Steady-state temperature solution for early design of Annealed Pyrolytic Graphite heat spreader: Full results

2016 ◽  
Author(s):  
Eric Monier-Vinard ◽  
Minh-Nhat Nguyen ◽  
Najib Laraqi ◽  
Valentin Bissuel ◽  
Olivier Daniel
Keyword(s):  
Steady State ◽  
Pyrolytic Graphite ◽  
Heat Spreader ◽  
Early Design ◽  
Steady State Temperature ◽  
Temperature Solution ◽  
Graphite Heat

Steady-State Temperature Solution for a Heat-Generating Circular Cylinder Cooled by a Ring of Holes

1964 ◽  
Vol 86 (4) ◽  
pp. 531-536 ◽  
Author(s):  
J. C. Rowley ◽  
J. B. Payne
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Circular Cylinder ◽  
Heat Conduction Equation ◽  
Series Solution ◽  
Concentric Circle ◽  
Optimum Location ◽  
Shape Factors ◽  
Steady State Temperature ◽  
Temperature Solution

A series solution is presented to the heat-conduction equation for a heat-generating circular cylinder pierced axially by a ring of equal holes spaced uniformly on a concentric circle. The solution is based upon a class of potential functions previously defined by Howland. Typical nondimensional curves for peak and average temperatures and optimum location of the ring of holes for uniform convective cooling are presented. In addition, some shape factors or conductances for the geometry are given.

Steady‐state temperature solution for the Joule heating of a conducting medium

1983 ◽  
Vol 51 (11) ◽  
pp. 1043-1045 ◽  
Author(s):  
John H. Young ◽  
William J. Atkinson ◽  
Ivan A. Brezovich
Keyword(s):  
Steady State ◽  
Joule Heating ◽  
Conducting Medium ◽  
Steady State Temperature ◽  
Temperature Solution

Practical analytical steady-state temperature solution for annealed pyrolytic graphite heat spreader

2017 ◽  
Vol 27 (1) ◽  
pp. 174-188 ◽  
Author(s):  
Nhat Minh Nguyen ◽  
Eric Monier-Vinard ◽  
Najib Laraqi ◽  
Valentin Bissuel ◽  
Olivier Daniel
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Pyrolytic Graphite ◽  
Heat Spreader ◽  
Content Type ◽  
Heat Spreaders ◽  
Operating Limits

Purpose The purpose of this paper is to supply an analytical steady-state solution to the heat transfer equation permitting to fast design investigation. The capability to efficiently transfer the heat away from high-powered electronic devices is a ceaseless challenge. More than ever, the aluminium or copper heat spreaders seem less suitable for maintaining the component sensitive temperature below manufacturer operating limits. Emerging materials, such as annealed pyrolytic graphite (APG), have proposed a new alternative to conventional solid conduction without the gravity dependence of a heat-pipe solution. Design/methodology/approach An APG material is typically sandwiched between a pair of aluminium sheets to compose a robust graphite-based structure. The thermal behaviour of that stacked structure and the effect of the sensitivity of the design parameters on the effective thermal performances is not well known. The ultrahigh thermal conductivity of the APG core is restricted to in-plane conduction and can be 200 times higher than its through-the-thickness conductivity. So, a lower-than-anticipated cross-plane thermal conductivity or a higher-than-anticipated interlayer thermal resistance will compromise the component heat transfer to a cold structure. To analyse the sensitivity of these parameters, an analytical model for a multi-layered structure based on the Fourier series and the superposition principle was developed, which allows predicting the temperature distribution over an APG flat-plate depending on two interlayer thermal resistances. Findings The current work confirms that the in-plane thermal conductivity of APG is among the highest of any conduction material commonly used in electronic cooling. The analysed case reveals that an effective thermal conductivity twice as higher than copper can be expected for a thick APG sheet. The relevance of the developed analytical approach was compared to numerical simulations and experiments for a set of boundary conditions. The comparison shows a high agreement between both calculations to predict the centroid and average temperatures of the heating sources. Further, a method dedicated to the practical characterization of the effective thermal conductivity of an APG heat-spreader is promoted. Research limitations/implications The interlayer thermal resistances act as dissipation bottlenecks which magnify the performance discrepancy. The quantification of a realistic value is more than ever mandatory to assess the APG heat-spreader technology. Practical implications Conventional heat spreaders seem less suitable for maintaining the component-sensitive temperature below the manufacturer operating limits. Having an in-plane thermal conductivity of 1,600 W.m−1.K−1, the APG material seems to be the next paradigm for solving endless needs of a thermal designer. Originality/value This approach is a practical tool to tailor sensitive parameters early to select the right design concept by taking into account potential thermal issues, such as the critical interlayer thermal resistance.

scholarly journals Identification of DC Thermal Steady-State Differential Inductance of Ferrite Power Inductors

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3854
Author(s):  
Salvatore Musumeci ◽  
Luigi Solimene ◽  
Carlo Stefano Ragusa
Keyword(s):  
Steady State ◽  
Input Voltage ◽  
Switching Frequency ◽  
Ohmic Losses ◽  
Steady State Temperature ◽  
Wide Range ◽  
Average Current ◽  
Power Inductors ◽  
Saturable Inductor ◽  
Thermal Steady State

In this paper, we propose a method for the identification of the differential inductance of saturable ferrite inductors adopted in DC–DC converters, considering the influence of the operating temperature. The inductor temperature rise is caused mainly by its losses, neglecting the heating contribution by the other components forming the converter layout. When the ohmic losses caused by the average current represent the principal portion of the inductor power losses, the steady-state temperature of the component can be related to the average current value. Under this assumption, usual for saturable inductors in DC–DC converters, the presented experimental setup and characterization method allow identifying a DC thermal steady-state differential inductance profile of a ferrite inductor. The curve is obtained from experimental measurements of the inductor voltage and current waveforms, at different average current values, that lead the component to operate from the linear region of the magnetization curve up to the saturation. The obtained inductance profile can be adopted to simulate the current waveform of a saturable inductor in a DC–DC converter, providing accurate results under a wide range of switching frequency, input voltage, duty cycle, and output current values.

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