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研究生:蘇良壁
研究生(外文):Soh, Leong-Pei
論文名稱: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
論文名稱(外文):Study of heating boundary conditions on an electrically conducting fluid driven by an unsteady plane stretching surface-flow and heat transfer problems
指導教授:劉一中劉一中引用關係
指導教授(外文):Liu, I-Chung
口試委員:彭逸凡蕭開龍
口試委員(外文):Peng, Yih-FerngHsiao, Kai-Long
口試日期:2012-07-24
學位類別:碩士
校院名稱:國立暨南國際大學
系所名稱:土木工程學系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:87
中文關鍵詞: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
外文關鍵詞:unsteady stretchingviscous dissipationelectrically conducting fluidEckert numberConvective heat flux
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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。

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.
誌謝…..................................................................................................................................Ⅰ
中文摘要….........................................................................................................................Ⅱ
英文摘要…..........................................................................................................................Ⅲ
目錄…..................................................................................................................................Ⅳ
圖目錄…..............................................................................................................................Ⅶ
表目錄…..............................................................................................................................Ⅹ
符號說明..............................................................................................................................Ⅺ
第一章 緒論…......................................................................................................................1
1.1 前言........................................................................................................................1
1.2 研究動機................................................................................................................1
1.3 研究目的................................................................................................................2
1.4 文獻回顧................................................................................................................2
1.4.1 給定表面溫度 (Prescribed Surface Temperature)......................................3
1.4.2 給定表面熱通量 (Prescribed Surface Heat Flux)......................................7
1.5 本文內容................................................................................................................7
1.6 工業應用機具示意圖.............................................................................................9
第二章 流動及熱邊界條件理論模式.........................................................................10
2.1基本原理及邊界假定....................................................................................10
2.1.1 流體物理性質...................................................................................10
2.1.1.1 黏滯係數...................................................................................10
2.1.1.2 熱傳導係數.................................................................................12
2.1.2 薄層流動及熱邊界假定...........................................................................12
2.2 流動、熱傳參數之特性.......................................................................................13
2.2.1 磁參數、艾特克數、熱輻射參數、必歐數..............................................13
2.2.2 表面摩擦係數,局部雷諾數Re_x,熱傳遞率係數..................................16
2.2.3 熱邊界條件................................................................................................17
2.2.3.1給定表面溫度 (Prescribed Surface Temperature).............18
2.2.3.2給定表面熱通量 (Prescribed Surface Heat Flux) ..............18
2.2.3.3給定對流熱通量 (Convective Heat Flux) .............................18
第三章 問題推導及求解...................................................................................................19
3.1 基本系統描述......................................................................................................19
3.2 基本假設..............................................................................................................19
3.3 控制方程式..........................................................................................................20
3.4 邊界條件..............................................................................................................22
3.5 相似變換 (similarity transform)...................................................................23
3.5.1速度場之相似變換...............................................................................24
3.5.2 溫度場之相似變換...................................................................................26
3.5.3無因次化之邊界條件...............................................................................28
