SOLUTION OF THE INVERSE HEAT CONDUCTION PROBLEM WITH NEUMANN BOUNDARY CONDITION BY USING THE HOMOTOPY PERTURBATION METHOD

In the paper a solution of the inverse heat conduction problem with the Neumann boundary condition is presented. For finding this solution the homotopy perturbation method is applied. Investigated problem consists in calculation of the temperature distribution in considered domain, as well as in reconstruction of the functions describing the temperature and the heat flux on the boundary, in case when the temperature measurements in some points of the domain are known. An example confirming usefulness of the homotopy perturbation method for solving problems of this kind are also included.

[1]  Damian Słota.  Restoring boundary conditions in the solidification of pure metals , 2011 .

[2]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[3]  Damian Słota,et al.  Homotopy Perturbation Method for Solving the Two-Phase Inverse Stefan Problem , 2011 .

[4]  Patrick Glouannec,et al.  Heat flux estimation in an infrared experimental furnace using an inverse method , 2009 .

[5]  Jafar Biazar,et al.  Homotopy perturbation method for solving hyperbolic partial differential equations , 2008, Comput. Math. Appl..

[6]  Davood Domiri Ganji,et al.  ASSESSMENT OF HOMOTOPY-PERTURBATION AND PERTURBATION METHODS IN HEAT RADIATION EQUATIONS , 2006 .

[7]  M. Turkyilmazoglu.  Convergence of the Homotopy Perturbation Method , 2011 .

[8]  Jacek Smolka,et al.  An effective 3-D inverse procedure to retrieve cooling conditions in an aluminium alloy continuous casting problem , 2010 .

[9]  Davood Domiri Ganji,et al.  Some nonlinear heat transfer equations solved by three approximate methods , 2007 .

[10]  Man Yao,et al.  Inverse problem-based analysis on non-uniform profiles of thermal resistance between strand and mould for continuous round billets casting , 2007 .

[11]  Jafar Biazar,et al.  He's homotopy perturbation method: A strongly promising method for solving non-linear systems of the mixed Volterra-Fredholm integral equations , 2011, Comput. Math. Appl..

[12]  Damian Słota,et al.  The application of the homotopy perturbation method to one-phase inverse Stefan problem , 2010 .

[13]  H. Jafari,et al.  Convergence of Homotopy Perturbation Method for Solving Integral Equations , 2012 .

[14]  Zhong Chen,et al.  Piecewise homotopy perturbation method for solving linear and nonlinear weakly singular VIE of second kind , 2011, Appl. Math. Comput..

[15]  Yasir Khan,et al.  On the coupling of the homotopy perturbation method and Laplace transformation , 2011, Math. Comput. Model..

[16]  Peter Woodfield,et al.  Implementation of an analytical two-dimensional inverse heat conduction technique to practical problems , 2006 .

[17]  Mehdi Dehghan,et al.  Inverse problem of diffusion equation by He's homotopy perturbation method , 2007 .

[18]  A. Fernandes,et al.  USE OF 3 D-TRANSIENT ANALYTICAL SOLUTION BASED ON GREEN ’ S FUNCTION TO REDUCE COMPUTATIONAL TIME IN INVERSE HEAT CONDUCTION PROBLEMS , 2009 .

[19]  Damian Slota,et al.  Application of the Ant Colony Optimization Algorithm for Reconstruction of the Thermal Conductivity Coefficient , 2012, ICAISC.

[20]  Kamel Al-khaled,et al.  Reliable algorithms for solving integro-differential equations with applications , 2010, Int. J. Comput. Math..

[21]  D. Ganji,et al.  Application of Variational Iteration and Homotopy-Perturbation Methods to Nonlinear Heat Transfer Equations with Variable Coefficients , 2007 .

[22]  Estimation of Uncertainty in an Analytical Inverse Heat Conduction Solution , 2009 .

[23]  Jacek Smolka,et al.  Application of Bezier surfaces to the 3-D inverse geometry problem in continuous casting , 2011 .

[24]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[25]  M. N. Özişik,et al.  Inverse Heat Transfer: Fundamentals and Applications , 2000 .

[26]  Yasir Khan,et al.  Coupling of homotopy and the variational approach for a conservative oscillator with strong odd-nonlinearity , 2012 .

[27]  Jafar Biazar,et al.  Study of convergence of homotopy perturbation method for systems of partial differential equations , 2009, Comput. Math. Appl..

[28]  A. Fernandes,et al.  Use of 3D-transient analytical solution based on Green’s function to reduce computational time in inverse heat conduction problems , 2010 .

[29]  N. S. Mera,et al.  A multi-population genetic algorithm approach for solving ill-posed problems , 2004 .

[30]  E. Hetmaniok,et al.  Application of the homotopy perturbation method for calculation of the temperature distribution in the cast-mould heterogeneous domain , 2010 .

[31]  Abdollah Shidfar,et al.  A computational procedure for estimation of an unknown coefficient in an inverse boundary value problem , 2007, Appl. Math. Comput..

[32]  Mehdi Dehghan,et al.  Study of the wave‐breaking's qualitative behavior of the Fornberg‐Whitham equation via quasi‐numeric approaches , 2012 .

[33]  Damian Słota,et al.  Reconstruction of the Boundary Condition in the Problem of the Binary Alloy Solidification , 2011 .

[34]  Damian Słota,et al.  Determination of Optimal Parameters for the Immune Algorithm Used for Solving Inverse Heat Conduction Problems with and without a Phase Change , 2012 .

[35]  Wei Liu,et al.  An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform , 2003 .

[36]  Damian Slota,et al.  A study of the convergence of and error estimation for the homotopy perturbation method for the Volterra-Fredholm integral equations , 2013, Appl. Math. Lett..

[37]  Damian Slota,et al.  Convergence and error estimation of homotopy perturbation method for Fredholm and Volterra integral equations , 2012, Appl. Math. Comput..

[38]  Jafar Biazar,et al.  Convergence of the homotopy perturbation method for partial differential equations , 2009 .

[39]  Mehdi Dehghan,et al.  Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method , 2007 .

[40]  Ji-Huan He.  A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[41]  I. Nowak,et al.  Application of the homotopy perturbation method for the solution of inverse heat conduction problem , 2012 .

[42]  Mehdi Dehghan,et al.  Solution of delay differential equations via a homotopy perturbation method , 2008, Math. Comput. Model..

[43]  Damian Slota,et al.  Solution of the Inverse Heat Conduction Problem by Using the ABC Algorithm , 2010, RSCTC.