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1.
Convective surface heat transfer measurements play an important role in many industrial, environmental and aerodynamic problems. In most of the cases, the flow is unsteady which results in temperature variation in the body. The surface heating rates are then predicted from the measured temperature histories by suitable heat transfer modeling. In this paper, the temperature history obtained from a nickel film sensor during a flight test is considered to study the effect of sensor thickness on surface heat flux measurements during the flight measurement. Inverse methods using analytical solutions as well as control volume approximations are used to infer the surface heat flux. The experimental temperature data are discretized using cubic-spline method to obtain the closed form solution which is used for inverse analysis. The results are compared with that of standard bench mark results with thin film gauge analysis based on semi-infinite one dimensional medium. No significant change in surface heat flux is observed between inverse and thin film analysis. However, when the thickness of nickel film is increased by 100 times during numerical simulation of inverse method, it is seen that peak surface heat flux increases by 20%.  相似文献   

2.
The applied heat flux on the drilling surface of drilling tool is estimated in the present three-dimensional inverse heat conduction problem. The inverse algorithm utilizing the Steepest Descent Method (SDM) and a general purpose commercial code CFX4.4 is applied successfully in this study based on the simulated and measured temperature distributions with time at four sensors embedded on the drilling surfaces. The numerical experiments are considered at the first stage to illustrate the validity of inverse determination of the unknown heat flux using exact and error measurements. Experimental data are then used to estimate the actual heat flux along the drilling edge at two different drill peripheral cutting speeds. Results of both the numerical and experimental examinations show that the reliable estimated heat flux can be obtained by using the present inverse algorithm.  相似文献   

3.
An inverse analysis of estimating a time-dependent surface heat flux for a three-dimensional heat conduction problem is presented. A global optimization method known as Particle Swarm Optimization (PSO) is employed to estimate the unknown heat flux at the inner surface of a crystal tube from the knowledge of temperature measurements obtained at the external surface. Three modifications of the PSO-based algorithm, PSO with constriction factor, PSO with time-varying acceleration of the cognitive and social coefficients, and PSO with mutation are carried out to implement the optimization process of the inverse analysis. The results show that the PSO with mutation algorithm is significantly better than other PSO-based algorithms because it can overcome the drawback of trapping in the local optimum points and obtain better inverse solutions. The effects of measurement errors, number of dimensionalities, and number of generations on the inverse solutions are also investigated.  相似文献   

4.
In a radiating-conducting planar medium with a boundary as the heater surface using an inverse analysis, this work deals with the design methodologies to understand the inherent relationship between heater surface temperature/flux, design surface temperature/flux, and medium properties. The heat flux on the heater surface is chosen as the fitness function. Subsequently, to achieve maximum and minimum design surface heat fluxes, an optimization was done to evaluate the zone of operation of the heater. In addition, the effect of medium properties on the temperature-flux relationships on both surfaces has been studied. The distance between the two surfaces is also considered a parameter. The medium properties, the distance between the surfaces, and the heater surface temperature have been found to have a great impact on the design surface heat flux. The inverse mixed boundary problem has been solved using the lattice Boltzmann method (LBM), the finite-volume method (FVM), and the genetic algorithm (GA). Results of the present study provide a guideline towards the efficient design of a heater in which conduction and radiation are the dominant modes of heat transfer.  相似文献   

5.
The inverse methodology is employed to estimate the unknown heat flux distribution over the heater surface of a channel formed by two parallel plates with forced convection and surface radiation exchange, from the knowledge of the desired temperature and heat flux distributions over a given design surface. The energy and radiative transfer equations are solved by the finite-volume method and the net radiation method, respectively. The conjugate gradient method is used for minimization of an objective function, which is expressed by the sum of square residuals between estimated and desired heat fluxes over the design surface. The performance and accuracy of the present method for solving inverse problems are evaluated by some numerical experiments.  相似文献   

6.
Laplace transform is used to solve the problem of heat conduction over a finite slab. The temperature and heat flux on the two surfaces of a slab are related by the transfer functions. These relationships can be used to calculate the front surface heat input (temperature and heat flux) from the back surface measurements (temperature and/or heat flux) when the front surface measurements are not feasible to obtain. This paper demonstrates that the front surface inputs can be obtained from the sensor data without resorting to inverse Laplace transform. Through Hadamard Factorization Theorem, the transfer functions are represented as infinite products of simple polynomials. Consequently, the relationships between the front and back surfaces are translated to the time-domain without inverse Laplace transforms. These time-domain relationships are used to obtain approximate solutions through iterative procedures. We select a numerical method that can smooth the data to filter out noise and at the same time obtain the time derivatives of the data. The smoothed data and time derivatives are then used to calculate the front surface inputs.  相似文献   

7.
Hossein Amiri 《传热工程》2017,38(2):227-243
In this work, the inverse analysis is applied to radiative heat transfer boundary design problems with non-gray media. The objective of the inverse problem is to find the power of the heaters on the heater surface that produces the desired output, that is, temperature and heat flux distribution over the design surface. The inverse problem is formulated as an optimization problem for minimization of an objective function, which is defined by the sum of the squared difference between estimated and desired heat flux distributions over the design surface. The non-gray optimization problem is solved using the conjugate gradient method, which is a gradient-based optimization method. The spectral line weighted-sum-of-gray-gases model (SLW) is used to account for non-gray gas radiation properties. The radiative transfer equation is solved by the discrete ordinates method combined with two models for simulation of non-gray media. Enclosures with diffuse and gray walls are considered. Radiation is assumed the dominant mode of heat transfer. Example problems including homogeneous/nonhomogeneous, isothermal/nonisothermal media are considered. The results obtained using the SLW model and the gray model are compared.  相似文献   

8.
ABSTRACT

In this article, a novel iterative physical-based method is introduced for solving inverse heat conduction problems. The method extends the ball spine algorithm concept, originally developed for inverse fluid flow problems, to inverse heat conduction problems by employing a subtle physical-sense rule. The inverse problem is described as a heat source embedded within a solid medium with known temperature distribution. The object is to find a body configuration satisfying a prescribed heat flux originated from a heat source along the outer surface. Performance of the proposed method is evaluated by solving many 2-D inverse heat conduction problems in which known heat flux distribution along the unknown surface is directly related to the Biot number and surface temperature distribution arbitrarily determined by the user. Results show that the proposed method has a truly low computational cost accompanied with a high convergence rate.  相似文献   

9.
The image deconvolution method is developed, which is coupled with the one-dimensional (1D) analytical inverse method to calculate more accurate heat flux fields by correcting the lateral heat conduction effect in image-based surface temperature measurements. The theoretical foundation is a convolution-type integral equation with a Gaussian filter (kernel) that relates a heat flux field obtained by using the 1D inverse method on a surface to the true heat flux field. The accuracy of this method is evaluated and the standard deviation in the Gaussian filter is determined for different materials through simulations. This method is used to calculate heat flux fields in temperature-sensitive-paint measurements on a 7°-half-angle circular cone at Mach 6 in a short-duration hypersonic wind tunnel. In addition, a simple method is proposed to solve a projection problem associated with image deconvolution for a highly curved developable surface.  相似文献   

10.
The glass pressing process involves heat transfer between the glass gob and the forming tool which are among the most important parameters influencing the thermo-mechanical stresses in the moulds. The present paper presents the development of the instrumentation of a mould for the measurement of temperatures during the production cycle. These measurements are exploited with an inverse method to evaluate the heat flux densities at the working surface of the mould. The influence of each process stage and of the location at the surface of the mould on the thermal loadings are described. The evaluated heat flux densities are used as boundary conditions in a finite element calculation. The validity of these results are discussed taking into account the differences between experiment and calculation, the hypothesis of the inverse method and the time response of the thermocouples.  相似文献   

11.
The two-dimensional inverse problem of estimating the unknown heat flux of a pin fin base has been solved using the conjugate gradient method. The advantage of the conjugate gradient method is that no information on the functional form of the unknown quantity is required beforehand. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements of temperature in an interior location of a pin fin. Numerical results show that good estimations on the heat flux can be obtained for all the test cases considered here. Furthermore, such a technique can be applied to determine the heat flux acting on an internal wall surface, where direct measurements are difficult to make.  相似文献   

12.
This paper aims to estimate a location- and time-dependent high-magnitude heat flux in a heat conduction problem. The heat flux is applied on a small region of a surface of a flat plate, while transient temperature measurements are taken on the opposite surface. This inverse problem is solved using the Kalman filter and a reduced forward model, obtained by simplifications of a three-dimensional and nonlinear heat conduction problem. To deal with the modeling errors of this reduced model, the Approximation Error Model is used. The results show that excellent estimates can be obtained at feasible computational times.  相似文献   

13.
A hybrid technique of the Laplace transform and finite-difference methods in conjunction with the least-squares method and experimental temperature data inside the test material is applied to investigate the spray cooling of a hot surface. In this study, the unknown surface temperature and heat flux will be predicted. Their functional forms are unknown a priori in the present study and are assumed to be the functions of time before performing the inverse calculation. The whole time domain is divided into several analysis sub-time intervals and then these unknown estimates on each analysis interval can be predicted. In order to validate the accuracy of the present inverse method, comparisons between the present estimates and previous estimated results are made. The results show that the present estimates of the unknown temperature at various measurement locations agree with the previous estimated results and experimental temperature data. However, the present estimates of the unknown surface heat flux deviate from the previous estimated results for larger times.  相似文献   

14.
In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space-and time-dependent heat flux at the surface of an initially hot cylinder cooled by a laminar confined slot impinging jet from the knowledge of temperature measurements taken on the cylinder’s surface. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. The results show that an excellent estimation on the space-and time-dependent heat flux can be obtained even the distributions of thermal properties inside the cylinder is unknown.  相似文献   

