Volume 2: Theory and Fundamental Research; Aerospace Heat Transfer; Gas Turbine Heat Transfer; Computational Heat Transfer 2009
DOI: 10.1115/ht2009-88501 View full text |Buy / Rent full text
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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 severa… Show more

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“…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.…”
Section: Heat Flux Retrievalsupporting
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“…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.…”
Section: Heat Flux Retrievalsupporting
“…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.…”
Section: Introductionmentioning
“…(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.…”
Section: Inverse Problemmentioning
“…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.…”
Section: Introductionmentioning
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