(Received July 12, 2009, accepted September 3, 2009) Abstract. In this paper we consider a numerical approach for the determination of an unknown boundary condition in the inverse heat conduction problem (IHCP). The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. The numerical algorithm based on finite-difference method an...

A nonlinear partial differential equation of the following form is considered: u − div ( a(u)∇u ) + b(u) |∇u| = 0, which arises from the heat conduction problems with strong temperature-dependent material parameters, such as mass density, specific heat and heat conductivity. Existence, uniqueness and asymptotic behavior of initial boundary value problems under appropriate assumptions on the mat...

The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuit...

In this study a multi block procedure is implemented to solve accurately two-dimensional transient Inverse Heat Conduction Problems (IHCPs). The multi block method is implemented for geometric decomposition of physical domain into regions with blocked-interface structured grids. The Finite Element Method (FEM) with Galerkin weighting function is employed for direct solution of transient heat co...

In this article, we consider a Cauchy problem of heat equation, that is, determining the unknown temperature and heat flux at an inaccessible boundary from scattered temperature measurements on an accessible boundary or in some interior locations. This method is similar to the boundary control approach proposed by Leevan Ling and Tomoya Takeuchi in [1] where the authors considered a Cauchy prob...