- 學位論文
暫態拉伸平面上磁流與熱傳之分析
Hydromagnetic flow and heat transfer analysis over an unsteady stretching sheet
摘要
本文以數值研究方式，探討邊界層流之流場與熱傳特性，流體之流動肇因於被暫態(unsteady)連續拉伸之平板穿越流體。流體為具有電導性之不可壓縮牛頓流體，承受均勻外部磁場及其所產生之歐姆熱(Ohmic heating)。同時，流體之黏滯性及熱傳導性假設為溫度函數。統禦方程式包括質量、動量與能量平衡方程式，經由適當的相似性(similarity)轉換，得到動量與能量兩個非線性常微分方程式，並藉由柴比雪夫(Chebyshev)有限差分法離散此常微分方程式，再以牛頓迭代技巧解代數聯立方程式。本研究考慮兩種流動狀況，分別是平板穿越無限流體介質的流動及有限流體介質在平板上的流動，即液體薄膜流。數值分析結果分別以各個參數對流場、溫度場、表面摩擦係數以及熱傳率之效應以明確圖形表示，同時詳細說明與討論其物理變化情形。 數值分析結果顯示，兩種流動狀況在固定暫態參數(unsteady parameter)時，普郎特數(Prandtl number)愈大使熱傳率提升，而磁場強度(magnetic field)、黏滯性參數(viscosity parameter) 及熱傳導性參數(thermal conductivity parameter)之增大則使熱傳效果降低。在拉伸平面上之表面摩擦會隨著磁場強度及黏滯性參數之增大而變大。在薄膜流的情況，薄膜厚度隨著暫態參數、磁場強度及黏滯性參數之減小而增大。暫態參數、磁場強度、艾力克數(Eckert number) 及黏滯性參數之增大會使薄膜自由表面溫度降低。
並列摘要
A numerical study of flow and heat transfer from boundary layer flow driven by a stretching impermeable plate is proposed. The flow with electrically Newtonian fluid due to the continuous stretching sheet in the presence of a transverse uniform magnetic field was molded as an unsteady, viscous, and incompressible, taking into account the variation of fluid viscosity and thermal conductivity and including the effects of Ohmic heating due to electromagnetic work in the energy equation. The effects of viscous dissipation are neglected in heat flow process. The fluid viscosity is assumed to vary as an inverse linear function of temperature and the thermal conductivity is variable and considered to vary as a linear function of temperature. Similarity analysis with Chebyshev finite difference method (ChFD) was developed to solve the governing equations for mass, momentum and energy. Two different cases are considered, one corresponding to a infinite fluid medium surrounding the stretching sheet and the other, a finite fluid medium, i.e. thin liquid film on a stretching sheet. Graphical results for the effects of various parameters on the fluid velocity and temperature and the skin-friction coefficient and heat transfer rate are presented and discussed. Numerical results showed, for a given unsteadiness parameter, that the local heat transfer rate increases as Prandtl number increase, while it decreases as magnetic field strength, thermal conductivity parameter and viscosity parameter increase. The skin friction, for a given unsteadiness parameter, increases as magnetic field strength and viscosity parameter increase. The film thickness increases with the decreasing in unsteadiness parameter, magnetic field strength, and viscosity parameter in liquid film case. The free-surface temperature decreases with the increasing in unsteadiness parameter, magnetic field strength, Eckert number and viscosity parameter in liquid film case.