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Natural convection experiments on the upward and downward faces of inclined plates using an electroplating system

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Abstract

Natural convection experiments were carried out on inclined plates. A copper sulfate electroplating system was adopted to simulate heat transfer based on analogy. The lengths of the copper plates were 0.1 and 0.35 m, corresponding to Grashof numbers of 8.06 × 107 and 3.45 × 109. The inclination of the plates varied from upward-facing (UF) horizontal to downward-facing (DF) horizontal. Test results for the DF plate agreed well with Rich’s theory, that the Nusselt number can be calculated by replacing g with g cosθ in the heat transfer correlation for a vertical plate and those for the UF plate reveal that the development of the boundary layer and the flow separation occurs repeatedly for the whole plate length. The copper-plating patterns for the UF plates visualized the location of flow separation. The empirical correlation predicting the critical distance and the heat transfer correlations was proposed.

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Abbreviations

C b :

Concentration in the bulk (mol/m3)

D m :

Diffusivity (m2/s)

F :

Faraday constant, 96,485 (C/mol)

Gr L :

Grashof number (gβΔTL 3/ν 2)

Gr C :

Critical Grashof number (gβΔTL 3 c /ν 2)

Gr * :

Modified Grashof number (gβq w L 4/kν 2)

g :

Gravitational acceleration (m/s2)

h h :

Heat transfer coefficient (W/m2 K)

h m :

Mass transfer coefficient (m/s)

I :

Electric current (A)

I lim :

Limiting current density (A/m2)

k :

Thermal conductivity (W/m K)

L :

Length of cathode (m)

L C :

Critical length (m)

L R :

Remaining length (m)

N :

Number of separation (m)

Nu L :

Nusselt number (h h L/k)

n :

Number of electrons in charge transfer reaction

Pr :

Prandtl number (ν/α)

Ra L :

Rayleigh number (gβΔTL 3/αν)

Ra * :

Modified Rayleigh number (gβq w L 4/kαν)

Sc :

Schmidt number (ν/D m )

Sh L :

Sherwood number (h m L/D m )

t n :

Transference number

U x :

Uncertainty of x

α :

Thermal diffusivity (m2/s)

β :

Volume expansion coefficient (1/K)

γ :

Dispersion coefficient

θ :

Inclined angle measured from the vertical (°)

μ :

Viscosity (kg/m s)

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

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Acknowledgments

This study was sponsored by the Ministry of Science, ICT & Future Planning (MSIP) and was supported by Nuclear Research & Development program grant funded by the National Research Foundation (NRF) (Grant Code: 2013M2A8A2025997).

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Authors and Affiliations

  1. Atomic Creative Technology Co. Ltd., #705 Gwangpyenong-dong, Yuseong-gu, Daejeon, 305-509, Korea

    Chul-Kyu Lim

  2. Department of Nuclear Engineering, Kyung Hee University, 1732 Deokyoung-daero, Giheung-gu, Yongin-si, Gyeonggi-do, 446-701, Korea

    Bum-Jin Chung

Authors
  1. Chul-Kyu Lim
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Correspondence to Bum-Jin Chung.

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Lim, CK., Chung, BJ. Natural convection experiments on the upward and downward faces of inclined plates using an electroplating system. Heat Mass Transfer 51, 713–722 (2015). https://doi.org/10.1007/s00231-014-1450-x

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