本文探討磁液動自然對流流場的熱傳特性與渦漩不穩定性分析，研究範圍包括磁場效應對鄰近水平板壁面自然對流流場及其渦漩不穩定性的影響與霍爾效應對非達西多孔性介質鄰近垂直板壁面磁液動自然對流流場性能的影響。研究內容包括下列四個主題：(1) 考慮慣性效應之多孔性介質鄰近水平板壁面磁液動自然對流流場及其渦漩不穩定性分析。(2) 考慮輻射與非達西效應之多孔性介質鄰近水平板壁面磁液動自然對流流場及其渦漩不穩定性分析。(3) 霍爾效應(Hall effect)對非達西多孔性介質鄰近垂直板壁面磁液動自然對流流場性能分析。(4) 考慮黏滯逸散(viscous dissipation)及焦耳加熱(Joule heating)效應之一般流體鄰近水平板壁面磁液動自然對流流場及其渦漩不穩定性分析。

考慮慣性效應之多孔性介質鄰近水平板壁面磁液動自然對流流場，其基本流場統御方程式為一組常微分方程式組，存在相似解(similarity solution)，使用郎吉-庫塔(Runge-Kutta)積分法配合射擊法(shooting method) 求解。考慮輻射與非達西效應之多孔性介質鄰近水平板壁面、霍爾效應對非達西多孔性介質鄰近垂直板壁面與考慮黏滯逸散及焦耳加熱效應之一般流體鄰近水平板壁面的磁液動自然對流流場，均無相似解存在，本文採用凱拉盒子(Keller Box)數值方法求解。關於渦漩不穩定性分析，則採用線性穩定理論(linear stability theory)和局部相似假設(local similarity method) 推導擾動流場統御方程式，再使用郎吉-庫塔(Runge-Kutta)積分法及葛雷-史密德(Gram-Schmidt)正交技術求出中性穩定曲線(neutral stability curves)、臨界雷利數(Rayleigh number)、臨界葛雷秀夫數 (Grashof number)及臨界波數(wave number)

由數值分析結果得知：(1)多孔性介質鄰近水平板壁面磁液動自然對流流場中，當邊界為等熱通量時，基本流場存在相似解。(2)在鄰近水平板壁面一般流體或多孔性介質流場中，磁場效應降低熱傳率，並使流場趨向不穩定。(3)在鄰近水平板壁面多孔性介質流場中，輻射效應提高切線速度，使溫度邊界層變薄，並使流場趨向穩定。(4) 在強磁場環境下，霍爾效應使流體沿垂直板壁面產生側向流動，流場變成了三維流場。(5) 霍爾效應使流體切線速度(tangential velocity)提高，但側向速度(lateral velocity)則隨霍爾參數增大，先增加而後再下降。(6) 在鄰近水平板壁面一般流體磁液動流場中，考慮黏滯逸散及焦耳加熱效應，流場切線速度增加，熱傳率下降，流場趨向不穩定。

Two main problems have been studied in this paper：First, magnetic effects on the flow and vortex instability of natural convection boundary layer flow over a horizontal plate are investigated；second，Hall effect on an electrically conducting fluid in magnetohydrodynamics (MHD) natural convection boundary layer past a vertical plate in porous medium are examined. The present investigated includes：(1) Magnetic and inertia effects on the vortex instability of natural convection flow over a horizontal plate in a saturated porous medium. (2) Radiation and non-Darcy effects on the vortex instability of MHD natural convection flow over a horizontal plate in a saturated porous medium. (3) Hall effect on MHD non-Darcy free convection flow from a vertical plate in porous medium with heat and mass transfer. (4) Viscous dissipation and Joule heating effects on the vortex instability of MHD natural convection flow over a horizontal plate.
For the case of the vortex instability of a horizontal MHD natural convection boundary layer flow in a saturated porous medium with surface mass flux, similarity solutions are admitted and can be solved by the sixth-order Runge-Kutta method. However, for the flows of radiation effect on horizontal plate in porous medium、Hall effect on vertical plate in porous medium and viscous dissipation and Joule heating effects on horizontal plate, similarity solutions are not existed. An efficient implicit Keller box finite difference method is employed to solve the governing equations. In stability analyses, the linear stability theory and local similarity approximation are applied in deriving the disturbance equations. The disturbance equations are solved by using the Runge-Kutta method incorporated with Gram-Schmidt orthogonalization procedure for neutral stability curves.
The numerical results show that：(1) For MHD natural convection flow over a horizontal plate in a saturated porous medium，the similarity solutions exist only if there is a constant heat flux boundary. (2) For MHD natural convection flow over a horizontal plate，the magnetic parameter increases， the heat transfer rate and tangential velocity decrease. The magnetic effect destabilizes the flow to vortex mode of disturbance. (3) For MHD natural convection flow over a horizontal plate in a saturated porous medium，the radiation effect increases the tangential velocity 、dccreases the thermal diffusion boundary layer thickness、and stabilizes the flow to vortex mode of disturbance. (4) For MHD natural convection flow from a vertical plate in porous medium，when the strength of the magnetic field is strong，the Hall effect induces the lateral velocity and gives rise to thermal and mass transfer in the porous medium. (5) For MHD natural convection flow from a vertical plate in porous medium，as the Hall parameter m is increased, the tangential velocity continues to increase but however, the lateral velocity only increases for m ≦ 1 while it decreases for m > 1. (6) For MHD natural convection flow over a horizontal plate， when viscous dissipation and Joule heating effects are included， increasing on the tangential velocity is observed 、a considerable reduction in heat transfer rate occurred、and the flow destabilized to vortex mode of disturbance.

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