3.5.4 考慮黏性耗散之推導...............................................................................33
3.5.5表面摩擦係數( )與紐塞數( )之推導...............................................34
3.6 數值方法與程序..................................................................................................36
第四章 結果與討論...........................................................................................................38
4.1 流體薄層厚度......................................................................................................38
4.1.1黏性係數為常數.……………….…...........................................................38
4.1.2 黏性為溫度的指數函數...........................................................................38
4.1.3黏滯參數的影響........................................................................................39
4.1.4磁參數的影響…........................................................................................40
4.2 流動、熱傳遞之不同參數特性的影響...............................................................40
4.2.1非穩態參數 ............................................................................................40
4.2.2普朗特數 ...............................................................................................41
4.2.3艾特克數 ...............................................................................................41
4.2.4輻射參數 ..............................................................................................42
4.2.5局部必歐參數 .......................................................................................43
4.2.6熱傳導參數 .............................................................................................43
4.3討論參數對表面摩擦係數的影響......................................................................44
4.4 討論參數對熱傳遞率係數的影響......................................................................45
第五章 結論與建議...........................................................................................................48
5.1 結論....................................................................................................................48
5.1.1 給定對流熱邊界.......................................................................................48
5.1.1.1 速度分佈情形..............................................................................48
5.1.1.2 溫度分佈情形..............................................................................48
5.2 建議....................................................................................................................49
參考文獻…..........................................................................................................................50
附錄….............................................................................................................................55
個人簡歷….........................................................................................................................87



圖目錄
圖1-1穩態拉伸無限流體示意圖.............................................................................55
圖1-2 非穩態拉伸流體薄層示意圖(PST).......................................................................55
圖1-3 非穩態拉伸流體薄層示意圖(PHF).......................................................................56
圖2-1 三種不同必歐數在無限大平板之非穩態導熱問題.............................................56
圖3-1 非穩態拉伸流體薄層示意圖(CHF)......................................................................57
圖 3-2 兩點邊界值問題-射擊法.......................................................................................57
圖4-1 不同之非穩態參數S對應流體薄層厚度β.......................................................58
圖4-2 不同黏滯參數α值之速度分佈情形.....................................................................58
圖4-3 不同黏滯參數α值之速度分佈情形(局部)..........................................................59
圖4-4 不同黏滯參數α值之溫度分佈情形.....................................................................59
圖4-5不同磁參數M值之速度分佈情形........................................................................60
圖4-6不同磁參數M值之速度分佈情形........................................................................60
圖4-7不同磁參數M值之溫度分佈情形........................................................................61
圖4-8不同磁參數M值之溫度分佈情形........................................................................61
圖4-9 不同非穩態參數S值之速度分佈情形.................................................................62
圖4-10不同非穩態參數S值之溫度分佈情形................................................................62
圖4-11不同非穩態參數S值之溫度分佈情形...............................................................63
圖4-12不同普朗特數Pr值之速度分佈情形..................................................................63
圖4-13不同普朗特數Pr值之速度分佈情形..................................................................64
圖4-14不同普朗特數Pr值之溫度分佈情形..................................................................64
圖4-15不同普朗特數Pr值之溫度分佈情形..................................................................65
