Y. Hu¹, T. Wei^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 307-326, 2012, DOI:10.3970/cmes.2012.087.307

Abstract This paper employ the method of fundamental solutions for determining an unknown heat source term in a heat equation from overspecified boundary measurement data. By a function transformation, the inverse source problem is changed into an inverse initial data problem which is solved by a method of fundamental solutions. The standard Tikhonov regularization technique with the generalized cross-validation criterion for choosing the regularization parameter is adopted for solving the resulting ill-conditioned system of linear algebraic equations. The effectiveness of the algorithm is illustrated by five numerical examples in one-dimensional and two-dimensional cases. More >

C. Shi¹, C. Wang¹, T. Wei^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 71-92, 2012, DOI:10.3970/cmes.2012.086.071

Abstract In this paper, we consider a typical ill-posed inverse heat source problem, that is, we determine a space-dependent heat source term in a multi-dimensional heat equation from a pair of Cauchy data on a part of boundary. By a simple transformation, the inverse heat source problem is changed into a Cauchy problem of a homogenous heat conduction equation. We use the method of fundamental solutions (MFS) coupled with the Tikhonov regularization technique to solve the ill-conditioned linear system of equations resulted from the MFS discretization. The generalized cross-validation rule for determining the regularization parameter is used. Numerical results for four… More >

A. Khosravifard¹, M.R. Hematiyan^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.3&4, pp. 185-208, 2011, DOI:10.3970/cmes.2011.078.185

Abstract An inverse method for optimal control of the freezing front motion in the solidification of pure materials is presented. The inverse technique utilizes the idea of a pseudo heat source to account for the latent heat effects. The numerical formulation of this inverse method is based on a formerly introduced meshless technique. In this method, the flux and the velocity of the liquid-solid interface are treated as secondary variables and the liquid and solid domains are modeled simultaneously. Some numerical examples are provided to demonstrate the efficiency of the presented method. The effects of regularization and the number of nodes… More >

Ching Kong Chao^1,2, Chin Kun Chen¹, Fu Mo Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.1, pp. 1-28, 2010, DOI:10.3970/cmes.2010.063.001

Abstract A general analytical solution for a reinforced elliptical hole embedded in an infinite matrix subjected to a point heat source is provided in this paper. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stresses in the reinforcement layer and the matrix are derived explicitly in a series form. Some numerical results are provided to investigate the effects of the material combinations and geometric configurations on the interfacial stresses. The solution obtained can be treated as Green's functions which enable us to formulate… More >

Weichung Yeih^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 107-128, 2009, DOI:10.3970/cmes.2009.046.107

Abstract We consider an inverse problem for estimating an unknown time dependent heat source H(t) in a heat conduction equation u_t(x,t) = u_xx(x,t) + H(t). First this inverse problem is formulated as a three-point boundary value problem (BVP) for ODEs discretized from the transformed homogeneous governing equation. To treat this three-point BVP we develop a two-stage Lie-group shooting method (TSLGSM). The novel approach is examined through numerical examples to convince that it is rather accurate and efficient; the estimation error is small even for identifying discontinuous and oscillatory heat sources under noise. More >

Leevan Ling¹, Tomoya Takeuchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 99-110, 2007, DOI:10.3970/cmes.2007.020.099

Abstract We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4):1289--1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence… More >

Ilhem Zeghbid¹, Rachid Bessaïh¹

FDMP-Fluid Dynamics & Materials Processing, Vol.13, No.4, pp. 251-273, 2017, DOI:10.3970/fdmp.2017.013.251

Abstract This paper presents a numerical study of two-dimensional laminar mixed convection in a lid-driven square cavity filled with a nanofluid and heated simultaneously at a constant heat flux q” by two heat sources placed on the two vertical walls. The movable wall and the bottom wall of the cavity are maintained at a local cold temperature T_C, respectively. The finite volume method was used to solve the equations of flow with heat transfer across the physical domain. Comparisons with previous results were performed and found to be in excellent agreement. Results were presented in terms of streamlines, isotherms, vertical velocity… More >

Fatima-zohra Bensouici^{1, *}, Saadoun Boudebous²

FDMP-Fluid Dynamics & Materials Processing, Vol.13, No.3, pp. 189-212, 2017, DOI:10.3970/fdmp.2017.013.189

Abstract A numerical work has been performed to analyze the laminar mixed convection of nanofluids confined in a lid driven square enclosure with a central square and isotherm heat source. All the walls are cooled at constant temperature, and the top wall slides rightward at constant velocity. The simulations considered four types of nanofluids (Cu, Ag, Al₂O₃ and TiO₂)-Water. The governing equations were solved using finite volume approach by the SIMPLER algorithm. Comparisons with previously published work are performed and found to be in good agreement. The influence of pertinent parameters such as Richardson number, size of the heat source, solid… More >

Mustapha FARAJI¹

FDMP-Fluid Dynamics & Materials Processing, Vol.13, No.1, pp. 19-36, 2017, DOI:10.3970/fdmp.2017.013.019

Abstract A two-dimensional numerical model that accounts for heat transfer by conduction and natural convection in the molten region of nano enhanced Phase Change Material (PCM) is performed. Numerical investigations were conducted using an enthalpy- porosity method in order to examine the impact of the dispersion of copper (CuO) nanoparticles on the heat source temperature and the effect on the heat sink secured working time and the melting rate. Results show that heat spreads more easily along the conducting plate and to the PCM and, consequently, the PCM melts rapidly and the heat source is efficiency cooled by the addition of… More >

Gnaneswara Reddy Machireddy¹

FDMP-Fluid Dynamics & Materials Processing, Vol.10, No.4, pp. 417-442, 2014, DOI:10.3970/fdmp.2014.010.417

Abstract This study deals with the investigation of the effects exerted by heat radiation and a first-order chemical reaction on the magnetohydrodynamics boundary layer slip flow which is established past a vertical permeable surface embedded in a porous medium (with uniform heat and mass flux). The heat equation includes the relevant terms, i.e. the viscous dissipation, radiative heat flux, Ohmic dissipation, and absorption of radiation. The mass transfer equation takes into account the effects related to the chemically reactive species. A classical model for optically thin media is used for studying the effect of radiation. The resulting non-linear coupled partial differential… More >