Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two-dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed...

H. Salt, Transient conduction in two-dimensional composite slab--I. Theoretical development of temperature modes, ht. J. Heat Mass Transfer 26, 1611-1616 (1983). H. Salt, Transient conduction in two-dimensional composite slab--II. Physical interpretation of temperature modes, ht. J. Heat Mass Transfe 26,1617-1623 (1983). M. D. Mikhailov, General solutions of heat equation in finite regions. ht....

We define and analyze a linear transformation – the heat transform – that allows to map solutions of hyperbolic equations to solutions of corresponding parabolic equations. The inversion of this mapping can be used to transform an inverse problem for the heat equation to a similar problem for the wave equation. This work is motivated by problems of finding interfaces, boundaries and associated ...

In this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the strength of the time- dependent heat source using the temperature distribution at a point in a three layer system. Also, the effect of noisy data on final solution is studied. The numerical solution of the governing equations is obtained b...

1 B. Terry Beck, Kansas State University, Mechanical and Nuclear Engineering Department, 302 Rathbone Hall, Manhattan, KS 66506 [email protected] Abstract  The main objective of this paper is to present two different experiments that have been developed to successfully demonstrate transient heat conduction phenomena. The first experiment illustrates the approximate measurement of transient local h...

small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. non-fourier heat transfer overcomes some shortcomings of fourier heat tran...

This paper deals with the theoretical investigation of the thermal instability of a thin layer of electrically conducting micropolar rotating fluid, heated from below in the presence of uniform vertical magnetic field in porous medium. A dispersion relation is obtained for a flat fluid layer, contained between two free boundaries using a linear stability analysis theory, and normal mode analysi...

I use a simple analytical model to show that simple heat conduction models cannot significantly suppress cluster cooling flows. I build a static medium where heat conduction globally balances radiative cooling, and then perturb it. I show that a perturbation extending over a large fraction of the cooling flow region and with an amplitude of ∼ 10%, will grow to the non-linear regime within a Hub...

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...