Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phas...

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

This paper gives a 2D hamonic lattices model with missing bond defects, when the capacity ratio of defects is enough large, the temperature gradient can be formed and the finite heat conduction is found in the model. The defects in the 2D harmonic lattices impede the energy carriers free propagation, by another words, the mean free paths of the energy carrier are relatively short. The microscop...

Linear boundary value problems in heat conduction have been investigated extensively for a diverse variety of boundary conditions, but almost invariably these have been of the type that produce self-adjoint problems. The property of selfadjointness makes it possible to obtain readily the solution of steady and unsteady-state heat conduction problems in the form of a series expansion of orthogon...

We introduce a central difference method and a quasi-reversibility method for solving a backward heat conduction problem (BHCP) numerically. For these two numerical methods, we give the stability analysis. Meanwhile, we investigate the roles of regularization parameters in these two methods. Numerical results show that our algorithm is effective. 2005 Elsevier Inc. All rights reserved.

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

We look at a basic introduction to classical models of heat conduction, with a few examples including both finite and infinite systems, with techniques appropriate to each based on the boundary and initial conditions. Portions of the paper follow chapter 11 of Theoretical Mechanics of Particles and Continua [1], where I have attempted to expand the analysis in an attempt to provide clarity wher...

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a ...

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...