Online proceedings - EDA Publishing Association

7-9 October 2009, Leuven, Belgium
Optimal Channel Width Distribution of Single-Phase
Microchannel Heat Sinks
T. Van Oevelen 1 , F. Rogiers, M. Baelmans
Katholieke Universiteit Leuven, Department of Mechanical Engineering,
Celestijnenlaan 300A, bus 2421
3001 Heverlee, Belgium
Abstract: The channel width distribution of single-phase
microchannel heat sinks is optimized based on 1D-modeling. Two
objectives are regarded, i.e. minimal thermal resistance and
minimal wall temperature gradient. The results differ significantly
from the present status in literature due to a new parameterization.
In addition the effects of axial conduction, fin width and pressure
drop are investigated.
Key words: microchannel, heat sink, optimal width distribution
I. INTRODUCTION
Single-phase microchannel heat sinks are considered as one
of the most promising cooling technologies to cope with the
increasing power densities in electronic chips. Hereby, a
cooling fluid flows through a large set of very small, parallel
channels in a heat sink mounted on the backside of the chip.
This provides a high surface area density and a high
convection heat transfer coefficient. As such, these systems
are capable of cooling large power densities, while keeping
the maximum chip temperature at an acceptable level.
Since the early work of Tuckerman and Pease [12] a lot of
optimization research has been conducted. Most authors used
analytical methods to search for the optimal width and/or
height of the microchannels ([3],[4],[5],[8],[11],[12]). Others
applied numerical optimization methods for this task
([2],[3],[9]), while some search for the optimum by scanning
the parameter field ([6],[7]).
Despite these efforts and the advantages of this cooling
technique, an important drawback of microchannel heat sinks
is still due to the fact that large temperature differences
between inlet and outlet regions may occur. This is caused by
a fluid temperature increase as it passes through the channels.
This phenomenon induces temperature gradients in the heat
sink and substrate, giving rise to thermal stresses.
Furthermore, since the maximum temperature occurs only at
the outlet of the channel, the substrate temperature in the
upstream part of the channel is generally far below this
maximum. As such, striving for higher wall temperatures in
this upstream part close to its maximal value yields a larger
effective temperature difference. This will facilitate heat
transfer. Therefore not exploiting this potential can be
considered as an unnecessary waste of performance.
Bau [1] presented a solution to exploit this potential by
introducing channels with a non-uniform cross-section. This
allows the entire channel width distribution to be optimized,
thereby increasing the number of degrees of freedom. It
appears that a reduction of the thermal resistance by 5%
compared to the uniform channels is possible. Also major
reductions in temperature gradients are shown.
The aim of this paper is to extend the analysis as presented
by Bau by introducing a more accurate parameterization of
the channel width distribution. This leads to a more detailed
description of optimal channel width distributions. As
objective, both minimal wall temperature gradient and
minimal thermal resistance are investigated. For the latter
objective, the effects of axial conduction are shown. Due to
the large number of design parameters, optimization is based
on numerical methods.
In the next section, two thermal-hydraulic models are
described: one with and one without axial conduction.
Subsequently, the objective functions and parameterization
are introduced. In section IV the optimization results are
presented and discussed, together with a sensitivity analysis
of fin width and pressure drop.
II.
MATHEMATICAL MODEL
The physics model that is used in this paper is a onedimensional
model, based upon integration of the flow and
heat transfer equations with respect to the cross-section of the
channels. A drawing of the channels cross-section is shown
in Fig. 1. In a real heat sink, this element can be repeated as
much as needed. The geometric variables of the cross-section
are also depicted in Fig. 1. The length of the channels is
denoted by L * . As a convention, dimensional variables are
marked with a star ‘*’, while dimensionless variables are not.
1 Corresponding author. Tel.: +32 16 322511; fax: +32 16 322985; email address: tijs.vanoevelen@mech.kuleuven.be
This work is sponsored by the IWT, The Institute for the Promotion of Innovation by Science and Technology in Flanders, Belgium, through project SBO 60830,
“HyperCool-IT”.
©EDA Publishing/THERMINIC 2009 157
ISBN: 978-2-35500-010-2