# Simplified Mathematical Model of a novel ‘Closed Loop Two-Phase Wicked Thermosyphon

### Significance Statement

Recent advances in semiconductor technology as well as fabrication methods have improved the performance of various electronics such as graphics processors and servers in data centers. However, this improvement demands improved thermal management of these electronics in a bid to realize the designed longevity and desired performance. Above all, ‘small’ is considered better in the world of electronics with regards to device size. However, this comes with a strain on thermal management of electronics.

Passive thermal management devices which utilize two-phase cooling including thermosyphons and heat pipes have become common in the last few decades. This stems from the fact that they use the high latent heats of vaporization as well as condensation of the circulating fluid to eliminate thermal power from the source to the heat sink. They also require no extra pumping for the working fluid.

Karthik Remella and Frank M. Gerner from the Microscale Heat Transfer Laboratory at the University of Cincinnati studied and analyzed a closed loop two-phase wicked thermosyphon, which was designed and fabricated by BritePointe Inc. of California for thermal management of light emitting diodes. The device was composed of a central evaporator and a heat exchanger coil linked by transport lines. This study proposed a model that simplified the existing evaporator model by mathematically decoupling the evaporator from the coil. The aim of the model was to get temperature estimates that were not based on the evaporator package geometry, and this allowed for investigating a wide range of operating powers. Their research work is published in the International Journal of Thermal Sciences.

The authors adopted the simplified mathematical model which differs from their earlier thermal resistance model in the sense that the simplified model utilizes the thermal solution from the condenser and the sub-cooler models and mass flow rate of the working fluid can be obtained from a pressure balance relationship. According to the authors, the simplified mathematical model disassociates the thermal performance estimates from the thermal resistances of the evaporator and disconnects the device performance from the evaporator package. The model assumes that any package ‘sized’ for a particular input power is integrated with the proposed coil design. For a selected thermal power, the proposed model assumes a ‘thermally sized’ loop is normally integrated with the right evaporator package.

Remella and Gerner obtained all outcomes from the coil side of the gadget. They assumed that the solutions could be obtained by integrating the same coil with varying geometries of the evaporator package. The simplified model does not estimate the board temperature of the light emitting diode. However, the model was important in predicting other performance parameters such as condenser saturation temperature, two-phase mixture quality, and sub-cooler temperature.

The simplified model results were more accurate despite the fact that the simplified mathematical and thermal resistance models predictions matched. The hydrostatic head provided the driving force for the circulating fluid. For a fixed fill volume, the authors observed that the convective resistance on the air side was uniform due to a constant condenser length as well as heat transfer coefficient. This caused a linear rise in the saturation as well as sub-cooler temperatures of the coil with an increase in the thermal power input. The rate of saturation temperature rise was higher than that of sub-cooler temperature.

When the thermal power was increased, power responsible for phase change was subsequently increased. Due to the constant mass flow rate of the working fluid, the two-phase quality indicated a linear rise with more thermal power.

Dr. Frank M. Gerner is the Senior Associate Dean for the College of Engineering and Applied Science at the University of Cincinnati.  In this capacity, he is responsible for graduate studies, personnel and college computing. He is also a Professor of Mechanical Engineering and has worked in the areas of MEMS and Microscale Heat Transfer.  He has also worked in the areas of condensation heat transfer, heat pipes, micro heat pipes, loop heat pipes and microelectronics cooling for the past quarter century.

Dr. Gerner has received support from NASA, NSF, AFOSR, DARPA, GE Global Research, and other industries to support these activities, and has published over 150 technical articles in these areas, including co-editing a research monograph on Microscale Energy Transport.  He has advised numerous MS and PhD students, was a Visiting Professor of Heat Transfer on the Microscale at the University of Tokyo and is co-inventor on four U.S. patents on loop heat pipes.