Cheng-Hung Huang

A three-dimensional inverse heat conduction problem in estimating surface heat flux by conjugate gradient method

Abstract In the present study a three-dimensional (3-D) transient inverse heat conduction problem is solved using the conjugate gradient method (CGM) and the general purpose commercial code CFX4.2-based inverse algorithm to estimate the unknown boundary heat flux in any 3-D irregular domain. The advantage of calling CFX4.2 as a subroutine in the present inverse calculation lies in that many difficult but practical 3-D inverse problems that can be solved under this construction. Results obtained by using the conjugate gradient method to solve these 3-D inverse problems are justified based on the numerical experiments. It is concluded that accurate boundary fluxes can be estimated by the CGM except for the final time. The reason and improvement of this singularity are addressed. Finally, the effects of the measurement errors on the inverse solutions are discussed.

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

Abstract 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.

An inverse geometry problem in identifying irregular boundary configurations

Abstract An inverse geometry heat conduction problem (shape identification problem) is solved to detect the unknown irregular boundary shape by using the boundary element method (BEM)-based inverse algorithms. They are the Levenberg-Marquardt method (L-MM) and the conjugate gradient method (CGM), respectively. A sequence of forward steady-state heat conduction problems is solved in an effort to update the boundary geometry by minimizing a residual measuring the difference between actual and computed temperatures at the sensors locations under the present two algorithms. Results obtained by using both schemes to solve the inverse problems are compared based on the numerical experiments. One concludes that the conjugate gradient method is better than the Levenberg-Marquardt method since the former one: (i) needs very short computer time; (ii) does not require a very accurate initial guess of the boundary shape; and (iii) needs less number of sensors. Finally the effects of the measurement errors to the inverse solutions are discussed.

A two-dimensional inverse problem in imaging the thermal conductivity of a non-homogeneous medium

Abstract A two-dimensional inverse heat conduction problem is solved successfully by the conjugate gradient method (CGM) of minimization in imaging the unknown thermal conductivity of a non-homogeneous material. This technique can readily be applied to medical optical tomography problem. It is assumed that no prior information is available on the functional form of the unknown thermal conductivity in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained on the medium surface. The advantages of applying the CGM in the present inverse analysis lie in that the initial guesses of the unknown thermal conductivity can be chosen arbitrarily and the rate of convergence is fast. Results show that an excellent estimation on the thermal conductivity can be obtained within a couple of minutes CPU time at Pentium II-350 MHz PC. Finally the exact and estimated images of the thermal conductivity will be presented.

A three-dimensional inverse problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers

Abstract A three-dimensional inverse heat conduction problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers utilizing the steepest descent method and a general purpose commercial code CFX4.4 is applied successfully in the present study based on the simulated measured temperature distributions on fin surface by infrared thermography. It is assumed that no prior information is available on the functional form of the unknown local heat transfer coefficients in the present study. Thus, it can be classified as function estimation for the inverse calculations. Two different heat transfer coefficients for in-line tube arrangements with different measurement errors are to be estimated. Results show that the present algorithm can obtain the reliable estimated heat transfer coefficients.

A transient inverse two-dimensional geometry problem in estimating time-dependent irregular boundary configurations

Abstract In the present study a transient inverse geometry heat conduction problem (shape identification problem) is solved using the Conjugate Gradient Method (CGM) and Boundary Element Method (BEM)-based inverse algorithm to estimate the unknown irregular boundary shape. Results obtained by using the conjugate gradient method to solve this inverse moving boundary problems are justified based on the numerical experiments. It is concluded that the accurate configuration can be estimated by the conjugate gradient method except for the initial and final time. The reason and improvement of this singularity are addressed. Finally the effects of the measurement errors on the inverse solutions are discussed.

An inverse problem in simultaneous estimating the Biot numbers of heat and moisture transfer for a porous material

Abstract A conjugate gradient method based inverse algorithm is applied in the present study in simultaneous determining the unknown time-dependent Biot numbers of heat and moisture transfer for a porous material based on interior measurements of temperature and moisture. It is assumed that no prior information is available on the functional form of the unknown Biot numbers in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of this inverse heat and moisture transfer problem is examined by using the simulated exact and inexact temperature and moisture measurements in the numerical experiments. Results show that the estimation on the time-dependent Biot numbers can be obtained with any arbitrary initial guesses on a Pentium IV 1.4 GHz personal computer.

A boundary element-based inverse-problem in estimating transient boundary conditions with conjugate gradient method

A Boundary Element Method (BEM)-based inverse algorithm utilizing the iterative regularization method, i.e. the conjugate gradient method (CGM), is used to solve the Inverse Heat Conduction Problem (IHCP) of estimating the unknown transient boundary temperatures in a multi-dimensional domain with arbitrary geometry. The results obtained by the CGM are compared with that obtained by the standard Regularization Method (RM). n nThe error estimation based on the statistical analysis is derived from the formulation of the RM. A 99 per cent confidence bound is thus obtained. Finally, the effects of the measurement errors to the inverse solutions are discussed. n nResults show that the advantages of applying the CGM in the inverse calculations lie in that (i) the major difficulties in choosing a suitable quadratic norm, determining a proper regularization order and determining the optimal smoothing (or regularization) coefficient in the RM are avoided and (ii) it is less sensitive to the measurement errors, i.e. more accurate solutions are obtained.

A three-dimensional inverse problem in predicting the heat fluxes distribution in the cutting tools

ABSTRACT The surface heat fluxes on the cutting edges of cutting tools are 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, are applied successfully in this study in accordance with simulated measured temperature distributions on tool surfaces by infrared thermography. Two different tool shapes are used to illustrate the validity of inverse determination of the unknown heat fluxes with different measurement errors. Results of the numerical simulation show that reliable estimated heat fluxes can be obtained by using the present inverse algorithm.

An inverse design problem of estimating optimal shape of cooling passages in turbine blades

Abstract An inverse design problem is solved to determine the shape of complex coolant flow passages in internal cooled turbine blades by using the conjugate gradient method (CGM). One of the advantages of using CGM lies in that it can easily handle problems having a huge number of unknown parameters and it converges very fast. The boundary element method (BEM) is used to calculate the direct, sensitivity and adjoint problems due to its characteristics of easily-handling the problem considered here. Results obtained by using the CGM to solve the inverse problems are verified based on the numerical experiments in the analysis model. One concludes that the CGM is applied successfully in estimating the arbitrary shape of cavities and the rate of convergence is also very fast even when the number of unknown parameters is large. Moreover, the design model of the inverse problem is also performed to estimate the optimal shape of cooling passages in accordance with the desired blade surface temperature distributions.