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instantaneous temperature T(t). The author does not believe this is a track to follow [8]. In fact temperature effects on the values of HTC in any correlation are exerted only through physical properties. In case fluid properties were temperature independent, the HTC would be time independent and hence would not capture the time constant needed to build the thermal boundary layer. Besides, any solution that does not incorporate the boundary layer thermal capacitance is vowed to failure in correctly modeling transient heat transfer. We have to model transient heat transfer by convection using a mathematical model that can be for instance of the following form: Q = H (T) + C th d(T)/dt (5.12) where C th is a new coefficient, acting like a thermal capacitance, taking and c into consideration (H considers only thermal conductivity ). Of course we will still have to upgrade the coefficient C th the same way we need to upgrade H, i.e. include profile sensitivity and multiple heat sources transforming it thus to a matrix. Let me suggest a new dimensionless number, the analog of Nusselt number Nu, for C th : C th /( c D) (5.13) This new dimensionless number needs to be first adopted, and then extensive experiments (physical or numerical) must be performed to characterize it. VI. Conclusion The heat transfer coefficient HTC can be quite misleading in case it is used for a case that is different from the one used to extract it. Even if the geometry was perfectly the same as that used for extracting HTC, results may still be quite different depending on wall and inlet profiles. This may explain why published correlations for the same geometry may show large discrepancies. For the same reason, using HTC in a conjugate problem may give results that are quite different from reality. The HTC only relates heat transfer between two bodies. Because it is a single scalar number, there is no way it can model multi-body problems with variable heat load on each body. HTC is a static parameter that can by no means model transient effects, without adding more parameters. Last but not least, due to its symmetric character, which contradicts the asymmetric nature of convection, it cannot be used in standard system simulators. Conferring it to hand calculations is a serious disadvantage. All these problems seem to be solvable in case we replace the single HTC scalar number by a matrix of numbers relating 7-9 October 2009, Leuven, Belgium many “temperatures” with many “heat powers”. In case transient effects were to be considered, a second matrix should be added relating time rate of change of temperatures with heat powers. Which “temperatures” and which “heat powers” are we willing to correlate The simplest answer would be “average values”. In this case the matrix degenerates into a scalar number, which is our good old HTC. But this description is too simplistic to model many real life problems as shown in this paper. There are at least two different approaches to define the required set of temperatures and heat powers, the socalled “nodal” and “modal” approaches. The latter seems to be preferable, but the community may find other more suitable approaches. The approach to follow should be accepted by the community in order to standardize exchange of heat transfer data. The community is invited to commonly prepare a white paper on modeling convection [4]. REFERENCES [1] C. Lasance, “Sense and nonsense of heat transfer correlations applied to electronics cooling”, Proceedings of the 6th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Micro-Electronics and Micro-Systems, 2005. EuroSimE 2005, pp 8-16 [2] R. Moffat, “Do’s and Don’ts in Thermal Management”, 2 nd International Conference on Thermal Issues in Emerging Technologies, Theory and Applications, ThETA2/144, Cairo, December 2008, pp.125 – 132. [3] R.J. Moffat, & A.M. Anderson, Applying Heat Transfer Coefficient Data to Electronics Cooling, Journal of Heat Transfer, Vol. 112, pp. 882-890, 1990. [4] http://www.thetaconf.org/Theta08/blog.htm [5] M. N. Sabry, Compact Thermal Models for Electronic Systems, IEEE – CPT, Part A, Vol. 26, pp. 179-185, 2002. [6] C. Lasance; D. Den Hertog and P. Stehouwer, “Creation and Evaluation of Compact Models for Thermal Characterisation Using Dedicated Optimisation Software”, 15 th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, SEMI-THERM, p.1, 1999 [7] M.N. Sabry, High Order Compact Thermal Models, Transactions of IEEE / Components, Packaging and Manufacturing Technology, Vol. 28, No.4, pp 623-629, 2005 [8] Compact Thermal Models For Internal Convection; Sabry, M.-N.; 2005; Transactions of IEEE / Components, Packagging and Mnufacturing Technology, Vol. 28, No.4, pp 623-629 ©EDA Publishing/THERMINIC 2009 7 ISBN: 978-2-35500-010-2
