Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

Abstract

Estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using the numerical experiments with the simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to conjugate gradient method with adjoint problem and variable metric method with adjoint problem. The obtained results show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

Novel gradient‐based methods for heat flux retrieval

“…The value of the objective function in the VMMAP cannot be decreased below 1.32 £ 10 2 2 , and continuing more iterations results in non-convergence. It might worth mentioning that the same behavior of the reduction function using BFGS version of VMM was also observed in Molavi et al (2010b) for one-dimensional problem. Furthermore, no convergence is yielded with or without errors in the simulated data when the developed technique by equation ( 14) is employed.…”

“…Their results indicated that the quasi-Newton method is faster and more accurate than the CGM in estimation of unknowns in the whole domain linear inverse problems. Recently Molavi et al (2010b) used a novel search gradient-type algorithm for the solution of one-dimensional linear Heat flux retrieval and non-linear IHCPs with and without moving boundary and compared their method to CGM and quasi-Newton methods. They showed that all studied algorithms could produce results with the same order of accuracy, while their method requires noticeably less number of iterations to converge.…”

A Modified Conjugate Gradient Method for Transient Nonlinear Inverse Heat Conduction Problems: A Case Study for Identifying Temperature-Dependent Thermal Conductivities

“…(16) In CVDM, the variable z of a real function ,v(z) is replaced by a complex one z + 1h, with the imaginary part h very small (usually h= [10][11][12][13][14][15][16][17][18][19][20]. In the present work, it is used for the determination of the sensitivity coefficients matrix, which is composed of first order derivatives.…”

“…Heat transfer problems [1][2][3][4][5][6] and the corresponding numerical solution methods [7][8][9][10][11][12][13][14][15][16][17][18][19][20] have always been hot issues. In the heat transfer field, direct heat conduction problems are concerned with the determination of the temperature field when the domain, boundary and initial conditions, thermo-physical properties, and geometric conditions are specified.…”

“…In the heat transfer field, direct heat conduction problems are concerned with the determination of the temperature field when the domain, boundary and initial conditions, thermo-physical properties, and geometric conditions are specified. The IHCPs have been extensively studied for different engineering applications in the past decades [14][15][16][17][18][19][20]. Consequently, an inverse approach should be employed to determine the unknowns [13].…”