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Numerical Results

Numerical Analysis

Extensive 2D simulations have been performed to fully characterize the working conditions of the cooler.  Numerical simulations were done using the finite element package contained in the software package FIDAP by FLUENT Inc.  The numerical study can be broken into two parts: (1), the heat transfer and (2) the stresses induced due to mismatches between the coefficient of thermal expansion.

Heat Transfer Analysis

The 2D mesh was generated using GAMBIT by FLUENT.  The mesh was optimized to least number of nodes while preserving the accuracy of the result, at a specified convergence.  The optimized mesh was fed into FIDAP, along with the appropriate boundary conditions and material properties.

Boundary Conditions

An adiabatic boundary condition was applied to all surfaces in contact with the air.  Although natural convection occurs, the heat loss to the surrounding air is negligible.  Along the bottom surface of the copper, two different boundary conditions were applied, depending on the analysis being done for the particular simulation run.  One boundary condition applied was a  large convective condition.  The other applied on a different run was a constant temperature, the value obtained from an experimental run.

Results

Design modifications have been done using the numerical model such than the temperature along the bottom surface of the copper are uniform to within 1.5 Celsius.  Inclusion of the diamond in the design has shown to increase efficiency by about 35% over a conventional, copper only heat sink.

Thermal Stress Analysis

Due to mismatches within the Coefficient of Thermal Expansion, stresses are produced within the cooling package and in the diode during operation.  FIDAP uses the results from the temperature calculations it makes, and uses them to calculate the amount of expansion or contraction which will occur in each material.  Because the materials are bonded together, and thus cannot move freely, stresses result at the interfaces.  Thus, the thermal stress is a function of the CTE mismatch at the interface and deviation of temperature from the state of zero stress.

Results

The highest predicted stresses will occur in areas of red.  The data indicates failure within the silicon or diamond, more likely the silicon due to the lower strength of this material.  Von Mises stress criterion are calculated within FIDAP and presented below: