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Heat transfer optimization for air-mist cooling between a stack of parallel plates

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Abstract

A theoretical model is developed to predict the upper limit heat transfer between a stack of parallel plates subject to multiphase cooling by air-mist flow. The model predicts the optimal separation distance between the plates based on the development of the boundary layers for small and large separation distances, and for dilute mist conditions. Simulation results show the optimal separation distance to be strongly dependent on the liquid-to-air mass flow rate loading ratio, and reach a limit for a critical loading. For these dilute spray conditions, complete evaporation of the droplets takes place. Simulation results also show the optimal separation distance decreases with the increase in the mist flow rate. The proposed theoretical model shall lead to a better understanding of the design of fins spacing in heat exchangers where multiphase spray cooling is used.

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Abbreviations

A :

Area (m2)

a, b :

Constants

c p :

Specific heat at constant pressure (J/kg.K)

D :

Plate-to-plate distance (m)

H:

Plate height (m)

h :

Enthalpy (J/kg)

h D :

Mass transfer coefficient (m/s)

h fg :

Enthalpy of vaporization (J/kg)

h g :

Gas heat transfer coefficient (W/m2.K)

k :

Conductivity (W/m.K)

L:

Length of the entire package of fins (m)

Le:

Lewis number

ṁ:

Mass flow rate (kg/s)

n :

Number of channels

Nu :

Nusselt number

P :

Pressure, total pressure (N/m2)

Pr :

Prandtl number

\( \dot Q \) :

Total heat transfer from n channels (W)

\( \dot Q \) ch :

Heat transfer rate per channel (W)

\( \dot q \) n :

Heat flux per plate (W/m2)

\( \dot q \) d :

Droplets sensible heating/volume (W/m3)

Re :

Reynolds number

T :

Temperature (K)

u :

x-component for velocity (m/s)

ν :

y-component for velocity (m/s)

Ū :

Average velocity for developed flow (m/s)

W :

Channel width (m)

χ :

Mist quality

x, y :

Rectangular coordinates (m)

ω :

Absolute humidity

ϕ :

Relative humidity

Φ :

Viscous energy source

α :

Liquid-to-air mass flow rate loading ratio

α g :

Gas thermal diffusivity (m2/s)

ρ :

Density (kg/m3)

μ :

Dynamic viscosity (N.s/m2)

τ :

Shear stress (N/m2)

V :

Kinematic viscosity (m2/s)

Δ :

Finite difference

δ :

Flow boundary layer thickness (m)

∂ :

Partial derivative notation

1:

Channel entry side

2:

Channel exit side

a :

Dry air

c :

Conduction/convection at the wall

ch :

Per channel

d :

Droplets

e :

Evaporation

g :

Gas (air and water vapor)

i :

at y equal to 0

l :

Liquid

opt :

Optimal

pl :

Plate

t :

Total

v :

Vapor

w :

Wall

x :

Channel cross-section

∞ :

Free stream

″:

Flux

–:

Average

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Authors and Affiliations

  1. Mechanical Engineering Division, Department of Engineering and Computer Science, West Texas A&M University, Canyon, Texas, 79016, USA

    Roy J. Issa

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  1. Roy J. Issa
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Issa, R.J. Heat transfer optimization for air-mist cooling between a stack of parallel plates. J. Therm. Sci. 19, 253–260 (2010). https://doi.org/10.1007/s11630-010-0253-8

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  • DOI: https://doi.org/10.1007/s11630-010-0253-8

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