The Effect of Base Temperature Variation on The Unsteady State Annular Heat Sink
نویسندگان
چکیده
The effect of base temperature variation on the heat transfer from unsteady state annular heat sink of cooling microelectronic device. Three types of the base temperature variation equations are taken in the present study. The Sine wave variation, Cosine wave variation & exponential variation of the base temperature. The finite element technique based on Galerkin method with axisymmetric rectangular elements is used in the present analysis. The base temperature variation effects on the effectiveness & the efficiency of the heat sink are studied during the present research. We were taken the base temperature is depends on the time & the height of the heat sink. A Quick Basic computer program were performed on a high performance PC & some typical results are plotted in graphical forms. These plots give the effectiveness & efficiency of annular heat sink as a function of the dimensionless time (Fourier no.) with different forms of base temperature. The exponential equation for the base temperature along for heat sink height will produce high temperature peak value compared with the others (Sine and Cosine), while Cosine wave produce high amplitude than Sine wave for the heat sink height. ةصلاخلا ةسارد مت دقل ريغت ةرارحلا ةِجرد ةدعاقلا ىلع هرارحلا لاقتنا ةِرقتسم ريغلا يرارح لبقتسم للاخ ) heat sink ( لكشلا يطيحم . ةِيلاحلا ةِساردلا يف , ةسارد مت عِاونأ ةثلاث نم تِلاداعم هدعاقلا ةرارح ةجرد . ةلاد بَيجلا ةِجوم و ةِجوم لا مامت بِيج لاا ةلادلا كلذآو ريغت للاخ تذخا ةيس ةرارحلا ةِجرد ةدعاقلا . ةقيرط ثحبلا للاخ تمدختسا هددحملا رصانعلا ) Finite Elements ( ةقيرط ىلع دامتعلااب ) Galerkin ( و هليطتسم رصانع مادختسا عم هرظانتم . يح ، يرارحلا لبقتسملا ةيلعافلا و هءافكلا نم لآ ىلع يرارحلا لبقتسملا ريغت ريثات ةسارد مت رابتعا مت ث يرارحلا لبقتسملا عافتراو و نمزلا عم بسانتت هدعاقلا هرارح ةجرد . ةغلب جمانرب ةباتآ مت دقل ) Quick Basic ( و موسر و تاططخم ىلا اهليوحت و اهميظنت مت جئاتنلا ضعب ، ةيلاع هءافآ تاذ ةبساح لامعتساب . تاططخملا هذه لا عم يرارحلا لبقتسملا هءافآ و ةيلعاف حضوت هدعاقلا ةرارح ةجرد ريغت و تقو . ريغتل ةيسلاا ةلادلا ةرارحلا ةِجرد ةدعاقلا ىلع ل ةميق ىلعا جتنت يرارحلا لبقتسملا عافترا ةرارحلا ةِجرد عم اًتنراقم ةلاد بَيجلا ةِجوم و ةِجوم لا بِيج مامت , ةلاد امنيب ةِجوم لا بِيج ل ةميق ىلعا جتنت ةرارحلا ةِجرد ةلاد عم اًتنراقم وم بَيجلا ةِج . NOMENCLATURES Symbol Description Unit Symbol Description Unit A Cross section area m [C] Elemental capacity matrix k Thermal conductivity W/m°C [N] Shape function vector T Temperature K [K] Elemental stiffness matrix t Time Sec [N*] Unsteady shape function vector Z Longitudinal coordinate (Zaxis) m {R} Residual vector r Longitudinal coordinate (raxis) m [W] Weighted function S Local coordinate in longitudinal direction m [Km] Elemental stiffness matrix due to boundary condition h The average heat transfer coefficient W/m °C L Extended surface length m C Heat Capacity q Heat transfer rate W Greek Symbols α Thermal diffusivity m/s η Overall efficiency of extended surface ε Extended surface effectiveness ρ Density Kg/m Subscript c Average value between two adjustment values o Initial
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