Effect of heat source orientation on the thermal behavior of N-layer electronic board Minh-Nhat Nguyen a , Eric Monier-Vinard b, * , Najib Laraqi a , Valentin Bissuel b a Universit e Paris Ouest, Laboratoire Thermique Interfaces Environnement (LTIE), EA 4415, 50 rue de S evres, 92410 Ville d’Avray, France b Thales Global Services,19-21 avenue Morane Saulnier, 78140 V elizy-Villacoublay, France article info Article history: Received 22 June 2015 Received in revised form 24 February 2016 Accepted 25 May 2016 Keywords: Analytical thermal modeling Multi-layer printed circuit board Multi-shape heating sources abstract The present work completes a range of analytical solutions that deal with the steady-state temperature calculations of a multi-layered structure heated by a single or multiple heat sources. Today, the surface- mount devices onto a printed circuit board are not only oriented vertically or horizontally, various angles have henceforth to be considered in thermal simulation to assess new placement design. Thus the problematic of heating sources, having any rotation, is solved to enlarge the capability of conventional analytical approaches for modeling more efficiently the thermal behavior of recent electronic boards. To demonstrate its relevance, the proposed analytical solution has been compared to numerical simulations on the case of a multi-layered electronic board submitted to different configurations of heating sources. The comparison shows a good agreement between analytical and numerical calculations to predict the centroid or average temperatures. The promoted analytical approach establishes a kit of practical ex- pressions, easy to implement, which would be cumulated, using superposition principle, to help elec- tronic designer to early detect excessive temperatures of components or board beyond manufacturer limits. The ability to eliminate bad concept candidates with a minimum of setup, relevant assumptions and low computation time can be more easily achieved. © 2016 Elsevier Masson SAS. All rights reserved. 1. Introduction More than ever, electronic board designers have to deal today with constraining powered devices on high-density electronic boards. The miniaturization of electronic component and theirs placement density are reinforcing the need to simulate in thinner details board architectures in order to efficiently manage their contribution to heat spreading. If numerical simulation methods are mandatory for delivering an optimized design of appropriate power dissipation of many components of an electronic board, the sensitivity of component temperatures to early conception changes is today a crucial concern. Moreover, numerical approaches can be often cumber- some, expensive and hard to assess by none-expert which are not familiar with theirs calculation rules. So, it seems much convenient to develop a more comprehensive approach allowing designers to early estimate critical temperatures of electronic components. Based on theoretical studies [1e21] a set of analytical models based on the three-dimensional Fourier series solution was derived [22,23] to target the thermal design of multi-layered PCB with multi-sources mounted on its external surfaces with the aim to assist designer to resolve their practical needs. 2. Initial status of the analytical approach The established analytical formulation allows fast evaluation of temperature profile of a set of constitutive cross-plane dielectric or conductive layers according with the following capabilities:  Quantification of steady state temperatures of superposed multiple sources,  Limited to rectangular or square board shape,  Consideration of orthotropic thermal conductivities,  Uniform Fourier-type (3rd) boundary condition on external upper and lower surfaces, Moreover, the uniform heat transfer coefficient of the external upper and lower surfaces can be minimized (e.g. 10 9 ) or maximized (e.g. 10 9 ) to cover Dirichlet- type (1st) or Neumann-type (2nd) kinds of boundary conditions on external plane surface. * Corresponding author. E-mail address: eric.monier-vinard@thalesgroup.com (E. Monier-Vinard). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts http://dx.doi.org/10.1016/j.ijthermalsci.2016.05.026 1290-0729/© 2016 Elsevier Masson SAS. All rights reserved. International Journal of Thermal Sciences 109 (2016) 23e32