Three-dimensional Steady-state Heat Research Articles

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.

실측실험과 3차원 정상상태 열전달 해석을 통한 발열유리의 온도 및 전열량 분석

실측실험과 3차원 정상상태 열전달 해석을 통한 발열유리의 온도 및 전열량 분석

Optical, spectral, and thermal characteristics of InGaN/GaN green flip-chip light-emitting diodes

We reported the temperature-dependent device characteristics of InGaN/GaN green flip-chip light-emitting diodes (large chip size of 1125×1125μm2) on patterned sapphire substrate. Through the experiments in the temperature range of 298–358K, optical, electrical, and spectral properties were measured and analyzed. At 350mA and 298K, the optical output power of 56.2mW, forward voltage of 3.26V, and emission peak wavelength of 503.6nm were obtained. The characteristic temperature was also estimated at an injection current of 350mA under pulsed mode, indicating a value of 1019K. The junction temperature was experimentally measured by the forward voltage method. For comparison with theoretically calculated results, three-dimensional steady-state heat transfer model based on finite element method was employed. The thermal resistance (∼12.76K/W) extracted from the experimental results exhibited a similar value with the simulated result (~14.22K/W).

A formalism for anisotropic heat transfer phenomena: Foundations and Green’s functions

A new complex-variable formalism for the analysis of three-dimensional (3D) steady-state heat transfer problems in homogeneous solids with general anisotropic behaviour is proposed in this paper. The derived method is based on the Radon transform, which is used in order to reduce the dimension of the problem to a two-dimensional (2D) Radon space where a solution can be easily handled via a complex-variable method. Subsequently, the 3D solution is obtained by applying the inverse Radon transform. Despite that the main goal of this work is to develop and illustrate the general methodology, the proposed formalism is further applied to derive new Green’s functions as application examples. Contributions include new forms for bimaterial and half-space Green’s functions for line, point, vortex and dipole heat sources. In particular Green’s functions due to heat vortex loop sources for infinite media, half-space and bimaterial systems are presented for the first time. The veracity and computability of the approach are demonstrated with some numerical examples.

Three-dimensional steady-state ground heat transfer for multi-zone buildings

A closed-form analytical solution is presented for steady-state ground heat transfer from buildings with multiple rectangular floors at different temperatures. The heat transfer results obtained using the analytical solution were found to be in close agreement with those obtained using a commercial numerical simulation software package for a two-zone building. For the case study, the ground heat transfer calculation using the analytical solution is several orders faster than the numerical simulation method. The analytical solution provides a fast and accurate calculation method for the steady-state ground heat transfer components for multi-zone buildings.

Dynamic three-dimensional heat transfer calculation for uninsulated slab-on-ground constructions

Analytical solutions for two-dimensional steady-state and transient heat transfer from exterior ground surface are obtained for uninsulated slab-on-ground constructions. Approximate three-dimensional steady-state and transient heat transfer expressions are constructed. It is demonstrated that the approximate three-dimensional expressions give heat transfer results in satisfactory agreement with the analytical solutions and verified numerical models for the IEA BESTEST cases. The computation time for an annual simulation of the hourly floor heat transfer for the IEA BESTEST cases was found to be less than 0.1s on a 2.6GHz laptop computer. The proposed approximate expressions can be conveniently implemented in dynamic building simulation tools for fast ground-coupled heat transfer calculation.

Device characteristics and thermal analysis of AlGaInP-based red monolithic light-emitting diode arrays

We investigated the device characteristics of AlGaInP/GaInP multiple quantum wells monolithic light-emitting diode (LED) arrays operating at λ ∼ 630 nm, together with experimental and theoretical thermal analysis. The optical and electrical properties were experimentally measured. The junction temperature of a single LED with 300 × 300 µm2 was experimentally determined by the electroluminescence emission peak shift method, which led to a thermal resistance of ∼47 K W−1. As the number of LEDs in arrays was increased, the optical power output (Popt) was also increased. For 1 × 4 and 2 × 2 LED arrays, the Popt was about 15 mW at 300 mA and it was maximized to ∼23 mW at 670 mA. From the measured light–current–voltage data, the detailed theoretical calculations on the thermal properties were carried out by a three-dimensional steady-state heat dissipation model using the measured heat source densities. The internal temperature profiles were obtained for different separation distances, array sizes and injection currents. The internal temperature was largely increased with the increase in array size and the decrease in the separation distance.

