Two-Dimensional Numerical Investigation on Applicability of 45。Heat Spreading Angle

The 45˚ heat spreading angle is familiar among thermal designers. This angle has been used for thermal design of electronic devices, and provides a heat spreading area inside a board, e.g. printed circuit board, which is placed between a heat dissipating element and a relatively large heat sink. By using this angle, the heat transfer behavior can be estimated quickly without using high-performance computers. In addition, the rough design can be made easily by changing design parameters. This angle is effective in a practical situation; however, the discussion has not been made sufficiently on the applicability of the 45˚ heat spreading angle. In the present study, therefore, the extensive numerical investigation is conducted for the rational thermal design using the 45˚ heat spreading angle. The two-dimensional mathematical model of the board is considered; the center of the top is heated by a heat source while the bottom is entirely cooled by a heat sink. The temperature distribution is obtained by solving the heat conduction equation numerically with the boundary conditions. From the numerical results, the heat transfer behavior inside the board is shown and its relation with the design parameters is clarified. The heat transfer behavior inside the 45˚ heat spreading area is also evaluated. The applicability is moreover discussed on the thermal resistance of the board obtained by the 45˚ heat spreading angle. It is confirmed that the 45˚ heat spreading angle is applicable when the Biot number is large, and then the equations are proposed to calculate the Biot number index to use the 45˚ angle. Furthermore, the validity of the 45˚ heat spreading angle is also confirmed when the isothermal boundary condition is used at the cooled section of the board.