Solution of inverse heat conduction problem using the lattice Boltzmann method

In this paper the D2Q9 lattice Boltzmann method (LBM) was utilized for the solution of a two-dimensional inverse heat conduction (IHCP) problem. The accuracy of the LBM results was validated against those obtained from prevalent numerical methods using a common benchmark problem. The conjugate gradient method was used in order to estimate the heat flux test case. A complete error analysis was performed. As the LBM is attuned to parallel computations, its use is recommended in conjugation with IHCP solution methods.     

A method of fundamental solutions for the radially symmetric inverse heat conduction problem

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric inverse heat conduction problem (IHCP). In the radially symmetric IHCP data on an inner fixed boundary is determined from Cauchy data given on an outer boundary. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach of Johansson et al. (2008) for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.     

Calculating transient wall heat flux from measurements of surface temperature

Wall heat fluxes can be derived from time resolved measurements of the surface temperature. This paper describes an analytical approach to calculate the heat flux from an analytical solution of the one-dimensional transient energy equation with transient boundary conditions using the Laplace transformation. The results are compared to simple test cases for which the heat fluxes are given in literature. The method is used to calculate the heat flux from a fuel spray to a wall at diesel engine conditions.     

Non-iterative estimation of temperature-dependent thermal conductivity without internal measurements

In this work a direct integration method is proposed to estimate temperature-dependent thermal conductivity in a one-dimensional heat conduction domain without internal measurements. By approximating the spatial temperature distribution in the domain as a third-order polynomial of position and by integrating the heat conduction equation over the spatial and temporal domain, the present method estimates the thermal conductivity directly. Also, this method does not require any prior information on the functional form of the thermal conductivity. Some illustrative examples are examined to verify the proposed approach. The proposed approach may also be useful to make sufficiently accurate initial guesses for sophisticated algorithms usually based on iterative refinement scheme.     

An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform

An analytical method has been developed for two-dimensional inverse heat conduction problems by using the Laplace transform technique. The inverse solutions are obtained under two simple boundary conditions in a finite rectangular body, with one and two unknowns, respectively. The method first approximates the temperature changes measured in the body with a half polynomial power series of time and Fourier series of eigenfunction. The expressions for the surface temperature and heat flux are explicitly obtained in a form of power series of time and Fourier series. The verifications for two representative testing cases have shown that the predicted surface temperature distribution is in good agreement with the prescribed surface condition, as well as the surface heat flux.     

基于共轭梯度法对T型管内壁瞬态温度的识别

构建了一种基于已知T型管道外壁面瞬时温度,反演管道内壁面瞬态温度的导热反问题数学模型和求解方法.利用有限单元法对管道模型进行离散,并利用共轭梯度法求解非稳态导热反问题.利用正问题得到的外壁面瞬态温度的数值结果作为反问题的输入条件,反演得到内壁面瞬态温度,此反演结果与作为边界条件的内壁面瞬态温度值进行了对比分析,对比结果...     

An inverse analysis of two-phase Stefan problems using imaginary heat sources

This paper presents a new methodology for the inverse analysis of time-dependent two-phase Stefan problems. The problem considered here is that of determining the time dependence of a phase-change interface at several observed temperatures. In our method, imaginary heat sources are arranged in an imaginary domain and then the phase-change interface is identified as the isothermal surface at the melting temperature by controlling the imaginary heat source intensities. Using delta-function imaginary heat sources and their corresponding Green functions, which are pre-calculated numerically, it is shown that the phase-change interface is determined non-iteratively at each time step. We offer numerical examples to demonstrate the capability of the proposed method. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(3): 179–191, 1998     

Shape design for a cylinder with uniform temperature distribution on the outer surface by inverse heat transfer method

Performance of the inverse heat transfer method in application to the shape design for the heat convection problems has been evaluated. The approach is constructed by combining curvilinear grid generation scheme, direct problem solver, conjugate gradient optimization method, and redistribution method. Shape design for the outer surface profile of a solid medium in a crossflow that contains a heating element and features an isothermal outer surface has been carried out. Practical cases under different combinations of the dominant physical parameters, including Reynolds number (Re), thermal conductivity ratio (k_f/k_s), desired outer surface temperature (θ_d), and Prandtl number (Pr), are studied to evaluate the effects of the physical parameters on the shape design.     

