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Theoretical–experimental study of commercial heat sinks for personal computers

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

An experimental apparatus was set up to analyze heat sinks commercialized in the Brazilian market for use in personal computers. Among the identified geometries, all in the configuration of plate-fin heat sink, five stood out for being the most used. The experiment was performed in plate-fin heat sinks subjected to horizontal parallel air flow by changing the velocity of the wind tunnel in the range of 0 to 8 m/s. A constant power at 1,000 W was provided to simulate the heat generated by electronic components. During the heat exchange by natural convection, the heat flux supplied to a heat sink base was in the range between 31,000 W/m2 and 43,100 W/m2, while for forced convection the values varied between 23,300 W/m2 and 73,800 W/m2. For natural convection, a correlation was suggested for the average Nusselt number, valid in the range of 3 < Ra < 35 with RMS of 10.1%. For forced convection, two correlations were developed, one without the use of correction, which presented an RMS of 23.4%, and the other with a correction factor with RMS of 7.6%; both valid in the range of 2,000 < Pe < 14,000. The uncertainties related to the instruments used were calculated with the highest value found being 1%, while the uncertainty related to the variables was 22.9%. A theoretical model for forced convection was developed using mass and energy conservation equations. The pressure loss and the deviation factor were determined considering the following assumptions: steady-state and fully developed flow, turbulent flow in the bypass (flow in the duct outside the heat sink channels), flow in the heat sink channels as laminar, incompressible, viscous, and internal, as in ducts, and constant fluid properties. The results showed a higher growth rate of the total pressure drop for heat sinks with an LZ/S ratio between 9.9 and 18.1 and with uniform spacing between the fins. For Reynolds number values less than 2,000, forced convection is no longer dominant, and the development of a thermal design in this region must focus on a mixed or natural convection.

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Abbreviations

a:

Constants for the correction factor, dimensionless

A:

Area, m2

b:

Constants for the correction factor, dimensionless

BF:

Bypass factor, dimensionless

c:

Constants for the correction factor, dimensionless

C:

Constant, dimensionless

D:

Diameter, m

f:

Friction coefficient, dimensionless

F:

Correction factor, dimensionless

g:

Gravity acceleration, m/s2

h:

Heat transfer coefficient, W/m2K

H:

Tunnel height, m

K:

Loss coefficient, dimensionless

L:

Length, m

N:

Number of fins

Nu:

Nusselt number, dimensionless

Q:

Volumetric flow rate, m3/s

p:

Perimeter, m

P:

Pressure, Pa

Pe:

Peclet number, dimensionless

Pr:

Prandtl number, dimensionless

q" :

Heat flux, W/m2

R:

Dependent variables

Ra:

Rayleigh number, dimensionless

Re:

Reynolds number, dimensionless

RMS:

Root mean square, [%]

S:

Fin spacing, m

T:

Temperature, ºC

t:

Thickness, m

u:

Average uncertainty, %

V:

Velocity, m/s

X:

Spatial coordinates, m

x1, x2,…xn :

Independent variables

W:

Tunnel width, m

Y:

Spatial coordinates, m

Z:

Spatial coordinates, m

\(\alpha\) :

Thermal diffusivity—air, m2/s

\(\beta\) :

Expansion coefficient—air, K−1

\(\kappa\) :

Thermal conductivity—fluid or solid, W/mºC

\(\lambda\) :

Dependent variable for the correction factor, dimensionless

\(\mu\) :

Dynamic viscosity, Ns/m2

\(\nu\) :

Kinematic viscosity—air, m2/s

\(\rho\) :

Density, kg/m3

\(\Delta\) :

Difference

AN:

Anemometer

C:

Clearance

CP:

Copper

CT:

Contraction

D:

Bypass

e:

Flow development region

EP:

Expansion

EXP:

Experimental

f:

Fluid

FC:

Forced convection

H:

Hydraulic

HE:

Heating element

HS:

Heat sink

NC:

Natural convection

R:

Dependent variables

S:

Surface

T:

Total

TS:

Test section

x1, x2,…xn :

Independent variables

X, Y, Z:

Direction

1 to 5:

Heat sink model

m n:

Constant

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Acknowledgements

The authors would like to acknowledge CNPq (call MCT/CNPq 014/2010) and FAPERJ (call 19/2008) for financial support during this work. They would also acknowledge Mr. Daniel Chaves de Oliveira, an undergraduate in Mechanical Engineering at FAT/UERJ, for his help in performing the experimental work.

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Authors and Affiliations

  1. Departamento de Mecânica e Energia – DME, Centro de Fontes Renováveis de Energia – CFRE, Faculdade de Tecnologia – FAT, Universidade do Estado do Rio de Janeiro – UERJ, Rodovia Presidente Dutra, km 298, Pólo Industrial, CEP 27.537-000, Resende, RJ, Brazil

    Newton G. C. Leite, Luiz Carlos B. S. Reis & Humberto Araujo Machado

  2. Instituto de Aeronáutica e Espaço – IAE, Departamento de Ciência e Tecnologia Aeroespacial – DCTA, Pç Mal Eduardo Gomes, 50, Vila das Acácias, CEP 12.228-904, São José dos Campos, SP, Brazil

    Humberto Araujo Machado

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  1. Newton G. C. Leite
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  2. Luiz Carlos B. S. Reis
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Correspondence to Newton G. C. Leite.

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Leite, N.G.C., Reis, L.C.B.S. & Machado, H.A. Theoretical–experimental study of commercial heat sinks for personal computers. J Braz. Soc. Mech. Sci. Eng. 43, 463 (2021). https://doi.org/10.1007/s40430-021-03181-4

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