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Analytical Solution of Non-ideal Gaseous Slip Flow in Circular Sector Micro-channel | ||
Journal of Heat and Mass Transfer Research | ||
دوره 7، شماره 2 - شماره پیاپی 14، بهمن 2020، صفحه 131-141 اصل مقاله (2.04 M) | ||
نوع مقاله: Full Length Research Article | ||
شناسه دیجیتال (DOI): 10.22075/jhmtr.2020.19129.1259 | ||
نویسندگان | ||
Mahdi Motamedian1؛ AhmadReza Rahmati* 2 | ||
1Departman mechanical engineerig, Kashan University,Kashan,iran | ||
2University of Kashan | ||
تاریخ دریافت: 24 آبان 1398، تاریخ بازنگری: 16 خرداد 1399، تاریخ پذیرش: 27 خرداد 1399 | ||
چکیده | ||
Abstract Analytical solutions of gaseous slip flow in a microchannel with different cross-sections play an important role in the understanding of the physical behavior of gases and other phenomena related to it. In this paper, the fully developed non-ideal gaseous slip flow in circular sector microchannel is investigated using the conformal mapping and the integral transform technique to obtain the analytical exact solution. Van der Waals equation is used as the equation of state for a non-ideal gas.It is developed the models for predicting the local and mean velocity, normalized Poiseuille number,and the ratio of density for conditions where the small radius of the circular sector cross-section is zero (r1*→0) and is the opposite of zero (r1*≠0, r1*=10µm).Rarefication process and effects of wall slippage are important physical phenomena that are studied. The results show that the rarefication process depends on Knudsen number, and cross-section geometry. In order to validate the analytical solution, the results of the problem are compared to the analytical and numerical solutions. Good agreement between the present study and other solutions has confirmed. | ||
کلیدواژهها | ||
Keywords: Slip flow؛ Microchannel؛ Circular sector؛ Integral transform؛ Conformal mapping | ||
عنوان مقاله [English] | ||
حل تحلیلی جریان لغزشی گاز غیر ایده آل در میکروکانال با مقطع قطاع دایره | ||
چکیده [English] | ||
حلهای تحلیلی جریان لغزشی گازها در یک میکروکانال با مقاطع عرضی مختلف، نقش مهمی را در فهم رفتار فیزیکی گازها و دیگر پدیدههای مربوط به آن ایفا میکند. در این تحقیق، جریان کاملاً توسعه یافته لغزشی گاز غیر ایده آل در میکروکانال با مقطع قطاع دایره به روش نگاشت همدیس و انتقال انتگرال برای رسیدن به حل دقیق تحلیلی بررسی شده است. معادله واندروالس به عنوان معادله حالت گاز غیر ایده آل به کار گرفته شده است. مدلهایی برای پیش بینی سرعت متوسط و لحظهای، عدد پوازی و نسبت چگالی برای شرایطی که در آن شعاع کوچک مقطع عرضی قطاع دایره برابر صفر (r1*→0) و مخالف صفر (r1*≠0, r1*=10µm) ارائه شده است. فرآیند رقیق سازی و اثرات لغزش دیواره مهمترین پدیده های فیزیکی هستند که مطالعه شده است. نتایج نشان میدهد که فرآیند رقیق سازی به عدد نادسن و هندسه مقطع عرضی وابسته است. برای صحت سنجی حل، نتایج مسئله با حل دقیق تحلیلی و عددی مقایسه شده است. تطابق خوبی بین مطالعه حاضر و حلهای دیگر تائید شده است. | ||
کلیدواژهها [English] | ||
واژگان کلیدی: جریان لغزشی, میکروکانال, قطاع دایره, انتقال انتگرال, نگاشت همدیس | ||
مراجع | ||
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