15.
In this paper, an inverse analysis is used to find an appropriate heat flux distribution over the heater surface of radiant enclosures, filled with nongray media at radiative equilibrium from the knowledge of desired (prespecified) temperature and heat flux distributions over the given design surface. Regular and irregular 2D enclosures filled with nongray combustive gas products are considered. Radiation is considered the dominant mode of heat transfer and the medium temperature is obtained from the energy equation. To evaluate the nongray behavior of the participating gases properly, the spectral‐line weighted‐sum‐of‐gray‐gases (SLW) model with updated correlations is used. The dependence of absorption coefficients and the weights of the SLW model on the temperature of the medium makes the inverse problem nonlinear and difficult to handle. Here, the inverse problem is formulated as an optimization problem and the Levenberg‐Marquardt method has been used to solve it. The finite volume method is exploited for the discretization of the energy equation and the spatial discretization of the radiative transfer equation (RTE). The discrete ordinates method (TN quadrature) is used for the angular discretization of RTE. Five test cases, including homogeneous and inhomogeneous media, are investigated to prove the ability of the present methodology for achieving the desired conditions.  相似文献   

16.
Inverse Heat Transfer Problems (IHTP) are characterized by estimation of unknown quantities by utilizing any given information of the system. In this study, the inverse problem of estimation of boundary heat flux for a given temperature distribution on the walls of a two dimensional square cavity with a finite wall thickness is considered. A non-iterative method is applied utilizing Artificial Neural Network (ANN) and Principal Component Analysis (PCA) to estimate the parameters that define the boundary heat flux. The forward model is numerically solved with Fluent 6.3 for known values of a linearly varying boundary heat flux and the temperature distribution thus obtained is utilized to train the ANN for the inverse model. A parametric study is carried out to determine the effect of the thermal conductivity of the top and bottom walls on the flow and temperature distribution in the cavity. PCA analysis is carried out to reduce the dimensions of the input data set for the inverse model. These reduced dimensions are used to train the network and due to low dimensionality of the input, the effort required to train the network is considerably less. The trained networks are finally used to estimate boundary heat flux for any desired temperature distribution on the top and bottom walls. Additionally, covariance analysis is carried out in order to estimate the required number of temperatures during an experiment, on the top and bottom walls for the prediction of heat flux with a reasonable accuracy. The inverse model with covariance analysis is compared with the inverse model with PCA and both the methods are found to be equally potent.  相似文献   

17.
We present a new method of solving the three-dimensional inverse heat conduction (3D IHC) problem with the special geometry of a thin sheet. The 3D heat equation is first simplified to a 1D equation through modal expansions. Through a Laplace transform, algebraic relationships are obtained that express the front surface temperature and heat flux in terms of those same thermal quantities on the back surface. We expand the transfer functions as infinite products of simple polynomials using the Hadamard Factorization Theorem. The straightforward inverse Laplace transforms of these simple polynomials lead to relationships for each mode in the time domain. The time domain operations are implemented through iterative procedures to calculate the front surface quantities from the data on the back surface. The iterative procedures require numerical differentiation of noisy sensor data, which is accomplished by the Savitzky–Golay method. To handle the case when part of the back surface is not accessible to sensors, we used the least squares fit to obtain the modal temperature from the sensor data. The results from the proposed method are compared with an analytical solution and with the numerical solution of a 3D heat conduction problem with a constant net heat flux distribution on the front surface.  相似文献   

18.
A shape design problem (or inverse geometry problem) in determining the geometry of interfacial surface between two conductive bodies in a three-dimensional multiple region domains, based on the desired system heat flux and domain volume, is examined in this study. The design algorithm utilized the Levenberg–Marquardt method (LMM), B-spline surface generation and the commercial software CFD-ACE+. The validity of this shape design analysis is examined using the numerical experiments. Different desired system heat fluxes are considered in the numerical test cases to justify the validity of the present algorithm in solving the three-dimensional shape design problems. Finally, the results show that for the two different cases considered in this work, the maximum increasing in the system heat flux is obtained as 11.3% and 14.1%, respectively. It is also concluded that when the boundary control points of interfacial surface are free to move, maximum system heat flux can be obtained by the present algorithm since it has more degree of freedom in describing the interfacial surface.  相似文献   

19.
An inverse problem for turbulent forced convection between parallel flat plates is investigated. The space- and time-dependent heat flux at the upper wall is estimated from the temperature measurements taken inside the flow. In the present study, the conjugate gradient method is adopted for the estimation of the unknown wall heat flux. No prior information is needed for the functional form of the wall heat flux in the inverse analysis. The effects of the measurement errors, the functional form of the wall heat flux, and the location of the sensors on the accuracy of the estimation are investigated. The reconstruction of the wall heat flux is satisfactory when simulated exact or noisy data are input to the inverse analysis. The sensitivity coefficients are discussed in this paper. As expected, it is shown that the accuracy of the estimation can be improved when the sensors are located closer to the upper wall.  相似文献   

20.
In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent base heat flux of an annular fin from the knowledge of temperature measurements taken within the fin. The inverse solutions will be justified based on the numerical experiments in which two specific cases to determine the unknown base heat flux are examined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent base heat flux can be obtained for the test cases considered in this study.  相似文献   

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