duction equations with linear and/or nonlinear boundary conditions can be formulated for the treatment of all these
In this study the inverse problem of the identification of temperature dependent thermal properties of a heat conducting body is problems. However, it should be said that simultaneous investigated. The solution of the corresponding direct problem is requests resulting from combining these inverse problems obtained using a time marching boundary element method (BEM), are yet to be investigated.
which allows, without any need of interpolation and solution do-Inverse problems are more difficult than their corremain discretisation, efficient and accurate evaluation of the temperature everywhere inside the space-time dependent domain. Since sponding direct formulated problems because they are illthe inverse problem, which requires the determination of the therposed; i.e., either existence, uniqueness, or continuous demal conductivity and heat capacity from a finite set of temperature pendence upon the data (stability) are violated. In general, measurements taken inside the body, possesses poor uniqueness both the IHCP and BHCP violate stability when uniquefeatures, additional information is achieved by assuming that the ness is satisfied, whilst the IDHCP is more difficult since thermal properties belong to a set of polynomials. Thus the inverse problem reduces to a parameter system estimation problem which the uniqueness problem has to be addressed.
is solved using the nonlinear least-squares method. Convergent and It is the purpose of this study to investigate one of the stable numerical results are obtained for the finite set of parameters identification problems which requires the simultaneous which characterise the thermal properties for various test examples.
estimation of the thermal conductivity and the heat capac-Once the thermal properties are accurately obtained then the BEM determines automatically the temperature inside the solution do-ity, which are temperature dependent, from boundary and main and the remaining unspecified boundary values and the nuinitial data and additional interior temperature measuremerically obtained results show good agreement with the correments. Also, the unknown temperature solution and the sponding analytical solutions.