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Research Papers: Natural and Mixed Convection

Two-Dimensional Free Convection Heat Transfer Below a Horizontal Hot Isothermal Flat Strip

[+] Author and Article Information
Milad Samie

Mechanical Engineering Department,
Sharif University of Technology,
Azadi Avenue,
Tehran 11155-9567, Iran
e-mail: samie@mech.sharif.edu

Arash Nouri Gheimassi

Mechanical Engineering Department,
Sharif University of Technology,
Azadi Avenue,
Tehran 11155-9567, Iran
e-mail: arash_nouri@mech.sharif.edu

Alinaghi Salari

Mechanical Engineering Department,
Sharif University of Technology,
Azadi Avenue,
Tehran 11155-9567, Iran
e-mail: a_salari@alum.sharif.edu

Mohammad Behshad Shafii

Associate Professor
Mechanical Engineering Department,
Sharif University of Technology,
Azadi Avenue,
Tehran 11155-9567, Iran
e-mail: behshad@sharif.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 23, 2013; final manuscript received January 30, 2015; published online February 25, 2015. Assoc. Editor: Terry Simon.

J. Heat Transfer 137(5), 052503 (May 01, 2015) (10 pages) Paper No: HT-13-1365; doi: 10.1115/1.4029742 History: Received July 23, 2013; Revised January 30, 2015; Online February 25, 2015

Convection heat transfer below a horizontal, hot, and isothermal strip of infinite length and width of 2L embedded in fluids with different Prandtl number (Pr) and Nusselt number (Nu) is analyzed with the aid of integral method. A new concept is utilized to determine the boundary layer thickness at the strip's edge, which is based on matching the flow rate of the boundary layer below the strip at its edge and the flow rate of the plume, which forms after the heated fluid detaches from the strip's edge. In addition to these novelties, a numerical model is developed to verify the analytical framework, and an excellent agreement is observed between the analytical and numerical models.

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Figures

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Fig. 1

Schematic of the isothermal strip subject to natural convection; the strip has 2L width in x-direction and infinite length in z-direction; (a) ζ < 1 and (b) ζ > 1

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Fig. 2

Ratio of thermal and momentum boundary layer thicknesses

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Fig. 3

(a) A plume created up at the center of the strip from combining two initial plumes and (b) a 2D plume forming after the flow detaches from the strip's edge

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Fig. 8

Dimensionless thermal boundary layer thickness defined as the distance from the plate at which (T-T∞)/(Tw-T∞)=0.03 at the strip's edge versus Prandtl number, ——: analytical model and •: numerical result

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Fig. 4

Numerical solution domain

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Fig. 5

Streamlines of a flow near the downward-facing surface embedded in air, Tw − T = 55.2 °C. (a) Experimental result taken from Aihara et al. [8] and (b) simulation.

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Fig. 6

Velocity profiles for three positions along the strip, (a) Tw − T = 55.2 °C; (b) Tw − T = 104.0 °C; experimental data taken from Aihara et al. [8] for ▪: x/L = 0.6, ▲: x/L = 0.8, and •: x/L = 0.9; ——: numerical result

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Fig. 7

Temperature profiles for two positions along the strip, (a) Tw − T = 52.8 °C; (b) Tw − T = 101.1 °C; experimental data taken from Aihara et al. [8] for ▪: x/L = 0 and •: x/L = 0.95; ——: numerical result

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Fig. 11

Nu/RaL1/5 versus Pr, ——: analytical model from Eq. (23), - - - -: correlation from Schulenberg [23], - ·- ·- ·: correlation from Clifton and Chapman [4], ○: theoretical points from Fuji et al. [22], and •: numerical result. Data shown from Refs. [22] and [23] are for strip with uniform heat flux, whereas Ref. [4] is for isothermal strip.

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Fig. 9

Dimensionless thermal boundary layer thickness for mercury, air, and engine oil; ——: analytical model, •: numerical simulation data for mercury, ▲: numerical simulation data for air, and ▪: numerical result for engine oil

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Fig. 10

Average Nusselt number versus Rayleigh number for: (a) mercury, (b) air, and (c) engine oil; ——: analytical model and •: numerical result

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