Dimensional Heat Conduction Research Articles

One dimensional transient heat conduction in segmented fin-like geometries with distinct discrete peripheral convection

This study presents the solution of transient heat conduction in a composite extended surface whose periphery is exposed to convection and whose thermophysical properties experience discontinuities along the longitudinal direction. The solution development uses the natural analytic approach and formats the description so that the constants of integration of each of the composite segments are expressed in terms of the previous segment's eigenfunctions. This allows the solution to be “built” in a very systematic and sequential manner. A three-segment case study is also provided to show the simplicity and applicability of the implementation of this solution.

Modeling and control for thermal balancing of multi-core processors

This paper presents an effective thermal balancing policy for multi-core processors thermal management systems. The paper contains two parts. First, a group of one dimensional (1D) partial differential equations (PDEs), which are derived from the normal three dimensional (3D) PDE heat conduction equation, are proposed to describe the thermal behavior of the multi-core processers. Then, an optimal output feedback regulator is designed to manage the power consumption and balance the temperature among the cores. Finally, the performance of the proposed controller is verified via an illustrative example.

A Revised Approach for One-Dimensional Time-Dependent Heat Conduction in a Slab

Classical Green’s and Duhamel’s integral formulas are enforced for the solution of one dimensional heat conduction in a slab, under general boundary conditions of the first kind. Two alternative numerical approximations are proposed, both characterized by fast convergent behavior. We first consider caloric functions with arbitrary piecewise continuous boundary conditions, and show that standard solutions based on Fourier series do not converge uniformly on the domain. Here, uniform convergence is achieved by integrations by parts. An alternative approach based on the Laplace transform is also presented, and this is shown to have an excellent convergence rate also when discontinuities are present at the boundaries. In both cases, numerical experiments illustrate the improvement of the convergence rate with respect to standard methods.

Simultaneous Estimation of Principal Thermal Conductivities of an Anisotropic Composite Medium: An Inverse Analysis

This paper reports the results of an experimental study to determine the principal thermal conductivities (kx,ky, and kz) of an anisotropic composite medium using an inverse heat transfer analysis. The direct problem consists of solving the three dimensional heat conduction equation in an orthotropic composite medium with the finite difference method to generate the required temperature distribution for known thermal conductivities. The measurement technique involves dissipating a known heat flux at the central region of a square sample and allowing it to conductively transfer the heat to an aluminium cold plate sink via a square copper ring. At steady state, temperatures at 28 (19 are used for retrievals due to symmetry) discrete locations are logged and used for parameter estimation. The entire measurement process is conducted in a vacuum environment. The inverse heat conduction problem (IHCP) for retrieving the orthotropic thermal conductivity tensor(parameter estimation) is then solved using a two layer feed forward back propagation artificial neural network (ANN) trained using the Levenberg–Marquardt algorithm (LMA), with temperatures as input and thermal conductivity values kx,ky, and kz as the output. The method is first validated against a stainless steel(SS-304) sample of known thermal properties followed by the determination of the orthotropic conductivities of the honeycomb composite material.

On the semi-inverse method and variational principle

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

Development of a Heat Conduction Model and Investigation on Thermal Conductivity Enhancement of AlN/Epoxy Composites

This work explores on the possibility of enhancement of heat conduction capability of a typical particulate filled polymer composite. A theoretical model for one dimensional heat conduction through such a composite has been developed using the law of minimal thermal resistance and equal law of the specific equivalent thermal conductivity. Based on this model, a mathematical correlation between the effective thermal conductivity of the composite and the filler content is proposed. The proposed model is then validated through experimentation conducted in controlled laboratory conditions. Different samples of aluminum nitride filled epoxy composites are prepared by simple hand layup technique. The content of the conductive filler (AlN) in the composites is varied in the range 0% to 15% by volume. Thermal conductivities of these composite samples are measured according to the ASTM standard E-1530 by using the UnithermTM Model 2022 tester, which operates on the double guarded heat flow principle. Gradual increase in thermal conductivity has been observed, with increase in conductive filler percentage in composite samples. Values obtained using the proposed mathematical correlation are then compared with the measured experimental results and also with values estimated with other established correlations such as Rule-of-Mixture (ROM), Maxwell's model, Bruggeman model and Nielson-Lewis model. This comparison reveals that while none of the above models are correctly predicting the effective thermal conductivity of the composites, the results obtained from the proposed model by incorporating a correction factor are in good agreement with the experimental data.

J053015 散逸粒子動力学法による非定常温度応答の解析(〔J053-01〕マイクロ・ナノスケールの熱流体現象(1))

Dissipative particle dynamics (DPD) has been regarded as one of an effective simulation method for mesoscopic system because the treatment of multi-body hydrodynamic interactions among particles is easy. Traditionally, DPD simulations have been used only for simulation of uniform temperature system because the temperatures of each particle are not defined. In this paper, energy conserved DPD simulation for one dimensional unsteady heat conduction problem has been conducted in order to verify the applicability for energy transport process. Energy conserved DPD simulation is accomplished by introducing an internal energy of each particles and the temperature of each particles are connected with internal energy. DPD simulation result of unsteady temperature response is compared with analytical solution of heat conduction equation and it is found that both results agree well. Furthermore, thermal conductivities are calculated from simulation results of steady heat conduction. It is clarified that the thermal conductivity of simulation system in DPD simulation is easily controllable by adjusting the energy transport coefficient k_o in formula of energy exchange between particles.

