Thermal Spreading Resistances in Rectangular Flux Channels: Part I Geometric Equivalences

Abstract

This paper presents a simple geometric tramsformation for predicting thermal spreading resistance in isotropic and compound rectangular flux channels using the solution for an isotropic or compound circular flux tube. It is shown that the results are valid for a wide range of channel aspect ratios and source to base coverage ratio. Since the circular disk solution requires a single series summation, it is preferable to the rectangular flux channel solution which requires the evaluation of two single series and one double series summation. NOMENCLATUREa, b = radial dimensions,m a, b, c, d = linear dimensions, m A b = baseplate area, m 2 A s = heat source area, m 2 A n , B n = Fourier coefficients Bi = Biot number, ht/k h = contact conductance or film coefficient, W/m 2

Thermal Spreading Resistance in Compound and Orthotropic Systems

“…In addition to these new solutions, the effect of shape was recently examined by the authors. Muzychka et al 11 showed that the thermal spreading resistance was a weak function of shape and geometry. Equivalency was established between the flux tube and the flux channel.…”

Engineering method for predicting junction temperatures of high-power light-emitting diodes

“…Spreading thermal resistance also exists when heat is conducted from disc 2 to disc 3. Spreading thermal resistance of disc 2 is calculated using the following expression [15], which depicts the explicit relationship with the geometry of the structure, according to the notion in Fig. 4.…”

“…When heat is conducted from the TIM to the aluminium stage or from the aluminium stage to the copper heat sink, there are spreading thermal resistances that comprise major portions of R alu and R cop . Muzychka et al [15] studied spreading thermal resistance in isotropic flux channels with rectangular heat source and isotropic discs with a circular heat source. The expressions for calculating spreading thermal resistance of the two systems were obtained.…”

“…In both systems, all of the surfaces, except the bottom surfaces, are adiabatic; the lower surfaces are convective cooling surfaces with a heat transfer coefficient. To use the expressions in [15] to calculate the R alu and R cop , equivalent heat transfer coefficient at the bottom surface should be found, which is equal to the actual heat conduction in the structure as shown in Fig. 3a.…”

Thermal analysis and optimization of multiple LED packaging based on a general analytical solution

“…Thermal spreading resistance theory is found to have widespread applications in electronics cooling, both at the board and chip level. These include, but are not limited to, the prediction of thermal resistance of electronic devices known as ball grid arrays [7], the effect of heat source eccentricity [8], the effect of heat spreaders in compound systems [9][10][11][12], the effect of orthotropic properties [13,14], and the issues of contact shape and edge cooling [15][16][17]. In a multi-chip packaging, huge heat generated from the LED chips is conducted through heat slug to the printed circuit board, and finally is transferred from the heat sink to environment.…”