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Article citations


W. Nakayama, K. Koizumi, T. Fukue, M. Ishizuka, T. Nakajima, H. Koike and R. Matsuki, “Thermal Characterization of High-Density Interconnects in the Form of Equivalent Thermal Conductivity,” Proceedings of the ASME2009 InterPACK Conference (IPACK2009), San Francisco, 19-23 July 2009, Article ID: 89086.

has been cited by the following article:

  • TITLE: Numerical Analysis of Printed Circuit Board with Thermal Vias: Heat Transfer Characteristics under Nonisothermal Boundary Conditions

    AUTHORS: Yasushi Koito, Yoshihiro Kubo, Toshio Tomimura

    KEYWORDS: Thermal Management; Printed Circuit Board; Thermal Via; Effective Thermal Conductivity; Nonisothermal Boundary Condition

    JOURNAL NAME: Journal of Electronics Cooling and Thermal Control, Vol.3 No.4, December 6, 2013

    ABSTRACT: A thermal via has been used to enhance the heat transfer through the printed circuit board (PCB). Because the thermal conductivity of a dielectric material is very low, the array of metal vias is placed to make thermal paths in the PCB. This paper describes the numerical analysis of the PCB having metal vias and focuses on the heat transfer characteristics under the nonisothermal boundary conditions. The mathematical model of the PCB has the metal vias between two metal sheets. Under 2nd and 3rd kinds of boundary conditions, the temperature distribution is obtained numerically by changing the design parameters. The discussion is also made on the effective thermal conductivity of the PCB. In industry, the use of effective thermal conductivity is convenient for thermal engineers because it simplifies the calculation process, that is, the composite board can be modeled as a homogeneous medium. From the numerical results, it is confirmed that the placement of metal sheets and the population of metal vias are important factors to dominate the heat transfer characteristics of the PCB. It is also shown that although the nonisothermal boundary conditions are applied at the boundary surface, the temperature difference between the heated and the cooled section is almost uniform when the metal vias are populated densely with the metal sheets. In this case, the effective thermal conductivity of the PCB is found to be the same irrespective of the boundary conditions, that is, whether the isothermal or the nonisothermal boundary conditions are applied.