For thermal management architectures wherein the heat sink is embedded close to a dynamic heat source, nonuniformities may propagate through the heat sink base to the coolant. Available transient models predict the effective heat spreading resistance to calculate chip temperature rise, or simplify to a representative axisymmetric geometry. The coolant-side temperature response is seldom considered, despite the potential influence on flow distribution and stability in two-phase microchannel heat sinks. This study solves three-dimensional transient heat conduction in a Cartesian chip-on-substrate geometry to predict spatial and temporal variations of temperature on the coolant side. The solution for the unit step response of the three-dimensional system is extended to any arbitrary temporal heat input using Duhamel's method. For time-periodic heat inputs, the steady-periodic solution is calculated using the method of complex temperature. As an example case, the solution of the coolant-side temperature response in the presence of different transient heat inputs from multiple heat sources is demonstrated. To represent a case where the thermal spreading from a heat source is localized, the problem is simplified to a single heat source at the center of the domain. Metrics are developed to quantify the degree of spatial and temporal nonuniformity in the coolant-side temperature profiles. These nonuniformities are mapped as a function of nondimensional geometric parameters and boundary conditions. Several case studies are presented to demonstrate the utility of such maps.
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June 2017
Research-Article
Transient Analysis of Nonuniform Heat Input Propagation Through a Heat Sink Base
Srivathsan Sudhakar,
Srivathsan Sudhakar
Cooling Technologies Research
Center (an NSF I/UCRC),
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: ssudhak@purdue.edu
Center (an NSF I/UCRC),
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: ssudhak@purdue.edu
Search for other works by this author on:
Justin A. Weibel
Justin A. Weibel
Cooling Technologies Research
Center (an NSF I/UCRC),
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: jaweibel@purdue.edu
Center (an NSF I/UCRC),
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: jaweibel@purdue.edu
Search for other works by this author on:
Srivathsan Sudhakar
Cooling Technologies Research
Center (an NSF I/UCRC),
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: ssudhak@purdue.edu
Center (an NSF I/UCRC),
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: ssudhak@purdue.edu
Justin A. Weibel
Cooling Technologies Research
Center (an NSF I/UCRC),
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: jaweibel@purdue.edu
Center (an NSF I/UCRC),
School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: jaweibel@purdue.edu
1Corresponding author.
Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received January 11, 2017; final manuscript received February 21, 2017; published online April 12, 2017. Assoc. Editor: S. Ravi Annapragada.
J. Electron. Packag. Jun 2017, 139(2): 020901 (7 pages)
Published Online: April 12, 2017
Article history
Received:
January 11, 2017
Revised:
February 21, 2017
Citation
Sudhakar, S., and Weibel, J. A. (April 12, 2017). "Transient Analysis of Nonuniform Heat Input Propagation Through a Heat Sink Base." ASME. J. Electron. Packag. June 2017; 139(2): 020901. https://doi.org/10.1115/1.4036065
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