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.
Cite this paper
Koito, Y. , Okamoto, S. and Tomimura, T. (2014) Two-Dimensional Numerical Investigation on Applicability of 45。
Heat Spreading Angle. Journal of Electronics Cooling and Thermal Control
, 1-11. doi: 10.4236/jectc.2014.41001
 Vermeersch, B. and Mey, G.D. (2008) A Fixed-Angle Dynamic Heat Spreading Model for (an) Isotropic Rear-Cooled Substrates. ASME Journal of Heat Transfer, 130, 121301. http://dx.doi.org/10.1115/1.2976557
 Balents, L., Gold, R.D., Kaiser, A.W. and Peterson, W.R. (1969) Design Considerations for Power Hybrid Circuits. Proceedings of the International Hybrid Microelectronics Symposium, Dallas, 29-30 October 1969, 323-344.
 Cook, K.B., Kerns, D.V., Nagle, H.T., Slagh, T.D. and Ruwe, V.W. (1976) Computer-Aided Thermal Analysis of a Hybrid Multistage Active Bandpass Filter/Amplifier. IEEE Transactions on Parts, Hybrids, and Packaging, 12, 344-350. http://dx.doi.org/10.1109/TPHP.1976.1135151
 Masana, F.N. (1996) A Closed Form Solution of Junction to Substrate Thermal Resistance in Semiconductor Chips. IEEE Transactions on Components, Packaging, and Manufacturing Technology, Part A, 19, 539-545.
 Guenin, B. (2003) The 45。
Heat Spreading Angle—An Urban Legend? Electronics Cooling.
 Malhammer, A. (2006) Spread Angels, Part 1. Cooling Zone.
 Lasance, C.J.M. (2010) How to Estimate Heat Spreading Effects in Practice. ASME Journal of Electronic Packaging, 132, 031004. http://dx.doi.org/10.1115/1.4001856
 Ha, M. and Graham, S. (2012) Development of a Thermal Resistance Model for Chip-On-Board Packaging of High Power LED Arrays. Microelectronics Reliability, 52, 836-844. http://dx.doi.org/10.1016/j.microrel.2012.02.005
 Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow. Hemisphere Pub. Corp., Washington DC.
 Lee, S., Song, S., Au, V. and Moran, K.P. (1995) Constriction/Spreading Resistance Model for Electronics Packaging. Proceedings of the 4th ASME/JSME Thermal Engineering Joint Conference, Hawaii, 19-24 March 1995, 4, 199-206.