反常擴(kuò)散和傳熱問題在許多科學(xué)研究和工程技術(shù)中有著非常重要的作用,許多科學(xué)技術(shù)工作者仍然從事這個(gè)領(lǐng)域?qū)Ω鞣N類型的反常擴(kuò)散及傳熱應(yīng)用問題的研究,本論文利用解析方法對幾類反常擴(kuò)散與傳熱問題開展研究,包括:具有n-擴(kuò)散型的反應(yīng)擴(kuò)散問題,激波邊界層流動,非牛頓流體邊界層流動與傳熱問題。對一類與n-擴(kuò)散相關(guān)的反應(yīng)擴(kuò)散問題基于同質(zhì)模型,研究了各種參數(shù)的影響,改進(jìn)了傳統(tǒng)的傅里葉導(dǎo)熱定律,研究了 p-Fisher-KPP反應(yīng)型反擴(kuò)散方程,Philip n-擴(kuò)散,具有反常特征的Cattaneo熱通量型擴(kuò)散和熱能,m-Zeldovich lakov型反常擴(kuò)散等問題和Stefan-Boltzmann反常傳遞問題等,得到了一些符合實(shí)際的有趣研究成結(jié)果。此外,利用圖形詳細(xì)討論了涉及的參數(shù)對溫度分布的影響。對于穩(wěn)定邊界層流,通過變換得到的相似解,利用Adomian方法和同倫分析方法(HAM)求問題的近似解。得到在不同速度比例參數(shù)和Prandlt的影響下速度和溫度場分布,并繪圖和詳細(xì)分析了各參數(shù)的影響規(guī)律。利用Adomian方法和同倫分析方得到的解非常吻合,顯示了兩種解析方法的有效性。關(guān)于非線性微分方程的解析研究,我...

【文章頁數(shù)】：121 頁

【學(xué)位級別】：博士

【文章目錄】：
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
作者簡歷及在學(xué)研究成果
學(xué)位論文數(shù)據(jù)集



本文編號：3835362