Application of the Kirchhoff Transform to Thermal Spreading Problems With Convection Boundary Conditions | IEEE Journals & Magazine | IEEE Xplore

Application of the Kirchhoff Transform to Thermal Spreading Problems With Convection Boundary Conditions


Abstract:

Thermal management and thermal analysis of microelectronic devices and packages are critical in ensuring the performance, reliability, and lifetime of today's electronic ...Show More

Abstract:

Thermal management and thermal analysis of microelectronic devices and packages are critical in ensuring the performance, reliability, and lifetime of today's electronic systems. When the thermal conductivity of a semiconductor or packaging material depends strongly on temperature, the use of a constant thermal conductivity value may significantly underestimate the temperature rise and thermal resistance. The Kirchhoff transform provides a convenient way of linearizing the heat conduction equation to use computationally efficient analytical solutions to calculate the device or package temperature. In the past, the application of the Kirchhoff transform has been restricted to temperature and heat flux boundary conditions in thermal spreading problems. In this paper, we developed an approximate solution for the application of the Kirchhoff transform to thermal spreading problems with convection in the sink plane and show the technique to be accurate to within 1% for relevant problems in device-level thermal analysis. The proposed technique is combined with a recently developed analytical solution for temperature rise in complex, multilayered structures in which a finite heat transfer coefficient in the sink plane needs to be considered. These analytical expressions and the Kirchhoff transform are valuable tools for accurately predicting the temperature in high-power, wide bandgap electronics, such as gallium nitride power amplifiers.
Page(s): 408 - 420
Date of Publication: 12 December 2013

ISSN Information:

Author image of Kevin R. Bagnall
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
Kevin R. Bagnall (s'12) received the B.S. degree in mechanical engineering from the University of Oklahoma, Norman, OK, USA, in 2009, and the M.S. degree in mechanical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, MA, USA, in 2013, where he is currently pursuing the Ph.D. degree in mechanical engineering.
He was an Intern with the Sustainability Technology Group, ConocoPhillips, Inc., Bartles...Show More
Kevin R. Bagnall (s'12) received the B.S. degree in mechanical engineering from the University of Oklahoma, Norman, OK, USA, in 2009, and the M.S. degree in mechanical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, MA, USA, in 2013, where he is currently pursuing the Ph.D. degree in mechanical engineering.
He was an Intern with the Sustainability Technology Group, ConocoPhillips, Inc., Bartles...View more
Author image of Yuri S. Muzychka
Memorial University of Newfoundland, Faculty of Engineering and Applied Sciences, St. John's, NL, Canada
Yuri S. Muzychka received the B.Eng. degree in mechanical engineering from the Memorial University of Newfoundland, St. John's, NL, Canada, in 1993, and the M.A.Sc. and Ph.D. degrees in mechanical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1995 and 1999, respectively.
He is a Professor with the Faculty of Engineering and Applied Science, Memorial University of Newfoundland. He joined Memorial Uni...Show More
Yuri S. Muzychka received the B.Eng. degree in mechanical engineering from the Memorial University of Newfoundland, St. John's, NL, Canada, in 1993, and the M.A.Sc. and Ph.D. degrees in mechanical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1995 and 1999, respectively.
He is a Professor with the Faculty of Engineering and Applied Science, Memorial University of Newfoundland. He joined Memorial Uni...View more
Author image of Evelyn N. Wang
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
Evelyn N. Wang received the B.S. degree in mechanical engineering from the Massachusetts Institute of Technology, Cambridge, MA, USA, in 2000, and the M.S. and Ph.D. degrees in mechanical engineering from Stanford University, Stanford, CA, USA, in 2001 and 2006, respectively.
She was a Post-Doctoral Researcher with Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ, USA, from 2006 to 2007. She is currently an Associate Pro...Show More
Evelyn N. Wang received the B.S. degree in mechanical engineering from the Massachusetts Institute of Technology, Cambridge, MA, USA, in 2000, and the M.S. and Ph.D. degrees in mechanical engineering from Stanford University, Stanford, CA, USA, in 2001 and 2006, respectively.
She was a Post-Doctoral Researcher with Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ, USA, from 2006 to 2007. She is currently an Associate Pro...View more

