Mixed Convection Flow in a Vertical Channel With Boundary Conditions of the Third Kind in the Presence of Heat Source/Sink
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摘要: 在竖向平行板通道中,研究粘性耗散和热源/热汇对充分发展的混合层状对流的影响.平板与外部流体进行了热交换,考虑了两种边界条件:与外部流体的参考温度相同的和不相同的.首先,数值地求解Brinkman数或Grashof数可以忽略的简单情况,然后,运用摄动级数法分析有热源/热汇存在时,浮力和粘性耗散对流动的组合影响,并证明摄动参数不大时是有效的.为了放宽摄动参数的使用条件,运用4阶Runge-Kutta打靶法,求解速度和温度场,对平板处的速度、温度、表面摩擦和Nusselt数进行数值讨论并绘出图形.
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关键词:
- 混合对流 /
- 粘性流体 /
- 摄动法 /
- Runge-Kutta打靶法 /
- 热源/热汇
Abstract: The effects of viscous dissipation and heat source/sink on fully-developed mixed convection for the laminar flow in a parallelplate vertical channel were investigated. The plate exchanged heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid were considered. First, the simple cases of negligible Brinkman number or negligible Grashof number were solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink were analyzed by a perturbation series method valid for small values of perturbation parameter. To relax the conditions on perturbation parameter, the velocity and temperature fields were solved using Runge-Kutta fourth-order method with shooting technique. The velocity, temperature, skin friction and Nusselt numbers at the plates were discussed numerically and presented through graphs.-
Key words:
- mixed convection /
- viscous fluid /
- perturbation method /
- Runge-Kutta shooting method /
- heat source/sink
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[1] Aung W, Worku G. Theory of fully developed, combined convection including flow reversal[J]. ASME Journal of Heat Transfer, 1986, 108(2):485-588. [2] Hamadah T T, Wirtz R A. Analysis of laminar fully developed mixed convection in a vertical channel with opposing buoyancy[J]. ASME Journal of Heat Transfer, 1991, 113(3):507-510. [3] Cheng C H, Kou H S, Huang W H. Flow reversal and heat transfer of fully developed mixed convection in vertical channels[J]. Journal of Thermophysics and Heat Transfer, 1990, 4(3):375-383. [4] Barletta A.Laminar mixed convection with viscous dissipation in a vertical channel[J]. International Journal of Heat and Mass Transfer, 1998, 41(22):3501-3513. [5] Zanchini E. Effect of viscous dissipation on mixed convection in a vertical channel with boundary conditions of the third kind[J]. International Journal of Heat and Mass Transfer, 1998, 41(23): 3949-3959. [6] Sparrow E M. Analysis of laminar forced convection heat transfer in entrance region of flat rectangular ducts [7] [R].Washington:National Advisory committee for Aeronautics, 1995. [8] Stephan K.Warmenbergang a Druckabfall Bei nicht ausgebildeter laminarstromung in Rohren und in ebenen spalten[J]. Chemie-Ing Techn, 1959, 31:773-778. [9] Hwang C L, Fan L T. Finite difference analysis of forced convection heat transfer in entrance region of a flat duct[J]. Appl Sci Res, 1964, 13(1):401-422. [10] Siegal R, Sparrow E M. Simultaneous development of velocity and temperature distributions in a flat duct with uniform wall heating[J]. AIChE Journal, 1959, 5(1): 73-75. [11] Javeri V. Heat transfer in laminar entrance region of a flat channel for the temperature boundary condition of the third kind[J]. Heat and Mass Transfer, 1977, 10(2):137-143. [12] Javeri V. Laminar heat transfer in a rectangular channel for the temperature boundary condition of the third kind[J]. Int J Heat Mass Transfer, 1978, 21(8):1029-1034. [13] Kumari M, Nath G. Mixed convection boundary layer flow over a thin vertical cylinder with localized injection/suction and cooling/heating[J]. International Journal of Heat and Mass Transfer, 2004, 47(5):969-976. [14] Umavathi J C, Mallikarjun Patil B, Pop I. On laminar mixed convection flow in a vertical porous stratum with asymmetric wall heating conditions[J]. IJTP, 2006, 8(2): 127-140. [15] Mahanthi N C, Gaur P. Effect of varying and thermal conductivity on steady free convective flow and heat transfer along an isothermal vertical plate in the presence of heat sink[J]. Journal of Applied Fluid Mechanics, 2009, 2(1):23-28. [16] Umavathi J C, Prathap Kumar J. Mixed convection flow of micropolar fluid in a vertical channel with symmetric and asymmetric wall heating conditions[J]. Int J Appl Mach and Engng, 2011, 16(1):141-159. [17] Arpaci V S, Larsen P S.Convection Heat Transfer[M]. NJ: Pentice Hall, 1984:51-54. [18] Aziz A, Na T Y.Perturbation Methods in Heat Transfer[M]. 1st ed. New York: Hemisphere, 1984.
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