Abstract

This paper presents experimental results on heat transfer and pressure drop for a compact heat sink made of fully triangulated, lightweight (porosity  0.938), aluminum lattice-frame materials (LFMs). Due to the inherent structural anisotropy of the LFMs, two mutually perpendicular orientations were selected for the measurements. Constant heat flux was applied to the heat sink under steady state conditions, and dissipated by forced air convection. The experimental data were compared with those predicted from an analytical model based on fin analogy. The experimental results revealed that pressure drop is strongly dependent upon the orientation of the structure, due mainly to the flow blockage effect. For heat transfer measurements, typical local temperature distributions on the substrate under constant heat flux conditions were captured with infrared camera. The thermal behavior of LFMs was found to follow closely that of cylinder banks, with early transition Reynolds number (based on strut diameter) equal to about 300. The Nusselt number prediction from the fin-analogy correlates well with experimental measurements, except at low Reynolds numbers where a slightly underestimation is observed. Comparisons with empty channels and commonly used heat exchanger media show that the present LFM heat sink can remove heat approximately seven times more efficient than an empty channel and as efficient as a bank of cylinders at the same porosity level. The aluminum LFMs are extremely stiff and strong, making them ideal candidates for multifunctional structures requiring both heat dissipation and mechanical load carrying capabilities.

Nomenclature

A

channel cross-section area (=H×W)

C_p

specific heat [J/kg K]

d

LFM bar diameter [m]

D_h

hydraulic diameter of channel [m]

f

friction factor

h

mean heat transfer coefficient (=q/(T_w−T_in))

h_∞

local heat transfer coefficient around LFM struts

H, L, W

channel height, length and width [m]

I

heat sink efficiency index (=j/f)

j

j-Colburn factor (=StPr^2/3)

k

thermal conductivity [W/mK]

l

individual strut length [m]

n

cell number along flow direction

N

total number of cells in flow direction

Nu_Dh

Nusselt number based on hydraulic diameter (=hD_h/k_f)

Nu_d

averaged Nusselt number based on bar diameter

ΔP

static pressure drop [Pa]

P

perimeter of wetted cross-section area [m]

Pr

Prandtl number

Q

heat released by a heating element [W]

q

heat flux [W/m²]

Re_d

Reynolds number based on LFM strut diameter

Re_Dh

Reynolds number based on channel hydraulic diameter

S

surface area of wetted cross-section [m²]

SR

strut ratio (=l/d)

S_x, S_y

longitudinal and transverse unit cell pitches

St

Stanton number (=Nu_Dh/(Re_DhPr))

T_in

coolant inlet temperature [K]

T_w(x)

local substrate temperature

U_m

coolant inlet mean velocity [m/s]

x, y, z

global coordinate system

porosity

ρ

density [kg/m³]

ρ_rel

relative density

η

local coordinate along cell strut

θ

non-dimensional temperature

f

coolant fluid

h

hydraulic parameter

in

inlet of heat sink

m

arithmetic mean

out

outlet of heat sink

s

LFM solid cell

SA

surface area

w

substrate wall

Article Outline

Nomenclature

1. Introduction

2. Specifications of LFM heat sink

3. Analysis

3.1. Mathematical formulations

3.2. Local heat transfer coefficient

4. Experimental details

4.1. Experimental apparatus

4.2. Experimental and data acquisition procedures

4.3. Measurement uncertainties

5. Results and discussion

5.1. Pressure drop

5.2. Heat transfer characteristics

5.3. Fin-analogy estimation

5.4. Thermal efficiency index

6. Conclusion

Acknowledgements

References