An inverse problem in simultaneously measuring temperature-dependent thermal conductivity and heat capacity

An inverse analysis utilizing the conjugate gradient method of minimization and the adjoint equation is used for simultaneously estimating the temperature-dependent thermal conductivity and heat capacity per unit volume of a material. No prior information is used for the functional forms of the unknown thermal conductivity and heat capacity in the present study, thus, it is classified as the function estimation by inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained within the medium. Results show that the CPU time used on a VAX-9420 computer is within 1.4–4.46 s for all the test cases considered here. Moreover, excellent estimations on the thermal properties can be obtained when a good initial guess of either thermal conductivity or heat capacity is given before the inverse calculations.     

The determination temperature-dependent thermal conductivity as inverse steady heat conduction problem

The paper deals with the non-iterative inverse determination of the temperature-dependent thermal conductivity in 2-D steady-state heat conduction problem. The thermal conductivity is modeled as a polynomial function of temperature with the unknown coefficients. The identification of the thermal conductivity is obtained by using the boundary data and additionally from the knowledge of temperature inside the domain. The method of fundamental solutions is used to solve the 2-D heat conduction problem. The golden section search is used to find the optimal place for pseudo-boundary on which are placed the singularities in the frame of method of fundamental solutions.     

A transient three-dimensional inverse geometry problem in estimating the space and time-dependent irregular boundary shapes

A transient three-dimensional shape identification problem (inverse geometry problem) to determine the unknown irregular and moving boundary configurations by utilizing the steepest descend method (SDM) and a general purpose commercial code CFD-RC is successfully developed and examined in this study based on the simulated measured temperature distributions on the bottom surface by infrared thermography. The advantage of calling CFD-RC as a subroutine in the present inverse calculation lies in that its auto-mesh function enables the handling of this moving boundary problem. Results obtained by using the technique of SDM to solve the inverse geometry problem are justified based on the numerical experiments. Two test cases are performed to test the validity of the present algorithm by using different types of boundary shapes, initial guesses and measurement errors. Results show that reliable estimations on the unknown space and time-dependent boundary geometry can be obtained when the measurement errors are considered.     

On the perturbation method for the Stefan problem with time-dependent boundary conditions

Perturbation methods are developed for Stefan problems with time-dependent boundary conditions. The methods are applied to melting of ice in the half-plane, outward spherical solidification and outward cylindrical solidification of a saturated liquid. The results are shown to compare well with those obtained by other numerical methods.     

A three-dimensional inverse geometry problem in identifying irregular boundary configurations

A three-dimensional inverse geometry problem (shape identification problem) in determining the unknown irregular surface configurations by utilizing the conjugate gradient method (CGM) and a general purpose commercial code CFD-RC is successfully developed and examined in this study based on the simulated measured temperature distributions on the bottom surface by infrared thermography. Results obtained by using the technique of CGM to solve the inverse geometry problem are justified based on the numerical experiments. Three test cases are performed to test the validity of the present algorithm by using different types of surface shapes, initial guess and measurement errors. Results show that excellent estimations on the unknown surface geometry can be obtained with any arbitrary initial guesses.     

Simple measurement of thermal diffusivity and thermal conductivity using inverse solution for one-dimensional heat conduction

A new method is proposed for measuring thermal diffusivity and thermal conductivity simultaneously using the inverse solution for one-dimensional unsteady heat conduction. Unlike previous method proposed by authors, the new procedure does not require the temperature measurement for a long time duration after the temperature starts changing at a sensor position; and then a selection of time duration can be chosen such that the measured temperature change becomes large enough to ensure a required accuracy for the estimated values of thermal diffusivity and thermal conductivity. The measurement is usually completed within 3 min until the temperature rise at the thermocouple position reaches a certain temperature level, for example 1% of an error level. This method has the additional advantage of being independent of the surface condition, except for the requirement of two or three sensing positions in the material. The accuracy of the estimated values is also similar to the error level of the sensor at these positions.     

