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Research Papers

# How to Estimate Heat Spreading Effects in Practice

[+] Author and Article Information
Clemens J. M. Lasance

Philips Research Laboratories, Eindhoven 5656AE, The Netherlandslasance@onsnet.nu

The authors forgot to define the external (convective) resistance $Rconv$.

For the reader who wants to consult the original papers, a word of caution should be issued because the three relevant papers differ in the definition of the parameters. In Ref. 11, the 1D conduction resistance and the spreading resistance are separated entities and $Rmax$ is only associated with the spreading resistance. In Ref. 10, $Rmax$ is defined as the sum of the two, resulting in different graphs. In Ref. 9, Eq. 1 is only correct if $R0$ equals $Rconv$. However, formally $R0$ represents the sum of $Rconv$ and $R1D(R0=1/hA+t/kA)$. Fortunately, in most cases the errors are negligible, but for those cases with $h/k>100$ and $d>10 mm$, the errors are of the order of 10% and beyond. In practice, especially the condition $d>10 mm$ is not likely to occur.

We have three independent parameters: $ε$, $τ$, and Bi (see Sec. 2). After having varied all three over a large range, the following more precise conclusion can be drawn: the 1D approximation can be used provided $h/k<1$ and $τ>0.05$. If $h/k$ becomes much smaller than 1 the limit for $τ$ can be relaxed. For example, for $h/k<0.01$, $τ>0.005$.

J. Electron. Packag 132(3), 031004 (Sep 09, 2010) (7 pages) doi:10.1115/1.4001856 History: Received November 15, 2009; Revised April 19, 2010; Published September 09, 2010

## Abstract

The nontrivial issues associated with calculating the steady state heat spreading effects generated by a heat source on top of a multilayer assembly such as a printed circuit board are discussed. It is argued that problems arise with the interpretation of heat spreading effects due to a misconception about the meaning of often-quoted flux limits and especially the physical meaning of thermal resistance. The usefulness of a number of approaches that are generally in use to analyze heat spreading effects is discussed and it is shown that the popular series-resistance approach has severe limitations. A number of test cases are covered in detail and the results testify to this assertion.

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## Figures

Figure 1

Two isothermal surfaces connected by a heat flux tube

Figure 2

Heat spreading from single source (left) and two sources (right)

Figure 3

Figure 4

Position of source: center, side, and corner

Figure 5

Left: cases that can be solved analytically. Right: cases that cannot be solved analytically.

Figure 6

Configuration studied: cross section through a planar source on a submount and a heat spreader

Figure 7

Graph showing optima in thermal resistance. Results of heat spreading from submount to ambient. Temperature rise as a function of spreader thickness with the thermal conductivity as parameter, for two values of h: 250 W/m2 K and 10,000 W/m2 K.

Figure 8

Single-layer case 1: source on submount

Figure 9

Single-layer case 2: source on spreader

Figure 10

Two-layer case

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