導電性流體受非穩態拉伸表面驅動之熱流研究－不同加熱條件的影響

Study of heating boundary conditions on an electrically conducting fluid driven by an unsteady plane stretching surface－ flow and heat transfer problems

蘇良壁(Leong-Pei Soh)

指導教授 ： 劉一中

國立暨南國際大學/科技學院/土木工程學系/碩士(2012年)

https://doi.org/10.6837/NCNU.2012.00288

摘要

本文研究主要探討導電性流體受非穩態拉伸表面驅動在不同加熱條件，考量黏性係數隨溫度而改變、熱傳導係數為溫度的線性函數之熱傳遞特性影響，拉伸表面系統受到磁場效應影響，能量方程式包含黏性耗散及熱輻射效應影響，邊界溫度與熱通量條件考慮沿著流動方向的距離及時間為冪次分佈，在拉伸表面之加熱條件為對流熱通量，非穩態的統御方程式以相似變換轉換為一組非線性常微分方程組並以五階精準Runge-Kutta 射擊法配合Newton-Raphson法之方法求解。其中伴隨著影響這些方程式的幾個重要的參數，有普朗特數Pr、艾特克數Ec 、非穩態參數S 、輻射參數Nr 、熱傳導參數ε 、黏滯參數α ，局部必歐參數Bi和磁參數M等參數。
計算結果顯示在固定S下，無因次溫度、拉伸表面溫度及自由液面溫度隨Pr，α的增加而減少，隨Nr，Bi，Ec的增加而增加。速度分佈受隨M的增加而減少，S的減少而增加，速度分佈隨α的增加而增加。在固定Pr下，表面摩擦係數與局部熱傳遞率係數隨Bi的增加而遞增。在艾克特數Ec下，表面摩擦係數與局部熱傳遞率係數隨α，ε和Bi的增加而遞減。

關鍵字

非穩態拉伸 ； 黏性耗散 ； 導電性液體薄層 ； 艾特克數 ； 對流熱通量

並列摘要

The heat transfer characteristics of a hydromagnetic liquid film flow over an unsteady stretching sheet subject to convective heat flux are investigated numerically. The effect of magnetic field, viscous dissipation and thermal radiation applying to an optically thick medium is also considered. The governing boundary layer equations are transformed into a set of nonlinear ordinary differential equations using a fifth-order step- adapted Runge-Kutta integration scheme together with Newton-Raphson method. The temperature profiles depending on the governing parameters are displayed in graphical form and the relevant thermal characteristics are depicted in tabular representation. It is found that the dimensionless temperature profile, sheet temperature and free surface temperature, for specific unsteadiness parameters, are enhanced as the increases in magnetic parameter, Eckert number and thermal radiation parameter, and they are reduced with an increase in Prandtl number. The local skin-friction coefficient and local Nusselt number increase with an increase in viscosity variation parameter, thermal conductivity parameter and the local Biot number for specific Prandtl number, and in contrast, they decrease for increasing values of Eckert number.

並列關鍵字

unsteady stretching ； viscous dissipation ； electrically conducting fluid ； Eckert number ； Convective heat flux

參考文獻

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