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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 2
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Original Articles

Thin-film evaporation on microgrooved heatsinks

, &
Pages 111-127 | Received 30 May 2016, Accepted 12 Oct 2016, Published online: 05 Jan 2017
 

ABSTRACT

A model was developed to simulate the performance of a microgrooved surface undergoing organized, steady-state, thin-film evaporation subject to a superheat at its base. The model is intended to serve as a comprehensive design tool that can be used to optimize the design of a microgrooved surface for a given application. A parametric study was conducted to evaluate the effects of base superheat, channel width, fin-channel width ratio, and channel aspect ratio on the base heat transfer coefficient. Multidimensional optimization was then performed, and it revealed a geometry capable of dissipating 320 W/cm2 with 10 K base superheat using octane.

Nomenclature

A=

disjoining pressure coefficient, J

AR=

aspect ratio (Lf/wch), -

hbase=

average base heat transfer coefficient, W/m2-K

hfg=

latent heat of vaporization, kJ/kg

kl=

thermal conductivity of liquid, W/m-K

ks=

thermal conductivity of solid, W/m-K

Lb=

length of substrate base, µm

Lf=

length of fin, µm

m=

interfacial evaporative mass flux, kg/m2-s

=

molecular mass of fluid, kg/mol

Nu=

Nusselt number, -

Pc, Pd, Pl, Pv=

capillary, disjoining, liquid, and vapor pressures, respectively, Pa

Psat=

equivalent saturation pressure at T = Tlv, Pa

Pv, eq=

equivalent vapor pressure at T = Tlv, Pa

q=

heat flux in thin film, W/m2

=

average Base Heat Flux, W/m2

Q=

total cumulative heat, W/m

R=

radius of curvature, m

=

universal gas constant, J/mol-K

R*=

radius of curvature of intrinsic meniscus, m

Tb, Tlv, Tv, Tw=

base, liquid–vapor, vapor, and wall temperatures, respectively, K

wch=

width of channel, µm

wf=

thickness of fin, µm

WR=

width ratio (wf/wch), -

z=

length along thin-film coordinate direction, µm

Γ=

liquid mass flow rate, kg/s

δ=

liquid film thickness; coordinate direction, m

ΔT=

base superheat (Tbase − Tv), K

ϵ=

initial adsorbed thin-film offset, -

υl=

kinematic viscosity of liquid, m2/s

ρl=

liquid density, kg/m3

σ=

liquid surface tension, N/m

=

evaporation coefficient, -

φ=

apparent contact angle, rad

ω=

angle at end of intrinsic meniscus, rad

Nomenclature

A=

disjoining pressure coefficient, J

AR=

aspect ratio (Lf/wch), -

hbase=

average base heat transfer coefficient, W/m2-K

hfg=

latent heat of vaporization, kJ/kg

kl=

thermal conductivity of liquid, W/m-K

ks=

thermal conductivity of solid, W/m-K

Lb=

length of substrate base, µm

Lf=

length of fin, µm

m=

interfacial evaporative mass flux, kg/m2-s

=

molecular mass of fluid, kg/mol

Nu=

Nusselt number, -

Pc, Pd, Pl, Pv=

capillary, disjoining, liquid, and vapor pressures, respectively, Pa

Psat=

equivalent saturation pressure at T = Tlv, Pa

Pv, eq=

equivalent vapor pressure at T = Tlv, Pa

q=

heat flux in thin film, W/m2

=

average Base Heat Flux, W/m2

Q=

total cumulative heat, W/m

R=

radius of curvature, m

=

universal gas constant, J/mol-K

R*=

radius of curvature of intrinsic meniscus, m

Tb, Tlv, Tv, Tw=

base, liquid–vapor, vapor, and wall temperatures, respectively, K

wch=

width of channel, µm

wf=

thickness of fin, µm

WR=

width ratio (wf/wch), -

z=

length along thin-film coordinate direction, µm

Γ=

liquid mass flow rate, kg/s

δ=

liquid film thickness; coordinate direction, m

ΔT=

base superheat (Tbase − Tv), K

ϵ=

initial adsorbed thin-film offset, -

υl=

kinematic viscosity of liquid, m2/s

ρl=

liquid density, kg/m3

σ=

liquid surface tension, N/m

=

evaporation coefficient, -

φ=

apparent contact angle, rad

ω=

angle at end of intrinsic meniscus, rad

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