Author image of Kevin R. Bagnall
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
Kevin R. Bagnall (s'12) received the B.S. degree in mechanical engineering from the University of Oklahoma, Norman, OK, USA, in 2009, and the M.S. degree in mechanical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, MA, USA, in 2013, where he is currently pursuing the Ph.D. degree in mechanical engineering.
He was an Intern with the Sustainability Technology Group, ConocoPhillips, Inc., Bartlesville, OK, USA, in 2009. Since 2011, he has been a Research Assistant with the Device Research Laboratory, Department of Mechanical Engineering, MIT. His current research interests include micro/nanoscale thermal transport, thermal issues in electronics, solid-state device physics, and thermal metrology techniques.
Mr. Bagnall is a Student Member of ASME. He received the National Defense Science and Engineering Graduate Fellowship and the MIT Rohsenow Mechanical Engineering Graduate Fellowship.
Kevin R. Bagnall (s'12) received the B.S. degree in mechanical engineering from the University of Oklahoma, Norman, OK, USA, in 2009, and the M.S. degree in mechanical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, MA, USA, in 2013, where he is currently pursuing the Ph.D. degree in mechanical engineering.
He was an Intern with the Sustainability Technology Group, ConocoPhillips, Inc., Bartlesville, OK, USA, in 2009. Since 2011, he has been a Research Assistant with the Device Research Laboratory, Department of Mechanical Engineering, MIT. His current research interests include micro/nanoscale thermal transport, thermal issues in electronics, solid-state device physics, and thermal metrology techniques.
Mr. Bagnall is a Student Member of ASME. He received the National Defense Science and Engineering Graduate Fellowship and the MIT Rohsenow Mechanical Engineering Graduate Fellowship.View more
Author image of Yuri S. Muzychka
Memorial University of Newfoundland, Faculty of Engineering and Applied Sciences, St. John's, NL, Canada
Yuri S. Muzychka received the B.Eng. degree in mechanical engineering from the Memorial University of Newfoundland, St. John's, NL, Canada, in 1993, and the M.A.Sc. and Ph.D. degrees in mechanical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1995 and 1999, respectively.
He is a Professor with the Faculty of Engineering and Applied Science, Memorial University of Newfoundland. He joined Memorial University in 2000. His research is focused on the development of robust models for characterizing transport phenomena using fundamental theory. These models are validated using experimental and/or numerical results. He also undertakes fundamental research in conduction and convection heat transfer, thermal management of microelectronics, contact heat transfer, and thermal design/optimization of energy systems. He has published over 60 papers in international refereed journals and over 60 papers in international conference proceedings. His current research interests include complex fluid dynamics and heat transfer problems in internal flows, transport in porous media, compact heat exchangers, two phase flows, microchannel flows, noncontinuum flows, and non-Newtonian flows.
Prof. Muzychka received the Petro-Canada Canada Young Innovator Award in 2004.
Yuri S. Muzychka received the B.Eng. degree in mechanical engineering from the Memorial University of Newfoundland, St. John's, NL, Canada, in 1993, and the M.A.Sc. and Ph.D. degrees in mechanical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1995 and 1999, respectively.
He is a Professor with the Faculty of Engineering and Applied Science, Memorial University of Newfoundland. He joined Memorial University in 2000. His research is focused on the development of robust models for characterizing transport phenomena using fundamental theory. These models are validated using experimental and/or numerical results. He also undertakes fundamental research in conduction and convection heat transfer, thermal management of microelectronics, contact heat transfer, and thermal design/optimization of energy systems. He has published over 60 papers in international refereed journals and over 60 papers in international conference proceedings. His current research interests include complex fluid dynamics and heat transfer problems in internal flows, transport in porous media, compact heat exchangers, two phase flows, microchannel flows, noncontinuum flows, and non-Newtonian flows.
Prof. Muzychka received the Petro-Canada Canada Young Innovator Award in 2004.View more
Author image of Evelyn N. Wang
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
Evelyn N. Wang received the B.S. degree in mechanical engineering from the Massachusetts Institute of Technology, Cambridge, MA, USA, in 2000, and the M.S. and Ph.D. degrees in mechanical engineering from Stanford University, Stanford, CA, USA, in 2001 and 2006, respectively.
She was a Post-Doctoral Researcher with Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ, USA, from 2006 to 2007. She is currently an Associate Professor with the Mechanical Engineering Department, Massachusetts Institute of Technology. Her current research interests include fundamental studies of micro and nanoscale heat and mass transport and the development of efficient thermal management, water desalination, and solar thermal energy systems.
Prof. Wang received the 2008 DARPA Young Faculty Award, the 2011 Air Force Office of Scientific Research Young Investigator Award, the 2012 Office of Naval Research Young Investigator Award, and the 2012 ASME Bergles-Rohsenow Young Investigator Award in Heat Transfer.
Evelyn N. Wang received the B.S. degree in mechanical engineering from the Massachusetts Institute of Technology, Cambridge, MA, USA, in 2000, and the M.S. and Ph.D. degrees in mechanical engineering from Stanford University, Stanford, CA, USA, in 2001 and 2006, respectively.
She was a Post-Doctoral Researcher with Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ, USA, from 2006 to 2007. She is currently an Associate Professor with the Mechanical Engineering Department, Massachusetts Institute of Technology. Her current research interests include fundamental studies of micro and nanoscale heat and mass transport and the development of efficient thermal management, water desalination, and solar thermal energy systems.
Prof. Wang received the 2008 DARPA Young Faculty Award, the 2011 Air Force Office of Scientific Research Young Investigator Award, the 2012 Office of Naval Research Young Investigator Award, and the 2012 ASME Bergles-Rohsenow Young Investigator Award in Heat Transfer.View more

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