圖4-16不同艾特克數Ec值在不同S之速度分佈情形..................................................65
圖4-17不同艾特克數Ec值在不同S之速度分佈情形..................................................66
圖4-18不同艾特克數Ec值在不同S之速度分佈情形..................................................66
圖4-19不同艾特克數Ec值在不同S之速度分佈情形..................................................67
圖4-20不同艾特克數Ec值在不同S之溫度分佈情形..................................................67
圖4-21不同艾特克數Ec值在不同S之溫度分佈情形..................................................68
圖4-22不同艾特克數Ec值在不同S之溫度分佈情形..................................................68
圖4-23不同艾特克數Ec值在不同S之溫度分佈情形.............................................69
圖4-24不同輻射參數Nr值之速度分佈情形...........................................................69
圖4-25不同輻射參數Nr值之溫度分佈........................................................................70
圖4-26不同畢歐數Bi值之速度分佈情形.....................................................................70
圖4-27不同畢歐數Bi值之速度分佈情形.....................................................................71
圖4-28不同畢歐數Bi值之溫度分佈情形.....................................................................71
圖4-29不同畢歐數Bi值之溫度分佈情形.....................................................................72
圖4-30不同熱傳導參數ε值之速度分佈情形...............................................................72
圖4-31不同熱傳導參數ε值之溫度分佈情形...............................................................73
圖4-32不同熱傳導參數ε,α對自由表面溫度分佈圖................................................73
圖4-33不同熱傳導參數ε,α對流體層厚度β分佈圖................................................74
圖4-34Pr=0.1~10,α對表面摩擦係數Re_x^(1/2) C_f /2分佈圖.......................................74
圖4-35Pr=0.1~10,Bi對表面摩擦係數Re_x^(1/2) C_f /2分佈圖......................................75
圖4-36Pr=0.1~10,ε對表面摩擦係數Re_x^(1/2) C_f /2分佈圖........................................75
圖4-37Pr=0.1~10,Ec對表面摩擦係數Re_x^(1/2) C_f /2分佈圖.....................................76
圖4-38Pr=0.1~10,α對熱傳遞率(1-at) Re_x^(-3/2) Nu_x分佈圖.....................................76
圖4-39Pr=0.1~10,Bi對熱傳遞率(1-at) Re_x^(-3/2) Nu_x分佈圖....................................77
圖4-40Pr=0.1~10,ε對熱傳遞率(1-at) Re_x^(-3/2) Nu_x分佈圖......................................77
圖4-41Pr=0.1~10,Ec對熱傳遞率(1-at) Re_x^(-3/2) Nu_x分佈圖...................................78



表目錄

表一 不同非穩態參數S所對應表面速度梯度f"(0)和β之值......................................79
表二 不同普朗特數Pr對應自由液面溫度θ(β)和表面溫度梯度-θ'(0)之值................80
表三 在無熱毛細和磁場,不同非穩態參數S所對應γ和表面速度梯度f"(0)之值....81
表四 在PST條件下,不同參數對應自由液面溫度θ(β)、-θ'(0)、β、f"(0)之值...82
表五 在CHF條件下,不同參數對應f'(β)、|f"(0)|、θ(β)、-θ'(0)之值....................83
表六 给定參數下,在單一參數遞增時,檢視變化示意圖..............................................85

[01]L.J. Crane, Flow past a stretching sheet, Z. Angew. Math. Phys., 21 (1970), 645-647.
[02]P.S. Gupta, A.S. Gupta, Heat and mass transfer on a stretching sheet with suction or blowing, Can. J. Chem. Eng., 55 (1977), 744-746.
[03]P. Carragher, L.J. Crane, Heat transfer on a continuous stretching sheet, ZAMM, 62 (1982) 564- 565.
[04]B.K. Dutta, P. Roy, A.S. Gupta, Temperature field in flow over a stretching sheet with uniform heat flux, Int. Commun. Heat Mass Transfer, 12 (1985), pp. 89-94
[05]C.Y Wang, Liquid film on unsteady stretching surface, Quart. Appl. Math., 48 (1990), 601-610.
[06]R. Cortell, Viscous flow and heat transfer over a nonlinearly stretching sheet, Appl. Math. Comp., 184(2) (2006), 864-873.
[07]H. I. Andersson, J. B. Aarseth, N. Braud, B.S Dandapat, Flow of a power-law fluid film on an unsteady stretching surface, J. Non-Newtonian Fluid Mech., 62 (1996), 1-8.
[08]I. Pop, T.Y. Na, Unsteady flow past a stretching sheet, Mech. Res. Commun., 23(4) (1996), 413-422.
[09]K.N. Lakshmisha, S. Venkateswaran, G. Nath, Three-dimensional unsteady flow with heat and mass transfer over a continuous stretching surface, ASME J. Heat Mass Transfer, 110 (1988) 590-595.
[10]H.I. Andersson, J.B. Aarseth, B.S. Dandapat, Heat transfer in a liquid film on an unsteady stretching surface, Int. J. Heat Mass Transfer, 43 (2000) 69-74.
[11]C.H. Chen, Heat transfer in a power-law fluid film over a unsteady stretching sheet, Heat Mass Transfer, 39 (2003) 791-796.
[12]B.S. Dandapat, B. Santra, H.I. Andersson, Thermocapillarity in a liquid film on an unsteady stretching surface, Int. J. Heat Mass Transfer, 46(2003), 3009-3015.
[13]I-C. Liu, Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field, Int. J. Non-Linear Mech., 40(2005), 465-474.
[14]I.C. Liu, Effect of viscous dissipation on heat transfer of a liquid film over an unsteady stretching sheet, ICAFMIE 06 (2006), Calcutta, India, 28-31, Aug.
[15]C. Wang, Analytic solutions for a liquid film on an unsteady stretching surface, Heat Mass Transfer, 42 (2006) 759-766.
[16]C. Wang, I. Pop, Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method, J. Non- Newtonian Fluid Mech., 138 (2006) 161-172.
[17]B. S. Dandapat, S. Maity, Flow of a thin liquid film on an unsteady stretching sheet, Phys. Fluids, 18 (2006). 102101.
