Deforming finite elements for the numerical solution of the nonlinear inverse heat conduction problem
Abstract
A numerical solution of the nonlinear inverse heat conduction problem is obtained using an inline method in conjunction with the measured thermocouple temperature history. The deforming finite elements technique is used to treat initial time delay in temperature response due to thermocouple location. In the absence of elements deformation, the method reduces to the conventional Galerkin formulation. A threetime level implicit scheme, which is unconditionally stable and convergent, is employed for the numerical solution. The temperaturedependent thermophysical properties in the matrices are evaluated at the intermediate level. The complication of solving a set of nonlinear algebraic equations at each step is avoided. Illustration of the technique is made on the onedimensional problem with a thermal radiation boundary condition. The results demonstrate that the method is remarkable in its ability to predict surface condition without debilitation.
 Publication:

Communications in Applied Numerical Methods
 Pub Date:
 June 1987
 Bibcode:
 1987CANM....3..167M
 Keywords:

 Computational Fluid Dynamics;
 Conductive Heat Transfer;
 Finite Element Method;
 Nonlinear Equations;
 Temperature Inversions;
 Boundary Conditions;
 Boundary Value Problems;
 Galerkin Method;
 Thermocouples;
 Time Lag;
 Fluid Mechanics and Heat Transfer