Estimation of heat flux imposed on the rake face of a cutting tool: A nonlinear,complex geometry inverse heat conduction case study

In this paper the sequential function specification method is used to estimate the transient heat flux imposed on the rake face of a cutting tool during the cutting operation with two different assumptions. In one of them the thermal conductivity is taken to be constant, and in the other one it varies with temperature. The cutting tool is modeled as a three dimensional object. The capabilities of the geometric modeling, mesh generation as well as solver of the commercial software ANSYS are utilized in order to reduce the time expended for modeling and direct heat conduction solution, in both linear and nonlinear problems. This way the inverse heat conduction algorithm employs ANSYS as a subprogram through the ANSYS Parametric Design Language (APDL). The stability as well as accuracy is compared for cases of linear and nonlinear heat conductions. The effect of nonlinearity, as well as different sensor locations is investigated in order to arrive at an optimal experimental procedure. Finally, a typical temperature data during the working condition are used to recover the heat flux at the cutting tool surface using linear as well as nonlinear solutions.     

Thermal diffusivity estimation using numerical inverse solution for 1D heat conduction

This work presents an improved apparatus and a numerical approach to obtain the estimate of thermal diffusivity of complex materials. Transient thermal response at the axis of cylindrical sample is measured when boundary temperature is suddenly changed. Instead of assuming an ideal step temperature excitement, a measured temperature of a material boundary was employed. An iterative procedure, based on minimizing a sum of squares function with the Levenberg–Marquardt method, is used to solve the inverse problem. A graphical user interface is built to enable easy use of the inverse thermal diffusivity estimation method. The reference materials used to evaluate the method are Agar water gel, glycerol and Ottawa quartz sand.     

Estimation of internal fuel cell temperatures from surface temperature measurements

In this paper, a method to monitor PEM fuel cells internal temperature from surface measurements is presented. The aim of this work is to monitor fuel cells to prevent damages due to internal overheating. The measurements are taken at the side of the bipolar plate, and heat flux and temperature at the border of the active zone are estimated. The method is based on sensitivity analysis and inverse problem algorithms. The mathematical formulation and algorithm are described. The model is a transient heat conduction model in two dimensions, the inverse problem is solved with an optimization method using adjoint equation. Numerical test cases are presented for graphite and steel bipolar plates. The results show that internal temperature can be correctly estimated. The response time of the method is limited by the heat transfer rate in the material. Therefore, the method is particularly appropriate to fuel cells made of steel bipolar plates.     

Application of the homotopy perturbation method for the solution of inverse heat conduction problem

This paper deals with an application of the homotopy perturbation method for the solution of inverse heat conduction problem. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of functions describing the temperature and heat flux on the boundary, when the temperature measurements in the domain are known. Examples illustrating discussed application and confirming utility of this method in such a type of problem was also presented.     

Estimation of the time-dependent heat flux using the temperature distribution at a point by conjugate gradient method

In this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time-dependent heat flux using the temperature distribution at a point. Also, the effects of noisy data and position of measured temperature on final solution are studied. The numerical solution of the governing equations is obtained by employing a finite-difference technique. For solving this problem the general coordinate method is used. We solve the inverse heat conduction problem of estimating the transient heat flux, applied on part of the boundary of an irregular region. The irregular region in the physical domain (r,z) is transformed into a rectangle in the computational domain (ξ,η). The present formulation is general and can be applied to the solution of boundary inverse heat conduction problems over any region that can be mapped into a rectangle. The obtained results for few selected examples show the good accuracy of the presented method. Also the solutions have good stability even if the input data includes noise and that the results are nearly independent of sensor position.     

Simple method for monitoring transient thermal stresses in pipelines

This paper presents a seminumerical method for solving inverse heat conduction problems (IHCP) encountered in the monitoring of thermal stresses in pressurized thick-walled elements of steam boilers. The objective is to give a simple and quick method of determining transient temperature histories in thick-walled components based on temperature measurements on the outer thermally insulated surface. The method is suitable for solving one-dimensional problems. However, it can be extended to multidimensional temperature fields. The IHCP will be solved using the control volume approach. The accuracy of the method is demonstrated by comparing computational and experimental results. Gram orthogonal polynomials are used to smooth the measured time-dependent temperature and for evaluating time derivatives of noisy data with high accuracy. Due to the simplicity of the final formulations, the developed method is very useful for estimating the thermal stresses and controlling the fatigue damage of boiler components.     