Thermo-elastic Damping in Nano-beam Resonators Based on Nonlocal Theory

In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by using, two dimensional non-Fourier heat conduction with one relaxation time based on continuum theory frame. Free vibration of the nano-beam resonators is analyzed using Galerkin reduced order model formulation for the first mode of vibration. In the present investigation a clamped-clamped nano-beam with isothermal boundary conditions at both ends is studied. This nonlocal nano-beam model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect. The obtained results are compared with the numerical results of the classical thermoelastic models. Thermoelastic damping effects on the damping ratio are studied for the various nano-beam thicknesses and ambient temperatures. In addition to, the study includes computations for different values of nonlocal theory parameter. The results show that with increasing the amount of nonlocal parameter and also with decreasing the length of the nano-beam, difference of the results of classical and nonlocal theory increases.

Analysis of One Dimensional Inverse Heat Conduction Problem : A Review

A procedure to solve inverse heat conduction problem (IHCP) is to derive surface heat flux and temperature from temperature change inside a solid. The method proves to be very useful and powerful when a direct measurement of surface heat flux and temperature is difficult, owing to several working condition. The literature reviewed here discussion one dimensional inverse heat conduction problem. Procedure, criteria, methods and important results of other investigation are briefly discussed.

Heat Conduction Equation Finite Volume Method to Achieve on MATLAB

Diffusion only, two dimensional heat conduction has been described on partial differential equation. Based on Finite Volume Method, Discretized algebraic Equation of partial differential equation have been deduced. different coefficients and source terms have been discussed under different boundary conditions, which include prescribed heat flux, prescribed temperature, convection and insulated. Transient heat conduction analysises of infinite plate with uniform thickness and two dimensional rectangle region have been realized by programming using MATLAB. It is useful to make the heat conduction equation more understandable by its solution with graphical expression, feasibility and stability of numerical method have been demonstrated by running result.

Study on the Temperature Filed of Wet Dual Clutch Transmission during Starting Process

Based on the analysis of starting process of wet dual clutch transmission, dynamic rules for piston pressure and relative angular velocity of wet clutch were determined, According to the unsteady heat exchanging theory and the heat exchanging process of clutch engagement, a two dimensional heat conduction model of wet clutch was developed with reasonable initial conditions and boundary conditions. Matlab/PDE toolbox was used to solve the established model. The temperature distribution of friction pairs along the axial and radial direction were revealed in the Simulation results. Testing program had been designed, and real vehicle test was done to the temperature field on friction interface of wet dual clutch transmission in starting process. The test result indicated that the temperature field model and its solution were reliability, and it was instructive to optimize the design of wet clutch and its engaging control in starting process.

Research of Hot Dry Rock on Fracture Temperature Distribution of Storage Layer in Shenyang

Hot dry rock is more and more appreciated as a kind of newly resource, which is up to the low carbon idea. Storage layer is the heat origin in heating system, is the exchange place for hot dry rock and water. So the temperature distribution tendency of the happening of storage layer and the heat exchange, the prediction for the service life of storage layer will affect the resource utilization and development. The paper uses one - dimensional simulate heat conduction formula based on FenDun mountain hot dry rock research, combined with deep rock parameters and heat conduction parameters of Shenyang to determine that using heat conducting research in storage layer of hot dry rock can simplify reservoir parameters for calculation. And then to get the temperature distribution discipline of storage layer of hot dry rock when hot exchanged.

Heat Conduction Equation Finite Volume Method to Achieve on MATLAB

Diffusion only, two dimensional heat conduction has been described on partial differential equation. Based on Finite Volume Method, Discretized algebraic Equation of partial differential equation have been deduced. different coefficients and source terms have been discussed under different boundary conditions, which include prescribed heat flux, prescribed temperature, convection and insulated.. Transient heat conduction analysis of infinite plate with uniform thickness and two dimensional rectangle region are realized by programming using MATLAB. It is useful to make the heat conduction equation more understandable by its solution with graphical expression, feasibility and stability of numerical method have been demonstrated by running result.

Determination of channel temperature for AlGaN/GaN HEMTs by high spectral resolution micro-Raman spectroscopy

Channel temperature determinations of AlGaN/GaN high electron mobility transistors (HEMTs) by high spectral resolution micro-Raman spectroscopy are proposed. The temperature dependence of the E2 phonon frequency of GaN material is calibrated by using a JYT-64000 micro-Raman system. By using the Lorentz fitting method, the measurement uncertainty for the Raman phonon frequency of ±0.035 cm−1 is achieved, corresponding to a temperature accuracy of ±3.2 °C for GaN material, which is the highest temperature resolution in the published works. The thermal resistance of the tested AlGaN/GaN HEMT sample is 22.8 °C/W, which is in reasonably good agreement with a three dimensional heat conduction simulation. The difference among the channel temperatures obtained by micro-Raman spectroscopy, the pulsed electrical method and the infrared image method are also investigated quantificationally.

