多孔介質中拉伸面上之黏彈性流體對流熱傳

Convection Heat Transfer of Visco-elastic Fluids over a Stretching Surface in Porous Media

陳哲娜(Che-Na Chen)

指導教授 ： 陳建信

國立虎尾科技大學/工程學院/機械設計工程研究所/碩士(2011年)

摘要

本文研究粘彈性流體受均勻磁場下通過多孔介質在拉伸平面上的流動與傳熱特性，並考慮黏性耗散、焦耳熱、內部能量的產生或吸收、磁場、熱輻射等效應。本問題之統御方程式為非線性偏微分方程式，故利用相似變換法將其轉化成非線性的常微分方程式，則可求得正解。速度場、溫度場、局部紐塞爾數、表面摩擦係數以Kummer’s function表示之。熱傳分析部分本文分別用兩種不同的非等溫熱邊界條件，（一）給定表面溫度（prescribed surface temperature，PST）及（二）給定表面熱通量（prescribed surface heat flux ，PHF）。

詳細討論各物理參數對速度、溫度分佈、紐塞爾數(Nusselt number)和摩擦係數的影響，如黏彈性參數(viscoelastic parameter, k1)、孔隙率(porosity, ε)、滲透參數(permeability parameter, K)、磁性參數(magnetic parameter, Mn)、熱輻射參數(radiation parameter, R)、艾克特數(Eckert number, Ec)及普朗特數(Prandtl number, Pr)、內部熱生成或吸收參數(heat source/sink parameter, Q)，並將一些特例與先前文獻作相互比對，速度場結果顯示黏彈參數、滲透參數、磁性參數都會降低速度分佈，而孔隙率增加使得速度分佈增加。而溫度場方面孔隙率、普朗特數都使溫度分佈減小，而磁性參數、黏彈參數、滲透參數、艾克特數與輻射參數會增加溫度邊界層厚度。

關鍵字

多孔介質 ； 黏彈性流體 ； 磁流動 ； 拉伸平面

並列摘要

The paper aims to study the flow and heat transfer characteristics of MHD viscoelastic fluid flow in a porous medium over a stretching sheet. The partial differential equations governing the flow and heat transfer are converted into ordinary differential equations by suitable similarity transformation. The present problem has been solved analytically by using Kummer’s function. Two thermal conditions at the surface are considered, i.e. (i) prescribed wall temperature (PST case) and (ii) prescribed heat flux (PHF case). To reveal the tendency of the solutions, representative results for velocity and temperature profiles, the local Nusselt number and the skin friction coefficient are presented for various governing parameters.

The effects of various physical parameters, such as viscoelasticity, porosity, permeability, magnetic parameter, thermal radiation parameter, heat source/sink parameter, Prandtl number, Eckert number and suction/injection parameter on the velocity and temperature profiles, skin friction coefficient and Nusselt number are examined and discussed in detail. For some special cases, The results of the present analysis are in excellent agreement with the existing literature. The velocity profile increases with ε but decreases with k1, K and Mn for other parameters fixed. The temperature profiles in both the PST and PHF cases increase with k1, K, R and Ec but decrease with ε and Pr.

並列關鍵字

porous media ； visco-elastic fluid ； MHD flow ； stretching sheet

參考文獻

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