High-accuracy maximum power point estimation for photovoltaic arrays

Quantitative information regarding the maximum power point (MPP) of photovoltaic (PV) arrays is crucial for determining and controlling their operation, yet it is difficult to obtain such information through direct measurements. PV arrays exhibit an extremely nonlinear current-voltage (I-V) characteristic that varies with many complex factors related to the individual cells, which makes it difficult to ensure an optimal use of the available solar energy and to achieve maximum power output in real time. Finding ways to obtain the maximum power output in real time under all possible system conditions are indispensable to the development of feasible PV generation systems. The conventional methods for tracking the MPP of PV arrays suffer from a serious problem that the MPP cannot be quickly acquired. Based on the p-n junction semiconductor theory, we develop a prediction method for directly estimating the MPP for power tracking in PV arrays. The proposed method is a new and simple approach with a low calculation burden that takes the resistance effect of the solar cells into consideration. The MPP of PV arrays can be directly determined from an irradiated I-V characteristic curve. The performance of the proposed method is evaluated by examining the characteristics of the MPP of PV arrays depending on both the temperature and irradiation intensity, and the results are discussed in detail. Such performance is also tested using the field data. The experimental results demonstrate that the proposed method helps in the optimization of the MPP control model in PV arrays.     

The application of the homotopy perturbation method to one-phase inverse Stefan problem

In this paper, the application of the homotopy perturbation method for solving the inverse Stefan problem is presented. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of the functions describing temperature and heat flux on the boundary, when the position of the moving interface is known.     

Inverse method in simultaneously estimate internal heat generation and root temperature of the T-shaped fin

This study employed the finite element method and rearranged the matrix to establish an inverse operation without iteration, in order to simultaneously estimate the internal heat generation and root temperature of the T-shaped fin. The results of numerical validation showed that the optimized the T-shaped fin has a good effect because of better efficiency of heat transfer. Regardless of the configurations, the estimation of internal heat generation is obviously affected by the measurement error. Nevertheless, the measurement of temperature in future time can reduce sensitivity of internal heat generation and root temperature to the measurement error.     

The inverse design of the wind turbine blade sections by the singularities method

The aerodynamic characteristics of wind turbines are closely related to the geometry of their blades. The innovation and the technological development of wind turbine blades can be centred on two tendencies. The first is to improve the shape of existing blades; the second is to design new shapes of blades. The aspiration in the two cases is to achieve an optimal circulation and hence enhancing some more ambitious aerodynamic characteristics. This paper presents an inverse design procedure, which can be adapted to both thin and thick wind turbine blade sections aiming to optimise the geometry for a prescribed distribution of bound vortices. A method for simulating the initial contour of the blade section is exposed, which simultaneously satisfy the aerodynamic and geometrical constraints under nominal conditions. A detailed definition of the function characterising the bound vortex distribution is presented. The inviscid velocity field and potential function distributions are obtained by the singularities method. In the design method implemented, these distributions and the circulation of bound vortices on the camber line of the blade profile, are used to rectify its camber in an iterative calculation leading to the final and optimal form of the blade section once convergence is attained. The scheme proposed has been used to design the entire blade of the wind turbine for a given span-wise distribution of bound circulation around the blade contour.     

A comparison between wind speed distributions derived from the maximum entropy principle and Weibull distribution. Case of study; six regions of Algeria

The knowledge of the probability density function of wind speed is of paramount importance in many applications such as wind energy conversion systems and bridges construction. An accurate determination of the probability distribution of wind speed allows an efficient use of wind energy, thus rendering wind energy conversion system more productive. In the present paper, the maximum entropy principle (MEP) is used to derive a family of pre-exponential distributions in order to fit wind speed distributions. Using averaged hourly wind speed of six different regions in Algeria, it has been found that the proposed pre-exponential distributions fit the wind speed distributions better than the conventional Weibull distributions in terms of root mean square error. However, it has been found also that MEP based distributions have shown some practical limitations such as the choice of pre-exponential order and interval of definition.