Numerical identification of source terms for a two dimensional heat conduction problem in polar coordinate system

This work investigates the inverse problem of reconstructing a spacewise dependent heat source in a two-dimensional heat conduction equation using a final temperature measurement. Problems of this type have important applications in several fields of applied science. Under certain assumptions, this problem can be transformed into a one-dimensional problem where the heat source only depends on the variable r. However, being different from other one-dimensional inverse heat source problems, there exists singularity on the coefficient of our model, which may make the analysis more difficult, regardless of theoretical or numerical. The inverse problem is reduced to an operator equation of the first kind and the corresponding adjoint operator is deuced. For the two dimensional case, i.e., f=f(r,θ), theoretical analysis can be done by similar derivation. Based on the landweber regularization framework, an iterative algorithm is proposed to obtain the numerical solution. Some typical numerical examples are presented to show the validity of the inversion method.

Thermoelastic damping in a micro-beam resonator tunable with piezoelectric layers

In this paper, thermoelastic damping (TED) in a micro-beam resonator with a pair of piezoelectric layers bonded on its upper and lower surfaces is investigated. Equation of motion is derived and the thermoelasticity equation is governed using two dimensional non-Fourier heat conduction model based on continuum theory frame. Applying Galerkin discretization method and complex-frequency approach to solve the equations of coupled thermoelasticity, we study TED of a clamped-clamped micro-beam resonator. The presented results demonstrate that thickness of the piezoelectric layers and application of DC voltage to them can affect the TED ratio and the critical thickness value of the resonator.

Heat Transfer in Narrow Rectangular Channels with Rib Turbulators

An experimental study of heat transfer characteristics of narrow rectangular channels with rib turbulators for Re in the range of 10000-60000 was performed. To simulate the actual geometry and heat transfer structure of blade/vane internal cooling passage, each of the test channels was welded by four stainless steel plates. Because of the three dimensional heat conduction in the walls and heat conduction between the ribbed and smooth walls, the measured temperature distribution along the axial direction of the test channel is a smooth continuous curve, and when the Re is low, the average Nu of the ribbed and smooth walls are nearly the same. For each aspect ratio channels, the average Nu for the channel of α=45° is about 15 to 25 percent higher than that of α=60°. In addition, we have developed the semi-empirical correlations, covering the range of Re, to predict heat transfer coefficient of the channels. The correlations can be used in the design of turbine blade/vane cooling channels.

Prediction of HAZ Width of Submerged Arc Welded Plates

This paper is focused on deriving an analytical solution to predict the transient temperature distribution on the plate during the process of Submerged Arc Welding (SAW). An analytical solution is derived from the transient three-dimensional heat conduction equation. The energy input that is applied on the plate is taken as the volume of heat lost from the electric arc. The electric arc is assumed to be a moving double-ellipsoidal heat source with a close proximity to a Gaussian distribution. It is observed that the predicted values are in good agreement with the experimental results. HAZ width calculation is also done with the help of the analytical solution of the transient-three dimensional heat conduction equation. Very good agreement between predicted and experimental values has been archived.

Prediction of Temperature Distribution on Submerged Arc Welded Plates through Gaussian Heat Distribution Technique

Submerged Arc Welding process (SAW) is a high quality, very high deposition rate welding process. It has lot of social and economical implecations.This paper makes an attempt to uncover an important area on studies of temperature distribution during submerged arc welding because this may pave the way for application of microstructure modeling, thermal stress analysis, residual stress/distribution and welding process simulation. Prediction of temperature variation of entire plates during welding through an analytical solution is derived from the transient multi dimensional heat conduction of semi infinite plate. The heat input that is applied on the plate is exactly same amount of heat lost for electric arc, which is assumed to be a moving double conical heat source with Gaussian distribution for Submerged Arc Welding process. Good agreement between predicted and experimental results has been achieved.

Simulation and Experimental Study of Inverse Heat Conduction Problem

In this paper, a neural network method is proposed to solve a one dimensional inverse heat conduction problem (IHCP). The method relies on input/output data of an unknown system to create an intelligent neural network model. Multi layer perceptrons with recurrent properties are utilised in the model. Prepared input/output data are used to train the neural network. Reliable checking processes are also offered to justify the robustness of the method. A numerical sequential function specification (SFS) method is used as another technique to solve the IHCP. The numerical result is compared with that of the proposed method and good agreement is shown between the two methods. However, the numerical method can be only used to solve the IHCP off-line due to the high computation requirement. The proposed neural network method can be used in real-time situations as shown in the experimental tests.