensional steady-state laminar flow and heat transfer model for fractal tree-like minichannel heat exchanger is developed.The fluid flow and heat transfer process is studied by CFD software. Because of its symmetric structure, only half body of the heat exchanger is calculated. The fluid-solid coupled method is applied and the hexahedral grid is used on the control volume.The temperature distribution and velocity distribution for different heat flux on top boundary surface are obtained with an inlet hydraulic diameter of 3.2mm.The simulated results show that the fractal tree-like minichannel heat exchanger has good temperature uniformity and small pressure drop.