几类反常扩散与传热问题的分析研究
发布时间：2023-06-27 21:24
反常扩散和传热问题在许多科学研究和工程技术中有着非常重要的作用,许多科学技术工作者仍然从事这个领域对各种类型的反常扩散及传热应用问题的研究,本论文利用解析方法对几类反常扩散与传热问题开展研究,包括:具有n-扩散型的反应扩散问题,激波边界层流动,非牛顿流体边界层流动与传热问题。对一类与n-扩散相关的反应扩散问题基于同质模型,研究了各种参数的影响,改进了传统的傅里叶导热定律,研究了 p-Fisher-KPP反应型反扩散方程,Philip n-扩散,具有反常特征的Cattaneo热通量型扩散和热能,m-Zeldovich lakov型反常扩散等问题和Stefan-Boltzmann反常传递问题等,得到了一些符合实际的有趣研究成结果。此外,利用图形详细讨论了涉及的参数对温度分布的影响。对于稳定边界层流,通过变换得到的相似解,利用Adomian方法和同伦分析方法(HAM)求问题的近似解。得到在不同速度比例参数和Prandlt的影响下速度和温度场分布,并绘图和详细分析了各参数的影响规律。利用Adomian方法和同伦分析方得到的解非常吻合,显示了两种解析方法的有效性。关于非线性微分方程的解析研究,我...
【文章页数】：121 页
【学位级别】：博士
【文章目录】：
Thanks and Appreciation
Gratitude
摘要
Abstract
Nomenclature
1 Introduction
2 Literature review
2.1 Background in heat transfer
2.1.1 Conduction heat transfer processes
2.1.2 Convection heat transfer processes
2.1.3 Radiation heat transfer processes
2.2 Research progress
2.2.1 Reaction-diffusion processes
2.2.2 Heat convection processes
2.3 Basic ideals analytical methods
2.3.1 Adomian decomposition method
2.3.2 Homotopy-perturbation method
2.3.3 Homotopy analysis method
3 Study of Fisher-KPP reaction and n-diffusion Cattaneo telegraph equation
3.1 Formulation of the problem
3.2 Mathematical model
3.3 Adomian decomposition method solution
3.4 Results and discussion
4 Study on kinetics of diffusion with effect of external force and Fisher-KPPreaction
4.1 Formulation of the problem
4.2 Mathematical model
4.3 The application of HPM and ADM in our problem
4.3.1 Homotopy-perturbation method
4.3.2 Adomian decomposition method
4.4 Numerical results and discussion
4.5 Comparison of HPM and ADM results
5 Study of Cattaneo telegraph equation with reaction term: effects of relaxtiontime, Philip n-diffusion and thermal diffusivity
5.1 Formulation of the problem
5.2 Mathematical model and method of solution
5.3 Results and discussion
5.3.1 Case A＝0,λ＝0
5.3.2 Case A＝0,λ≠0
5.3.3 Case A≠0
6 Study of Zeldovich Lakov reaction and n -diffusion equation
6.1 Formulation of the problem
6.2 Mathematical formulation of the problem
6.3 The application of HPM and ADM in the problem
6.3.1 Homotopy-perturbation method
6.3.2 Adomian decomposition method
6.4 Results and discussion
7 Study of Boundary layer flow and Heat transfer
7.1 Formulation of the problem
7.2 Mathematical formulation
7.3 Adomian decomposition method solutions
7.4 Homotopy analysis method solutions
7.5 Results and discussion
8 n-Diffusion with reaction term model in porous media
8.1 Formulation of the problem
8.2 Mathematical formulation of the problem
8.3 Method of solving
8.4 Results and discussion
9 Heat transfer model in partially saturated heterogeneous aquifers
9.1 Formulation of the problem
9.2 Mathematical formulation of the problem
9.3 Solving the problem
9.3.1 Adomian decomposition method
9.3.2 Homotopy analysis method
9.4 Results and discussion
10 Conclusions
References
作者简历及在学研究成果
学位论文数据集
本文编号：3835362
【文章页数】：121 页
【学位级别】：博士
【文章目录】：
Thanks and Appreciation
Gratitude
摘要
Abstract
Nomenclature
1 Introduction
2 Literature review
2.1 Background in heat transfer
2.1.1 Conduction heat transfer processes
2.1.2 Convection heat transfer processes
2.1.3 Radiation heat transfer processes
2.2 Research progress
2.2.1 Reaction-diffusion processes
2.2.2 Heat convection processes
2.3 Basic ideals analytical methods
2.3.1 Adomian decomposition method
2.3.2 Homotopy-perturbation method
2.3.3 Homotopy analysis method
3 Study of Fisher-KPP reaction and n-diffusion Cattaneo telegraph equation
3.1 Formulation of the problem
3.2 Mathematical model
3.3 Adomian decomposition method solution
3.4 Results and discussion
4 Study on kinetics of diffusion with effect of external force and Fisher-KPPreaction
4.1 Formulation of the problem
4.2 Mathematical model
4.3 The application of HPM and ADM in our problem
4.3.1 Homotopy-perturbation method
4.3.2 Adomian decomposition method
4.4 Numerical results and discussion
4.5 Comparison of HPM and ADM results
5 Study of Cattaneo telegraph equation with reaction term: effects of relaxtiontime, Philip n-diffusion and thermal diffusivity
5.1 Formulation of the problem
5.2 Mathematical model and method of solution
5.3 Results and discussion
5.3.1 Case A＝0,λ＝0
5.3.2 Case A＝0,λ≠0
5.3.3 Case A≠0
6 Study of Zeldovich Lakov reaction and n -diffusion equation
6.1 Formulation of the problem
6.2 Mathematical formulation of the problem
6.3 The application of HPM and ADM in the problem
6.3.1 Homotopy-perturbation method
6.3.2 Adomian decomposition method
6.4 Results and discussion
7 Study of Boundary layer flow and Heat transfer
7.1 Formulation of the problem
7.2 Mathematical formulation
7.3 Adomian decomposition method solutions
7.4 Homotopy analysis method solutions
7.5 Results and discussion
8 n-Diffusion with reaction term model in porous media
8.1 Formulation of the problem
8.2 Mathematical formulation of the problem
8.3 Method of solving
8.4 Results and discussion
9 Heat transfer model in partially saturated heterogeneous aquifers
9.1 Formulation of the problem
9.2 Mathematical formulation of the problem
9.3 Solving the problem
9.3.1 Adomian decomposition method
9.3.2 Homotopy analysis method
9.4 Results and discussion
10 Conclusions
References
作者简历及在学研究成果
学位论文数据集
本文编号：3835362
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