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Research Papers: Natural and Mixed Convection

Experimental Validation of Analytical Solutions for Vertical Flat Plate of Finite Thickness Under Natural-Convection Cooling

[+] Author and Article Information

Department of Mechanical Engineering,  The University of Auckland, Auckland, New Zealand 1142v.yadav@auckland.ac.nz

Keshav Kant1

Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208 016, Indiakeshav@iitk.ac.in

1

Corresponding author.

J. Heat Transfer 130(3), 032503 (Mar 06, 2008) (11 pages) doi:10.1115/1.2804938 History: Received September 08, 2006; Revised August 19, 2007; Published March 06, 2008

Abstract

The analytical solution for a vertical heated plate subjected to conjugate heat transfer due to natural convection at the surface and conduction below is presented. The heated surface is split into two regions; the uniform heat flux region toward upstream and remaining fraction as the uniform wall temperature region. The fractional areas under the two regions are considered variable. Adopting thermally thin wall regime approximation, the possible solutions were investigated and found to satisfactorily deal with longitudinal conduction and temperature variation in the transverse direction. A test setup was developed and the experiments were conducted to obtain relevant data for comparison with the analytical solutions. The ranges for Rayleigh number and heat conduction parameter $(α)$ during various test conditions were $2×108–6×108$, and 0.001–1, respectively. The limiting solutions for stipulated conditions are analyzed and compared with experimental data. Reasonable agreement is observed between the experimental and analytical results.

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Figures

Figure 3

Comparison of normalized first order solution for nondimensional temperature, θan, as a function of r for different α and γ

Figure 8

Dependence of dimensionless surface temperature at the plate surface upon the nondimensional plate height for r=0.4 and (a) γ=0.2, (b) γ=0.5, and (c) γ=1.0

Figure 9

Dependence of normalized heat generation under the plate surface upon the nondimensional plate height for r=0.6 and (a) γ=0.2, (b) γ=0.5, and (c) γ=1.0

Figure 10

Dependence of dimensionless surface temperature at the plate surface upon the nondimensional plate height for r=0.6 and (a) γ=0.2, (b) γ=0.5, and (c) γ=1.0

Figure 11

Dependence of dimensionless surface temperature at the plate surface upon the nondimensional plate height for r=0.8 and (a) γ=0.2, (b) γ=0.5, and (c) γ=1.0

Figure 7

Dependence of normalized heat generation under the plate surface upon the nondimensional plate height for r=0.4 and γ=0.5

Figure 6

Dependence of normalized heat generation under the plate surface upon the nondimensional plate height for r=0.2 and (a) γ=0.2 and (b) γ=1.0

Figure 5

Variation of normalized heat flux at the plate surface with increase in nondimension distance over the surface from leading edge

Figure 4

Schematics for (a) experimental setup and (b) heated plate

Figure 2

(a) Comparison of Φfn along the plate height for different values of UWT/UHF fraction r and dimensionless mean temperature γ. (b) Comparison of leading order solution for average nondimensional temperature at the plate surface as a function of r and α with γ=1.0.

Figure 12

Comparison of current work with data from the literature

Figure 1

Schematics of heated plate in vertical channel

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