A three-dimensional inverse geometry problem in estimating the space and time-dependent shape of an irregular internal cavity

A three-dimensional inverse geometry problem (or shape identification problem) to estimate the unknown space and time-dependent irregular shape of internal cavity by utilizing the gradient-based steepest descent method (SDM) and a general purpose commercial code CFD-ACE+ is considered in the present study. The validity of the present inverse algorithm is examined based on the simulated measured temperature distributions on the outer surface by an imaginary infrared scanner. The advantage of calling CFD-ACE+ as a subroutine in this shape identification problem lies in its characteristics of automatic mesh generation since this function of CFD-ACE+ enables the easily-handling of the moving boundary problem. Two numerical test cases are performed to test the validity and accuracy of the present shape identification algorithm by using different types of cavity shapes, initial guesses and measurement errors. Results show that excellent estimations on the unknown geometry of the internal cavity can be obtained.     

New temperature dependent thermal conductivity data for water-based nanofluids

This paper presents effective thermal conductivity measurements of alumina/water and copper oxide/water nanofluids. The effects of particle volume fraction, temperature and particle size were investigated. Readings at ambient temperature as well as over a relatively large temperature range were made for various particle volume fractions up to 9%. Results clearly show the predicted overall effect of an increase in the effective thermal conductivity with an increase in particle volume fraction and with a decrease in particle size. Furthermore, the relative increase in thermal conductivity was found to be more important at higher temperatures. Obtained results compare favorably with certain data sets and theoretical models found in current literature.     

Natural convection in partially divided square enclosures: Effects of thermal boundary conditions and thermal conductivity of the partitions

Natural convection in partitioned square enclosures filled with air is numerically studied, trying to characterize these enclosures mainly in what concerns its overall heat transfer performance. Two partitions of finite thickness are considered, placed in the enclosure following an ordered arrangement, which position, length and thermal conductivity are varied for some values of Rayleigh number and for different thermal boundary conditions. Study starts considering the simplest enclosures with two adiabatic partitions, after the more realistic enclosures of heat conductive walls and partitions are considered, and finally the even more realistic situation of enclosures with heat conductive partitions and walls subjected to cyclic thermal boundary conditions in the vertical direction is also considered. Position and length of the enclosures’ effects depend on the thermal boundary conditions prescribed for the enclosure, and different thermal boundary conditions (corresponding to the heating or cooling operations or seasons) are considered to capture this effect. Fluid flow field, thermal field and heat transfer are analyzed for some particular situations through the streamlines, isotherms, and heatlines. The overall thermal performance of the enclosure is analyzed through the overall Nusselt number, and many data are compactly presented for different placements and lengths of the partitions, for different thermal conductivity of the walls and partitions of the enclosure, for different Rayleigh numbers and for different thermal boundary conditions imposed to the enclosure. Considered boundary conditions and the enclosure walls and partitions of finite thickness and finite thermal conductivity are much more realistic conditions than simply the single cavity without walls and with perfectly adiabatic partitions usually considered in many studies of this kind.     

A phase change problem with temperature-dependent thermal conductivity and specific heat

A semi-analytic solution is obtained to model conduction heat transfer with phase change into a semi-infinite slab, where the thermal conductivities and specific heats of both phases are a linear function of the temperature. This model extends the model of a previous work to include temperature-dependent specific heats.     

An inverse radiation boundary design problem for an enclosure filled with an emitting,absorbing, and scattering media

This work is an inverse radiative design problem in which the objective is to determine the spatial distribution of heat source strengths which produces a desired temperature and heat flux distribution on the design surface. The furnace whose walls are diffuse-grey is assumed to be filled with an absorbing, emitting, and scattering medium. The function to be minimized is the sum of squares of the differences between the desired and calculated radiative heat fluxes at the design surface. Radiative heat flux calculations are accomplished by means of the Modified Discrete Transfer Method MDTM using the correction factors suggested by Coelho and Carvalho [P.J. Coelho, M.G. Carvalho, Conservative formulation of the discrete transfer method, ASME J. Heat Transfer, 119 (1997) 118–128.] and Cumber [P.S. Cumber, Improvements to the discrete transfer method of calculating radiative heat transfer, Int. J. Heat Mass Transfer, 38 (12) (1995) 2251–2258.]. For inverse design calculations the Conjugate Gradient Method CGM is employed, in which the sensitivity coefficients are defined and used as needed by the algorithm. Our investigation shows that the presented algorithm is able to estimate heater strengths accurately.     

