Inverse Retrival of Parameters In Inverse Heat Conduction Problems

Abstract

In this thesis the direct problem is related to heat conduction problem which is used to deter- mine the temperature distribution from the intial boundary conditions and intial temperature which leads to the well-posed problems. Generally, it is impossible to specify the intial bound- ary conditions and intial temperature in many situations so inverse problems arrived. Here, in this thesis we used two techniques for solving the Inverse Heat Conduction Problems. First technique is the Singular Value Decomposition where decomposition of the matrices is done and also repesented the Truncated Singular Value Decomposition but this method has lots of limitations and also does not provide the stable solution of the problem. This problem is overcome by using Tikhonov regularization method. Second method is the regularization of the solution to the inverse heat conduction problems in discrete fourier fixed domain and given only boundary condition which is also known to be as modified Tikhonov regularization method which leads to more stable and accurate solution. We have also represented the modified regularization method to solve the inverse heat conduction problem with the only boundary conditions value in the bounded domain where the boundary value is given which is x=0. The soluton soughted in the interval x ∈ (0, 1]. This method of modified regularization method is introduced in order to recover the stability of the solution. The order optimal error is estimated between the exact solution and approximate solution. In this thesis also represented the integral solution of the inverse heat conduction problems which involves the calculation of the surface heat flux and temperature from transient, mea- sured temperatures at an interior point of the thermally conducting bodies. The inverse heat conduction problems is a mathematically improper ill -posed problems which means a small er- ror in the interior of data induce a large error in the surface heat flux solutions and heat surface temperature. The steps involved to solve the inverse heat conduction problems are to derive the temperature & heat fluxes of the body by changing the temperatures inside the solid. The literature reviews presented in this thesis discussed about the one-dimensional inverse heat conduction problems. The various methods prooves are very much effective and useful when a measurement of tem- perature and heat flux(directly) is very much tough, in several working conditions.