Optoelectronic and thermal characteristics of GaN-based monolithic light emitting diode arrays

We investigated the optoelectronic and thermal characteristics of InGaN/GaN monolithic light emitting diode (LED) arrays operating at λ∼ 470 nm. The optical output power (Pout) and forward voltage (VF) were almost linearly increased with the number of LEDs for series arrays. In the case of parallel LED arrays, the maximum operating current was increased by increasing the number of devices, but the VF was kept almost constant. Around 235 mA, the maximum Pout of 55.6 mW was obtained for the 1 × 3 series LED array fabricated with a separation distance of 1000 µm, while the Pout was 20.4 mW for the 1 × 3 parallel LED array. From the measured light–current–voltage data, the maximum internal temperature (Tmax), i.e. a maximum value of internal temperature rise within the devices under operation, was theoretically determined using a three-dimensional steady-state thermal heat dissipation model based on the finite element method. Also, the temperature profiles were obtained for various separation distances and array sizes. At injection current of 220 mA, the Tmax was theoretically calculated as 325.6 K and 306.6 K for 1 × 3 series and parallel LED arrays with a 1000 µm separation distance, respectively. The Tmax was increased and decreased on decreasing the separation distance and substrate thickness, respectively, and its dependence on Tmax became more significant at higher injection current.

Meshless Local Petrov-Galerkin Method for 3D Steady-State Heat Conduction Problems

The Meshless Local Petrov-Galerkin (MLPG) method is applied for solving the three-dimensional steady state heat conduction problems. This method is a truly meshless approach; also neither the nodal connectivity nor the background mesh is required for solving the initial boundary-value problems. The penalty method is adopted to enforce the essential boundary conditions. The moving least squares (MLS) approximation is used for interpolation schemes and the Heviside step function is chosen for representing the test function. The numerical results are compared with the exact solutions of the problem and Finite Difference Method (FDM). This comparison illustrates the accuracy as well as the capability of this method.

Meshless analysis of three-dimensional steady-state heat conduction problems

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.

Prediction of solidification behaviour of weld pool through modelling of heat transfer and fluid flow during gas tungsten arc welding of commercial pure aluminium

A mathematical model is developed to assess the solidification behaviour of the weld pools. To do so, during gas tungsten arc welding of commercial pure aluminium, equations of conversation of mass, energy and momentum are numerically solved considering three-dimensional steady state heat transfer and fluid flow conditions. The weld pool geometry, weld thermal cycles and various solidification parameters are calculated using temperature and velocity fields acquiring from the utilised model. The solidification behaviour of the weld pool at the weld centreline and the fusion line is then studied using the solidification parameters including temperature gradient G, solidification rate R and the combined forms G/R and GR. In order to verify the predictions, welding experiments are performed and geometry of the weld fusion zone is measured. The calculated geometry of the weld fusion zone is found to be in good agreement with the corresponding experimental result. The predictions show that the cooling rate GR increases toward the centreline while the other solidification parameter G/R shows a different behaviour. In addition, it is found that under the employed welding conditions, as the welding speed increases temperature gradients both at the weld centreline and at the fusion line are reduced.

An efficient BEM formulation for three-dimensional steady-state heat conduction analysis of composites

In this work, an efficient boundary element formulation has been presented for three-dimensional steady-state heat conduction analysis of fiber reinforced composites. The cylindrical shaped fibers in the three-dimensional composite matrix are represented by a system of curvilinear line elements with a prescribed diameter which facilitates efficient analysis and modeling together with the reduction in dimensionality of the problem. The variations in the temperature and flux fields in the circumferential direction of the fiber are represented in terms of a trigonometric shape function together with a linear or quadratic variation in the longitudinal direction. The resulting integrals are then treated semi-analytically which reduces the computational task significantly. The computational effort is further minimized by analytically substituting the fiber equations into the boundary integral equation of the material matrix with hole, resulting in a modified boundary integral equation of the composite matrix. An efficient assembly process of the resulting system equations is demonstrated together with several numerical examples to validate the proposed formulation. An example of application is also included.

An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells

We analyze the steady-state response of a functionally graded thick cylindrical shell subjected to thermal and mechanical loads. The functionally graded shell is simply supported at the edges and it is assumed to have an arbitrary variation of material properties in the radial direction. The three-dimensional steady-state heat conduction and thermoelasticity equations, simplified to the case of generalized plane strain deformations in the axial direction, are solved analytically. Suitable temperature and displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the thermoelastic equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which are then solved by the power series method. In the present formulation, the cylindrical shell is assumed to be made of an orthotropic material, although the analytical solution is also valid for isotropic materials. Results are presented for two-constituent isotropic and fiber-reinforced functionally graded shells that have a smooth variation of material volume fractions, and/or in-plane fiber orientations, through the radial direction. The cylindrical shells are also analyzed using the Flügge and the Donnell shell theories. Displacements and stresses from the shell theories are compared with the three-dimensional exact solution to delineate the effects of transverse shear deformation, shell thickness and angular span.

