‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

Stochastic inverse problems in heat conduction with consideration of uncertainties in the measured temperature data, temperature sensor locations and thermophysical properties are addressed using a Bayesian statistical inference method. Both parameter estimation and thermal history reconstruction problems, including boundary heat flux and heat source reconstruction, are studied. Probabilistic s...

In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (I...

The inverse analysis is encountered in various branches of science and engineering. In the field of heat transfer, inverse analysis is used for the estimation of surface conditions such as temperature and heat flux. Also, the determination of thermal properties such as thermal conductivity and heat capacity of solids by utilizing transient temperature measurements collected from points within t...

A Bayesian inference approach is presented for the solution of the inverse heat conduction problem. The posterior probability density function (PPDF) of the boundary heat flux is computed given temperature measurements within a conducting solid. Uncertainty in temperature measurements is modeled as stationary zero-mean white noise. The inverse solution is obtained by computing the expectation o...

A spectral stochastic approach to the inverse heat conduction problem (IHCP) is presented. In IHCP, one computes an unknown boundary heat flux from given temperature history data at a sensor location. In the stochastic inverse heat conduction problem (SIHCP), the full statistics of the boundary heat flux are computed given the stochastic nature of the temperature sensor data and in general acco...

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...