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NUMERIC SOLVER FOR MULTIMODE HEAT TRANSFER
IN A HIGH TEMPERATURE HEAT SINK
Ben Jones
Purdue University
Mark Kimber
Purdue University
ABSTRACT
A finite volume based numerical scheme is developed to
estimate the temperature distribution within a high temperature
rectangular fin heat sink.
A coupled conduction, convection,
and radiation problem is solved with conduction occurring
through the substrate and radiation and convection boundary
conditions on the surfaces of the fins.
Those boundaries
involving both radiation and convection to the ambient are
accounted for by linearizing radiation terms and updating the
temperaturebased radiosities at each iteration.
The convection
coefficient and heat sink thermal conductivity are assumed to
be uniform and independent of temperature.
A geometric
multigrid method is implemented to drastically decrease
computation time.
A number of test cases are analyzed for a
heat sink with overall dimensions of 50 mm x 50 mm x 5 mm
while varying the fin thickness and number of channels.
Using the performance metric of thermal resistance based on
differences
between
base
and
ambient
temperatures,
the
optimum design composes of 6 channels with 1 mm thick fins
corresponding to a thermal resistance of 13.6 K/W.
INTRODUCTION
Heat sinks are commonly used in many industries to
increase the rate of heat removal over which forced or free
convection can occur.
They can most often be found in various
electronic
devices
such
as
microprocessors
and
high
performance video cards.
In many cases, heat sinks are coated
with a high emissivity paint to further increase the heat removal
rate.
Radiation then becomes important and determining the
temperature distribution within the heat sink is nontrivial and
must account for radiosities of all exposed surfaces and view
factors from one fin to the next.
The current work provides a
numerical approach to solving this problem.
For reference, the
code in its entirety is included in Appendix A and is based on a
finite volume approach.
In the remainder of this paper, the
problem is first described in more detail including treatment of
all boundary conditions.
Discretized equations representing the
heat transfer throughout the entire domain are presented in
forms most easily implemented into line by line tridiagonal
matrix (LBLTDMA) solvers.
The exchange of radiation is then
discussed with methods for calculating view factors and
radiosities of all surfaces exposed to ambient conditions.
The
overall solution procedure is given as well as a description of
the multigrid scheme implemented to accelerate convergence.
This is followed by a code validation comparing the present
work with similar results obtain using Fluent.
Finally results
from a number of test cases are given showing the ability to
optimize the geometric dimensions of the heat sink.
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 Fall '10
 NA
 Heat, Heat Transfer, Thermal conductivity, heat sink

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