This study represents a novel approach to speed up the solution of nonlinear inverse heat conduction problems (IHCPs) by the implementation of the complex variable differentiation method (CVDM). A difficulty appeared ...
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This study represents a novel approach to speed up the solution of nonlinear inverse heat conduction problems (IHCPs) by the implementation of the complex variable differentiation method (CVDM). A difficulty appeared in the solution of nonlinear problems is the great amount of computational time. To handle this problem, a new scheme is introduced to improve the conjugate gradient method (CGM). The main contribution in the improvement of conventional CGM is the simultaneous solution of direct and sensitivity problems by applying the complexvariablemethod. The derivation of sensitivity problem by utilizing the analytic derivative is difficult or impossible, since the direct problem is complicated mathematically in many cases. By this approach, the analytic derivation of sensitivity problem is circumvented, while the Jacobian matrix components are obtained accompanied by the solution of the direct problem. Therefore, the developed scheme results in the reduction of mathematical manipulations. Due to the high nonlinearity of moving boundary inverse problems, the ablation problem is considered as the benchmark to examine the accuracy and effectiveness of the proposed scheme. The simulated results illustrate that the developed scheme has the potential to significantly reducing of the computational expenses while maintaining the quality of numerical solution.
We present an efficient numerical scheme to evaluate hypersingular integrals appeared in boundary element methods. The hypersingular integrals are first separated into regular and singular parts, in which the singular...
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We present an efficient numerical scheme to evaluate hypersingular integrals appeared in boundary element methods. The hypersingular integrals are first separated into regular and singular parts, in which the singular integrals are defined as limits around the singularity and their values are determined analytically by taking the finite part values. The remaining regular integrals can be evaluated using rational interpolatory quadrature or complexvariabledifferentiation (CVDM) for the regular function when machine precision like accuracy is required. The proposed method is then generalised for evaluating hypersingular surface integrals, in which the inner integral is treated as the hypersingular line integral via coordinate transformations. The procedure is implemented into 8-node rectangular boundary element and 6-node triangular element for numerical evaluation. Finally, several numerical examples are presented to demonstrate the efficiency of the present method. To the best of our knowledge, the proposed method is more accurate, faster and more generalised than other methods available in the literature to evaluate hypersingular integrals. (C) 2017 Elsevier Inc. All rights reserved.
Inverse heat transfer is a more efficient method for estimating unknown quantities of variable interest. The aim of present research work is to successfully predict the energy consumption to bake the bread at differen...
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Inverse heat transfer is a more efficient method for estimating unknown quantities of variable interest. The aim of present research work is to successfully predict the energy consumption to bake the bread at different baking oven temperatures during baking processes using the inverse heat transfer method. This inverse technique allows researchers to avoid the usage of intricate and expensive instrumentation. This study also compared different numerical techniques for estimating accurate sensitivity coefficients. The inverse heat transfer problem is presented as a multi-parameter estimation of heat flux and solved by the Levenberg-Marquardt algorithm. The finite element method is applied to solve the transient standard heat transfer problem while considering nonlinear two-dimensional heat transfer. The results demonstrated that the complex variable differentiation method was given the satisfactory results than the forward difference method and central difference approximation method. In order to demonstrate the accuracy of the results, statistical analysis is performed for estimated parameters. A good agreement of results is obtained with help of the inverse heat transfer problem. This developed model provides the information to enable the energy required to cook any food product in food thermal processing accurately.
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