[18]C.H. Chen, Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet, J. Non-Newtonian Fluid Mech., 135 (2006) 128-135.
[19]B.S. Dandapat, B. Santra, K. Vajravelu, The effect of variable properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet, Int. J. Heat Mass Transfer, 50 (2007) 991-996.
[20]A. Raptis, C. Perdikis, Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field, Int. J. Non-Linear Mech., 41 (2007), 527-529.
[21]C.H. Chen, Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface, Phys. Letters, A 370 (2007) 51-57.
[22]N.S. Elgazery, M.A. Hassan, The effects of variable fluid properties and magnetic field on the flow of non-Newtonian fluid film on an unsteady stretching sheet through a porous medium, Comm. Numer. Methods Eng., 24 (2008), 2113–2129.
[23]Z. Abbas, T. Hayat, M. Sajid, S. Asghar, Unsteady flow of a second grade fluid film over an unsteady stretching sheet, Math. Comp. Modelling, 48 (2008) 518-526.
[24]T. Hayat, S. Saif, Z. Abbas, The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet, Phys. Letters, A 372 (2008) 5037-5045.
[25]I.C. Liu, H.I. Andersson, Heat transfer in a liquid film on an unsteady stretching sheet, Int. J. Thermal Sci., 47 (2008) 766-772.
[26]M.A.A. Mahmoud, A.M. Megahed, MHD flow and heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet with variable fluid properties, Can. J. Phys., 87 (2009) 1065-1071.
[27]M.S. Abel, M. Mahesha, J. Tawade, Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in the presence of external magnetic field, Appl. Math. Modelling, 33 (2009) 3430-3441.
[28]M.S. Abel, J. Tawade, M.M. Nandeppanavar, Effect of non-uniform heat source on MHD heat transfer in a liquid film over an unsteady stretching sheet, Int. J. Non-Linear Mech., 44 (2009) 990-998.
[29]N.F.M. Noor, I. Hashim, Thermocapillarity and magnetic field effects in a thin liquid film on an unsteady stretching surface, Int. J. Heat Mass Transfer, 53 (2010) 2044-2051.
[30]I.C. Liu, H.H. Wang, L.P. Soh, Effect of Variable Heat Flux on Heat Transfer in a Liquid Film Due to an Unsteady Stretching Surface, 中華民國第35屆全國力學會議, 台南, 民國100年11月.
[31]A. Aziz, A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Commun. Nonlinear Sci. Numer. Simulat., 14 (2009) 1064-1068.
[32]A. Ishak, Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition, Appl. Math. Comp., 217 (2010) 837-842.
[33]M.M. Nandeppanavar, K. Vajravelu, M.S. Abel, S. Ravi, H. Jyoti, Heat transfer in a liquid film over an unsteady stretching surface, Int. J. Heat Mass Transfer, 55 (2012) 1316-1324.
[34]I.C. Liu, A.M. Megahed, H.H. Wang, Heat transfer in a liquid film due to an unsteady stretching surface with variable heat flux, ASME J. Appl. Mech., (2012), on publish.
[35]I.C. Liu, A.M. Megahed, Numerical study for the flow and heat transfer in a thin liquid film over an unsteady stretching sheet with variable fluid properties in the presence of thermal radiation, J. Mech., 28 (2012) 551-565.
[36]林冠宏, 以數值模擬探討微管流之物理效應, 國立中央大學機械工程研究所碩士論文 (2003).
[37]Frank P. Incropera, David P. Dewitt 原著, Fundamentals of Heat and Mass Transfer, John Wiley & Sons (Asia), Pte Ltd出版社 (2005).
[38]陳世周, 非穩態拉伸下黏性耗散對流體薄層熱傳輸之影響, 國立暨南國際大學土木工程研究所碩士論文 (2006)
[39]蕭開龍, 陳冠邦, 二階非牛頓流體流過擠壓成型薄板的混合對流共軛熱傳分析, 中華民國力學學會第三十屆全國力學會議(The 30th National Conference on Theoretical and Applied Mechanics),議程手冊(論文摘要) , P103, 編號A1-6. (2006)

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