7-9 October 2009, Leuven, Belgium Equivalent Electrothermal Circuit Model for Vertical-Cavity Surface-Emitting Lasers on Silicon Optical Bench C. C. Chen 1 , C. Singh 1 , Y. C. Chen 1 , Hsu-Liang Hsiao 2 , Chia-Yu Lee 2 , Y. T. Cheng 1 , and Mount-Learn Wu 2 1 National Chiao Tung University, Dept. of Electronics Engineering, Hsinchu 300, Taiwan, R.O.C., 2 National Central University, Institute of Optical Sciences, Jhongli 32001, Taiwan, R.O.C. Abstract-This paper physically and conceptually provides a general electrothermal network π-model. Basing on the proposed network π-model, an equivalent electrothermal circuit model (ETCM) and the associated thermal behavior analysis are also demonstrated for the SiOB with VCSELs in terms of characteristics of device materials and geometries. The introduced complicated structure of VCSELs constructed in simulators can be greatly simplified by using the equivalent ETCM to predict the probable thermal flow paths, and eventually can achieve the goal of CPU time-saving without having complex mesh studying or scaling. In the case, comparison results between measured data, simulation and the equivalent ETCM calculation show an excellent temperature matching within ±2°C as well as achieving 90% CPU time-saving. Keywords: equivalent electrothermal circuit model, general electrothermal network π-model, SiOB, VCSELs. this paper, by analog with a common π-circuit model, we physically and conceptually introduced a general electrothermal network π-model, shown in Fig. 1. Meanwhile, an equivalent ETCM established according to the network π-model is also presented for the thermal behavior analysis of silicon optical bench (SiOB) with vertical-cavity surface-emitting lasers (VCSELs) as shown in Fig. 2 for 160Gbp/s high speed interconnected optical data communication application. Since late 1980’s, it has been proposed to utilize silicon substrate as a cost effective functional carrier to integrate optical and microelectronic components. The implementation I. INTRODUCTION Inevitable non-uniform thermal effect due to increasing power dissipation within intensive operating chips has been one of significant hindrances for the developments of next generation high performance microsystem [1-3], that would promote the design consideration of associated configurations and arrangements of device packaging and cooling system, and limitation of maximum power in IC design stage [2]. Therefore, there has been a drastic proliferation of strategy and technique concerned with the predictions of thermal effect on microsystem performance and reliability in terms of circuit design. So far, the establishment of equivalent electrothermal circuit model (ETCM) is the most efficient thermal analysis scheme which can be easily incorporated with CAD tool for optimal system-IC designs to avoid unexpected functionality degradation or even device failure due to excess thermal accumulation. In comparison with other analysis methods for the predictions of non-uniform thermal effect, such as numerical solutions based on Laplace’s equation [2], finite-element analysis (FEA), or boundary element method (BEM) for simulators [5-7],…etc., ETCM can effectively avoid the issues of data unwieldiness and time-consuming due to complicated boundary conditions resulted by system configuration. Nevertheless, the proposed ETCM analysis is still case-dependent which requires detail system configurable for model development. Therefore, in Fig. 1. Scheme of the general electrothermal network π-model. By analysis with the common π-circuit model, there are three main blocks, heating source, propagated resistance, and common base resistance, are adopted to present the thermal source, thermal flow path, and the common base, respectively. SiOB 4700µm Contact Pad Ground BCB Thermal Via 625µm VCSELs Fig. 2. Scheme of the Vertical-Cavity Surface-Emitting Lasers (VCSELs) on Silicon Optical Bench (SiOB). It is obviously that there should be complicated thermal behavior inside the SiOB due to its large volume and aspect ratio. The insertion of upper-right corner shows complicated structure of the VCSELs, the adjacent contact pads, and the thermal via in detail. ©EDA Publishing/THERMINIC 2009 8 ISBN: 978-2-35500-010-2
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