An investigation into the lattice thermal conductivity of random nanowire composites

The lattice thermal conductivity of compact random silicon and germanium nanowire composites was investigated by using a Monte-Carlo (MC) simulator, which was developed based on the gray medium approximation and unstructured grids. By defining the local equilibrium temperature as the one which preserves the local phonon energy in the interested heterogeneous subregion, we are able to obtain the effective thermal conductivity of random nanowire composites and explore the effects of the wire shape and the composition concentration on it. The results show that among the three kinds of wire shapes investigated – triangle, quadrangle, and voronoi, the random quadrilateral nanowire composites are the best thermal conductor under a fixed interface density or a fixed characteristic wire size and that the dependence of the effective thermal conductivity on the silicon volume concentration is approximately parabolic. The influences of these two factors are equally strong. Moreover, the parabolic dependence can be well explained by the effective medium approximation model for three bond percolation systems.     

一种高导热材料导热系数测试仪的研制

对经典周期热流法进行了研究和改进,采用实验测试和数值仿真相结合的研究方法,设计开发了一套简单实用,数据可靠的高导热材料导热系数测试装置。通过编程技术,实现了数据的自动采集及处理。应用有限容积法建立二维模型,借助Visual Basic语言,开发了该测试系统在线仿真的软件系统。最后根据实验结果和文献值对该测试系统进行评价。     

A decentralized fuzzy inference method for solving the two-dimensional steady inverse heat conduction problem of estimating boundary condition

This paper addresses a new technique for solving the two-dimensional steady inverse heat conduction problem, which named decentralized fuzzy inference (DFI) method. First of all, a group of decentralized fuzzy inference units are designed, and the fuzzy inference for each fuzzy inference unit is conducted which bases on the difference between the measured and the computed temperature at each measuring location. The computed temperatures are obtained by solving the direct heat conduction problem with the finite difference method. And then, inference results of fuzzy inference units are weighted to yield compensation values of the unknown boundary temperatures. The unknown boundary temperatures are estimated by updating guess temperatures continuously with compensation values. Numerical experiments are carried out with different initial guesses, the number of measuring points and measurement errors. Comparing results of DFI method and Levenberg–Marquardt (L–M) method, we can conclude that DFI method is valid.     

An inverse biotechnology problem in estimating the optical diffusion and absorption coefficients of tissue

An inverse algorithm for biotechnology problem utilizing the conjugate gradient method is applied in the present study in determining the unknown spatial-dependent optical diffusion and absorption coefficients of the biological tissue based on irradiance and temperature measurements. The accuracy of this inverse problem is examined by using the simulated exact and inexact irradiance and temperature measurements in the numerical experiments. Results show that the estimation on the spatial-dependent diffusion and absorption coefficients can be obtained with any arbitrary initial guesses on a Pentium IV 1.4 GHz personal computer for the test cases considered in the present study.     

Non-linear fitting method of finding equilibrium temperature from BHT data

The real formation temperature is a very useful parameter in geothermal investigations and hydrocarbon maturation studies. Several models have been proposed for obtaining the real formation temperature from BHT data. This paper describes a non-linear fitting method of these models for obtaining equilibrium temperature and calculating the results from observed data. A preference is assumed for nonlinear fitting of Middleton's (1979) formula with observed data.     

A Novel Variational Formulation of Inverse Problem of Heat Conduction with Free Boundary on an Image

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