Journal article Open Access

Comparison of Three Versions of Conjugate Gradient Method in Predicting an Unknown Irregular Boundary Profile

V. Ghadamyari; F. Samadi; F. Kowsary

An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

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  • A. Ellabib and A. Nachaoui, "On the numerical solution of a free boundary identification problem", Inverse Problems Eng. 9(3), pp.235- 260, 2001.
  • A.N. Tikhonov and V.Y. Arsenin, Solution of Ill-Posed Problems, Winston and Sons, Washington, DC (1977). [10] J.V. Beck, B. Blackwell, C.St. Clair, "Inverse Heat Conduction: Illposed Problems", Wiley, New York, 1985 [11] M. J. Colaco, H. R. B. Orlande, "Comparison of different versions of the Conjugate Gradient Method of Function Estimation", Numerical Heat Transfer, Part A, 36, pp. 229-249, 1999. [12] H. M. Park, O. Y. Chung, "On the solution of an inverse natural convection problem using various conjugate gradient methods", International Journal for Numerical Methods In Engineering, vol. 47, pp. 821-842, 2000. [13] C.H. Huang, B.H. Chao, "An inverse geometry problem in identifying irregular boundary configurations", Int. Journal of Heat Mass Transfer, vol. 40, pp. 2045-2053, 1997. [14] M. Ozisik, H.R.B. Orlande, "Inverse Heat Transfer", Taylor & Francis, 2000.
  • C. H. Huang, S.P. Wang, "A three-dimensional Inverse heat conduction problem in estimating surface heat flux by conjugate gradient method", International Journal of Heat and Mass Transfer, vol. 42, pp. 3387- 3403, 1999.
  • C. R. Su and C. K. Chen, "Geometry estimation of the furnace inner wall by an inverse approach", International Journal of Heat and Mass Transfer, vol. 50, pp. 3767-3773, 2007.
  • D. Lesnic, L. Elliott, B. Ingham, "Application of boundary element method to inverse heat conduction problems", International Journal of Heat and Mass Transfer, vol. 39, No. 7, pp. 1503-1517, 1996.
  • F. Y. Zhao, D. Liu, G. F. Tang, "Numerical determination of boundary heat fluxes in an enclosure dynamically with natural convection through Fletcher-Reeves gradient method", Computer and Fluids, vol. 38, pp. 797-809, 2009.
  • H. M. Park, O. Y. Chung, "An inverse natural convection problem of estimating the strength of a heat source", International Journal of Heat and Mass Transfer, vol. 42, pp.4259-4273, 1999.
  • H. R. B. Orlande, G. S. Dulikravich, "Inverse heat transfer problems and their solutions within the Bayesian framework", in 2012 Numerical Heat Transfer, ECCOMAS Special Interest Conference
  • T. P. Lin, "Inverse heat conduction problem of simultaneously determining thermal conductivity, heat capacity and heat transfer coefficient", Master thesis, Department of Mechanical Engineering, Tatung Institute of Technology, Taipei, Taiwan, 1998.
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