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Local mass transfer measurements in an inclined enclosure at high Rayleigh number

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Abstract

An electrochemical technique is used to study local mass transfer coefficients on surfaces of inclined enclosures over the range 1.1×104 < RaH < 1.4×1010 for a nominal Schmidt number of 2280. Scaling with gcosθ instead of g in the Rayleigh number correlates the data well at low angles of inclination; however, as either the aspect ratio or the angle of inclination increase, the longitudinal density stratification causes the data to deviate from a power law scaling.

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Notes

  1. We assume that for the fluid of interest, density decreases with temperature

Abbreviations

ΔCi::

Concentration difference for species i(mol/l)

Di::

Diffusion coefficient of species i (m2/s)

F::

Faraday’s constant (96,487 C/g mol)

g::

Acceleration due to gravity (9.8 m/s2)

h::

Mass transfer coefficient

H::

Thickness of fluid layer between electrodes (m)

i::

Species of interest (copper ions)

I::

Current (A)

L::

Length of cathode surface (m)

ni::

Valence of transferred ion

Pr::

Prandtl number (ν/α)

RaL::

Mass transfer Rayleigh number based on cathode length [g(ρbulk-ρc) L3/ρν Di]

RaH::

Mass transfer Rayleigh number based on enclosure height [g(ρbulk-ρc)H3/ρν Di]

Rax::

Local mass transfer Rayleigh number [g(ρbulk-ρc) x3/ρν Di]

Sc::

Schmidt number (ν/Di)

Sh::

Sherwood number (hL/Di)

Shx::

Local Sherwood number (hx/Di)

ti::

Transference number

W::

Width of cathode plate (m)

x::

Position from leading edge of cathode surface (m)

δ::

Boundary layer thickness (m)

λr::

Width between adjacent rolls (m)

ν::

Kinematic viscosity (m2/s)

θ::

Angle of enclosure inclination from horizontal (degrees)

θ*::

Transition angle from longitudinal rolls to unicellular flow (degrees)

ρ::

Density (kg/m3)

References

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Authors and Affiliations

  1. Heat Transfer Laboratory, Department of Mechanical Engineering, University of Minnesota, MN, 55455, USA

    R. J. Goldstein & V. Srinivasan

  2. Clean Energy Technology Division, Energy& Resources Laboratories, Industrial Technology Research Institute, Taipei, Taiwan

    H. D. Chiang

  3. Center for Advanced Communication, Department of Mechanical Engineering, Villanova University, Philadelphia, PA, 19085, USA

    A. S. Fleischer

Authors
  1. R. J. Goldstein
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  2. H. D. Chiang
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  3. V. Srinivasan
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  4. A. S. Fleischer
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Correspondence to R. J. Goldstein.

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Goldstein, R.J., Chiang, H.D., Srinivasan, V. et al. Local mass transfer measurements in an inclined enclosure at high Rayleigh number. Heat Mass Transfer 41, 991–998 (2005). https://doi.org/10.1007/s00231-005-0630-0

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  • DOI: https://doi.org/10.1007/s00231-005-0630-0

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