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An Efficient Approach for Solving One-Dimensional Fractional heat conduction equation

Frontiers in heat and Mass Transfer 2023年第1期21卷 487-504页

作者： Iqbal M.Batiha IqbalH.Jebril Mohammad Zuriqat Hamza S.Kanaan Shaher Momani Department of Mathematics Al Zaytoonah University of JordanAmman11733Jordan Nonlinear Dynamics Research Center(NDRC) Ajman UniversityAjmanUnited Arab Emirates Department of Mathematics Al al-Bayt UniversityMafraq130095Jordan Department of Mathematics Irbid National UniversityIrbid2600Jordan Department of Mathematics The University of JordanAmman11942Jordan

Several researchers have dealt with the one-dimensional fractional heat conduction equation in the last decades,but as far as we know,no one has investigated such a problem from the perspective of developing suitable fractional-order *** has actually motivated us to address this problem by the way of establishing a proper fractional approach that involves employing a combination of a novel fractional difference formula to approximate the Caputo differentiator of orderαcoupled with the modified three-point fractional formula to approximate the Caputo differentiator of order 2α,where 0heat conduction equation is then reexpressed numerically using the aforementioned formulas,and by dividing the considered mesh into multiple nodes,a system is generated and algebraically solved with the aid of *** would allow us to obtain the desired approximate solution for the problem at hand.

关键词： heat conduction equation fractional difference formula modified three-points fractional formula

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3D Radiative Transfer equation Coupled with heat conduction equation with Realistic Boundary Conditions Applied on Complex Geometries

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Journal of Applied Mathematics and Physics 2016年第8期4卷 1488-1493页

作者： D. Le Hardy Y. Favennec G. Domingues B. Rousseau Université de Nantes Nantes France

This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem is considered steady-state but solved at each time iteration of the transient conduction problem. The discrete ordinate method along with the decentered streamline-upwind Petrov-Galerkin method is developed. Since specular reflection is considered on borders, a very accurate algorithm has been developed for calculation of partition ratio coefficients of incident solid angles to the several reflected solid angles. The developed algorithms are tested on a paraboloid-shaped geometry used for example on concentrated solar power technologies.

关键词： Radiative Transfer equation heat conduction equation Finite Element Methods SUPG DOM Specular Reflection Complex Geometry

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Mathematical Modeling of heat Transfer Processes of Coal Waste Combustion in a Chamber of Automated Energy Generating Complex

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Journal of Thermal Science 2013年第2期22卷 174-179页

作者： Sergey P. Mochalov Sergey N. Kalashnikov Pavel S. Mochalov Guolin Song Guoyi Tang Siberian State Industrial University Advanced Materials Institute Graduate School at ShenzhenTsinghua University

The automated energy generating complex allows obtaining heat energy from waste coal-water slurry fuel （WCF） that is a mixture of fine coal particles from coal enrichment wastes with water. The mixture is blown into the swirl chamber under the pressure through the special sprayers. The received heat energy is used in different ways. One of the important issues is to estimate the heat losses through the walls of this chamber. In this paper we solved the boundary problem of mathematical physics to estimate the temperature fields in the walls of the swirl chamber. The obtained solution allows us to estimate the heat losses through the waUs of the swid chamber. The task of the mathematical physics has been solved by a numerical finite-difference method. The method for solving this prob- lem can be used in the calculation of temperature fields and evaluation of heat losses in other thermal power units.

关键词： heat transfer heat conduction equation boundary conditions the heat transfer coefficient tempera-ture distribution.

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An analytical model for estimating soil temperature profiles on the Qinghai-Tibet Plateau of China

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Journal of Arid Land 2016年第2期8卷 232-240页

作者： HU Guojie ZHAO Lin WU Xiaodong LI Ren WU Tonghua XIE Changwei QIAO Yongping SHI Jianzong CHENG Guodong Cryosphere Research Station on Qinghai-Xizang Plateau State Key Laboratory of Cryospheric SciencesCold and Arid Regions Environmental and Engineering Research InstituteChinese Academy of Sciences

Soil temperature is a key variable in the control of underground hydro-thermal processes. To estimate soil temperature more accurately, this study proposed a solution method of the heat conduction equation of soil temperature （improved heat conduction model） by applying boundary conditions that incorporate the annual and diurnal variations of soil surface temperature and the temporal variation of daily temperature amplitude, as well as the temperature difference between two soil layers in the Tanggula observation site of the Qinghai-Tibet Plateau of China. We employed both the improved heat conduction model and the classical heat conduction model to fit soil temperature by using the 5 cm soil layer as the upper boundary for soil depth. The results indicated that the daily soil temperature amplitude can be better described by the sinusoidal function in the improved model, which then yielded more accurate soil temperature simulating effect at the depth of 5 cm. The simulated soil temperature values generated by the improved model and classical heat conduction model were then compared to the observed soil temperature values at different soil depths. Statistical analyses of the root mean square error （RMSE）, the normalized standard error （NSEE） and the bias demonstrated that the improved model showed higher accuracy, and the average values of RMSE, bias and NSEE at the soil depth of 10-105 cm were 1.41℃, 1.15℃ and 22.40%, respectively. These results indicated that the improved heat conduction model can better estimate soil temperature profiles compared to the traditional model.

关键词： soil temperature heat conduction equation daily amplitude boundary condition

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Stable and Fast Algorithm for Parameter Identification in heat conduction Problems

Stable and Fast Algorithm for Parameter Identification in He...

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The Sixth International Conference of Matrices and Operators

作者： Jun-li Zhang Hai-yan Yu School of Mathematics Inner Mongolia University for the Nationalities

＜正＞A regularization method for an inverse problem of determination of unknown parameter in heat conduction problems is *** approach of the proposed method is to add constraint condition of derivative and get a well-posed operator equation which can approximate the ill-posed problem discussed. The numerical results show that our algorithm is stable and precise.

关键词： heat conduction equation inverse problem parameter identification constraint condition.

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