Estimation of thermal conductivity, heat transfer coefficient, and heat flux using a three dimensional inverse analysis

• This paper proposes a new methodology to solve the inverse heat transfer problem.
• The methodology is based on using 3D elliptic grid generation to map the physical domain into a computational one.
• A new methodology for computing the sensitivities is proposed based on explicit formulae.
• The method is successfully tested on a range of benchmark cases.

This paper presents a numerical inverse analysis to estimate the thermal conductivity, the heat transfer coefficient, and the heat flux in three dimensional irregular bodies in steady state heat conduction problems. In this study, a 3-D elliptic grid generation technique is used to mesh the irregular body. The 3-D Laplace equation is solved in the computational domain to compute the temperature at any grid point in the meshed body. A novel and very efficient sensitivity analysis scheme is introduced to compute the sensitivity coefficients in gradient based optimization method. Using this sensitivity analysis scheme, one can solve the inverse problem without need to the solution of adjoint equation. The main advantages of the sensitivity analysis scheme are its simplicity, accuracy, and independency of the number of the direct problem solution from the number of the unknown variables which makes the numerical inverse analysis presented here very accurate and efficient. The conjugate gradient method (CGM) is used to minimize the objective function which is the difference between the computed temperature on part of the boundary and the measured temperature. The obtained results confirm that the proposed algorithm is very accurate, robust, and efficient.