Permeable Porosity and Thermal Conductivity of Construction Materials

Water permeable porosities and thermal conductivity of ceramic construction materials have been experimentally determined in this work. The samples were selected so as to obtain a wide variation in their apparent porosity. To study the influence of porosity on thermal conductivity, thermal conductivities of all the samples were measured in oven dried and water saturated conditions. A model relating porosity with thermal conductivity of these materials is proposed. In the model, two types of pores are hypothesized, namely; enclosed pores and enclosing pores. The three-dimensional steady-state heat transfer through unit cells containing each of the two types of pores, is solved to evaluate their effective thermal conductivity. By using the law of mixture for the random distribution of the type of pores, an equation combining the conductivities of the two cells is framed to get overall effective thermal conductivity of the material, in both dry and saturated states. The experimentally determined values of thermal conductivities reported in literature for some bricks are then compared with those predicted through this model.

Modeling of three-dimensional steady state non-linear heat transfer in CANDU nuclear fuel

Modeling and analysis of three-dimensional steady-state heat transfer in a CANDU6 1 1 CANadian Deuterium and Uranium and trademark of Atomic Energy of Canada Ltd. nuclear fuel rod are presented in this paper. A special three-dimensional finite element, developed through combining the nine-node two-dimensional isoparametric finite element and the Fourier series, is employed to model the temperature distribution in the pellets and the sheath. To achieve high accuracy and a high convergence rate, the temperature-dependent thermal conductivity matrices of UO 2 and Zircaloy are allowed to vary with spatial coordinates in the same manner as temperature within a finite element. The non-linear algebraic equations of nodal temperatures are formulated using the Galerkin method and solved using the iteration approach. A computer code, fuel3d, which contains the finite element modeling and solution schemes described in this paper, was developed for heat transfer analysis of nuclear fuel rods. Numerical simulation results obtained using fuel3d have shown excellent agreement with other independent solutions.

Novel approach to the solution of temperature distribution in the stator of an induction motor

In this paper a three-dimensional thermal model of an induction motor is presented. Excepting for providing a more accurate representation of the problem, the proposed model can also reduce computing costs. The finite element method is used to solve the three-dimensional steady-state and/or transient heat flow equation which describes the thermal model. A temperature-time method is employed to evaluate the distribution of loss in various parts of the machine. Using these loss distributions as an input for finite element analysis, more accurate temperature distributions can be then obtained. The validity and accuracy of the proposed method are checked by comparing the results with those obtained from test.

Error analysis in applying a boundary element method for three-dimensional steady state potential problems

The boundary element method (BEM) has been applied to the case of three-dimensional steady state heat flow with no internal heat generation. The edge and corner effects and the near surface difficulties due to singular integral kernels of BEM are considered. Certain existing methods to overcome these difficulties have been implemented and tested. An algorithm is proposed which considers floating temporary nodes and local refinements of the mesh for interior points close to the boundary. The effects of the different methods of reducing the error are studied in the case of temperature distribution in a cube. The severity of the various errors increases with the coarsening of the mesh. The proposed method, however, is found to solve the near surface problems very effectively, even in the case of a very coarse mesh with negligibly small excess processing time.

The best approximation method applied to three-dimensional steady-state heat transport

The best approximation method is extended to the numerical solution of three-dimensional steady-state heat transport problems. Two families of trial functions are used in the numerical solution; namely, harmonic polynomials and constant sources. Numerical approximation error is evaluated by means of approximate boundaries whereby error is visualized as a geometric displacement of the problem boundary. The problem considered is the determination of temperatures within a nuclear reactor.

Steady state heat flow in a random medium and the linear heat flow‐heat production relationship

The heat transfer in the earth's crust is described by three‐dimensional steady state heat conduction in a heterogeneous medium with randomly varying thermal conductivity and heat production. The heat flow‐heat production relationship generally emerges as the regression of the surface heat flow on surface heat production. The case of normally distributed thermal conductivity and heat production in an upper heterogeneous slab yields a linear relation, the slope and intercept of which depend on the horizontal and vertical correlation scales of heterogeneity, the correlation between thermal conductivity and heat production, and the ratio of heat produced within the zone of heterogeneity to heat from deeper origin. The model is a stochastic extension of the traditional homogeneous slab model, and the intercept of the linear relationship predicts the true average heat flow at a depth equal to the slope, when this depth is smaller than the true slab thickness.

Three-Dimensional, Steady-State Heat Conduction in Cylinders of General Anisotropic-Media

This paper provides the analytical solution of three-dimensional steady-state heat conduction in solid and hollow cylinders of general anisotropic-media. By the use of Fourier transforms and a change of variables the partial differential equation is reduced to Kummer’s equation. Some calculated results for a solid cylinder are shown and discussed. A parameter γ is found to represent the coupling effect of three-dimensional anisotropy. For small values of γ, an approximate solution is recommended. The inequality σ > 0 which was found in an earlier paper is further discussed.