WU XueHong¹, SHEN ShengPing², TAO WenQuan^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.1, pp. 65-76, 2007, DOI:10.3970/cmes.2007.022.065

Abstract Meshless local Petrov-Galerkin collocation method is applied to compute two-dimensional heat conduction problems in irregular domain. By taking the Dirac's Delta function as the test function, the local domain integration is avoided. The essential boundary conditions can be implemented easily in this method. A case that has analytical solution shows the present method can obtain desired accuracy and efficient. Two cases in engineering are computed to validate the approach by comparing the present method with the finite volume method (FVM) solutions obtained from a commercial CFD package FLUENT 6.3. The results show that the present More >

N. Osawa¹, K. Hashimoto¹, J. Sawamura¹, J. Kikuchi², Y. Deguchi², T. Yamaura²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 43-54, 2007, DOI:10.3970/cmes.2007.020.043

Abstract A new hypothesis regarding heat transmission during line heating is proposed. It states that the distribution of the temperature of the gas adjacent to the plate, T_G, and the overall local heat transfer coefficient, α, depend only on the distance from the torch. An identification technique for T_G and α is developed. The validity of the employed hypothesis and the proposed technique is demonstrated by comparing the measured and identified T_G during a spot heating test. The plate temperature calculated by direct heat conduction analysis closely approximates the one measured for the spot and line heating tests, More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 77-90, 2006, DOI:10.3970/cmes.2006.014.077

Abstract In this paper we derive the first-order and second-order one-step GPS applied to the estimation of thermophysical properties. Solving the resultant algebraic equations, which usually converges within ten iterations, it is not difficult to estimate the unknown temperature-dependent thermal conductivity and heat capacity simultaneously, if some supplemented data of measured temperature at a time T is provided. When the measured temperature in the conducting slab is contaminated by noise, our estimated results are also good. The new method does not require any prior information on the functional forms of thermal conductivity and heat capacity. Numerical examples More >

Xianwu Ling¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 219-228, 2006, DOI:10.3970/cmes.2006.013.219

Abstract In this paper, two matrix algebraic tools are provided for studying the solution-stabilities of inverse heat conduction problems. The propagations of the computed temperature errors, as caused by a noise in temperature measurement, are presented. The spectral norm analysis reflects the effect of the computational time steps, the sensor locations and the number of future temperatures on the computed error levels. The Frobenius norm analysis manifests the dynamic propagations of the computed errors. As an application of the norm analysis, we propose a method for the best positioning of the thermocouples. More >

C.-S. Liu¹, C.-W. Chang², J.-R. Chang²

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 67-82, 2006, DOI:10.3970/cmes.2006.012.067

Abstract In this paper we are concerned with the backward problems governed by differential equations. It is a first time that we can construct a backward time dynamics on the past cone, such that an augmented dynamical system of the Lie type X^˙ = B(X,t)X with t ∈ R⁻, X ∈ Mⁿ⁺¹ lying on the past cone and B ∈ so(n,1), was derived for the backward differential equations system x^· =f(x,t), t ∈ R⁻, x ∈ Rⁿ. These two differential equations systems are mathematically equivalent. Then we apply the backward group preserving scheme (BGPS), which is an explicit single-step algorithm… More >

Y.C. Hon¹, T. Wei²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 119-132, 2005, DOI:10.3970/cmes.2005.007.119

Abstract We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply the Tikhonov regularization method based on the generalized cross-validation criterion for choosing the regularization parameter to obtain a stable approximation to the solution. The effectiveness of the algorithm is illustrated by several numerical two- and More >

S. Bargmann, P. Steinmann¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 133-150, 2005, DOI:10.3970/cmes.2005.009.133

Abstract The present contribution is concerned with the modeling and computation of non-classical heat conduction. In the 90s Green and Naghdi presented a new theory which is fully consistent. We suggest a solution method based on finite elements for the spatial as well as for the temporal discretization. A numerical example is compared to existing experimental results in order to illustrate the performance of the method. More >

C.-W. Chang¹, C.-S. Liu², J.-R. Chang^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 13-38, 2005, DOI:10.3970/cmes.2005.010.013

Abstract In this paper, the inverse heat conduction problem governed by sideways heat equation is investigated numerically. The problem is ill-posed because the solution, if it exists, does not depend continuously on the data. To begin with, this ill-posed problem is analyzed by considering the stability of the semi-discretization numerical schemes. Then the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by the group preserving scheme, and the stable range of the index r = 1/2ν Δt is investigated. When the numerical results are compared with exact solutions, it More >

M. Mosaad², A. Ben-Nakhi², M. H. Al-Hajeri²

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.4, pp. 301-314, 2005, DOI:10.3970/fdmp.2005.001.301

Abstract This work deals with the problem of thermal interaction between two fluid media at two different bulk temperatures and separated by a vertical plate. The problem is analyzed by taking into account the heat conduction across the separating plate. The flow configuration considered is one in which the two vertical boundary layers of free and forced convection developed on plate sides are in parallel flow. The dimensionless parameters governing the thermal interaction mechanisms are analytically deduced. The obtained results are presented in graphs to demonstrate the heat transfer characteristics of investigated phenomenon. The work reports More >

Eduardo Divo¹, Alain J. Kassab²

CMC-Computers, Materials & Continua, Vol.2, No.4, pp. 277-288, 2005, DOI:10.3970/cmc.2005.002.277

Abstract A Dual Reciprocity Boundary Element Method is formulated to solve non-linear heat conduction problems. The approach is based on using the Kirchhoff transform along with lagging of the effective non-linear thermal diffusivity. A posteriori error estimate is used to provide effective estimates of the temporal and spatial error. A numerical example is used to demonstrate the approach. More >