The object of the present paper is to study temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature. The nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity is reduced t...

Abstract – A one-dimensional inverse heat conduction problem (IHCP) of estimating an unknown heat flux, given experimental temperature measurements at a point in the domain, is solved using evolutionary algorithms (EA). The EA based methods used to solve the one-dimensional IHCP in the literature involve minimization of the Tikhonov functional. In this paper, a modified approach is utilized whe...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

In this paper, the Method of Fundamental Solutions (MFS) is extended to solve some special cases of the problem of transient heat conduction in functionally graded materials. First, the problem is transformed to a heat equation with constant coefficients using a suitable new transformation and then the MFS together with the Tikhonov regularization method is used to solve the resulting equation.

In this paper we study a free boundary problem modeling a phase-change process by using microwave heating technique. The mathematical model consists of Maxwell’s equations coupled with nonlinear heat conduction with a phase-change. The enthalpy form is used to characterize the phase-change process in the model. It is shown that the problem has a global solution.

In this paper an inverse problem for the space fractional heat conduction equation is investigated. Firstly, we describe the approximate solution of the direct problem. Secondly, for the inverse problem part, we define the functional illustrating the error of approximate solution. To recover the thermal conductivity coefficient we need to minimize this functional. In order to minimize this func...