فصلنامه علمی کارافن

فصلنامه علمی کارافن

بررسی عددی جریان خون پالسی در طول رگ گرفته شده با تأثیر میدان مغناطیسی با استفاده از تقریب کرانک-نیکلسون

نوع مقاله : مقاله پژوهشی (توسعه ای)

نویسندگان
1 استاد، گروه ریاضی، دانشکده آمار، ریاضی و رایانه، دانشگاه علامه طباطبائی، تهران، ایران.
2 استادیار، گروه ریاضی،دانشگاه پیام نور، تهران، ایران.
چکیده
در این مقاله، یک مدل ریاضی برای جریان خون دوبعدی پالسی ، در حضور میدان مغناطیسی و شتاب بدن در طول سرخرگ گرفته شده شبیه سازی شده است. با هدف شبیه سازی شرایط واقعی بدن انسان، سرخرگ مورد مطالعه به صورت الاستیک و هندسه گرفتگی وابسته به زمان مدل سازی می شود. جریان خون به صورت غیر خطی، تراکم ناپذیر و کاملاً گسترش یافته فرض شده است. همچنین به دلیل گرادیان فشار ضربانی ناشی از عملکرد سیستماتیک قلب و شتاب بدن، جریان خون به صورت ناپایا در نظر گرفته می شود. به‌ منظور تسهیل در اعمال روش تفاضلات متناهی، با استفاده از تبدیل مختصات مناسب، سرخرگ الاستیک گرفته شده، به سرخرگ مستطیلی شکل تبدیل می‌شود. معادلات مومنتوم غیرخطی و پیوستگی با اعمال شرایط مرزی و شرایط اولیه مناسب به صورت عددی با استفاده از روش کرانک نیکلسون حل می‌شوند. مشخصه‌های اصلی جریان خون از جمله پروفیل سرعت، دبی حجمی و مقاومت در برابر جریان بدست آمده است و در مورد تأثیر میزان گرفتگی و میدان مغناطیسی بر روی آن‌ها بحث شده است. همچنین مشخصه‌های جریان خون در طول سرخرگ الاستیک و غیر‌الاستیک با همدیگر مقایسه می‌شوند.
کلیدواژه‌ها
موضوعات

عنوان مقاله English

Numerical investigation of pulsatile blood flow in a stenosed artery with magnetic field influence using a Crank–Nicolson approach

نویسندگان English

ahmadreza haghighi 1
Ayatollah yari 2
1 1Department of Mathematics, Faculty of Statistics, Mathematics, and Computer, Allameh Tabataba'i University, Tehran, Iran.
2 Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.
چکیده English

In this study, a mathematical model for a two-dimensional pulsatile blood flow through a stenosed artery in the presence of a magnetic field and body acceleration is simulated. The artery is assumed to be an elastic cylindrical tube and stenosis's geometry is considered time-dependent to provide resemblance to the in-vivo situations. The blood flow has been assumed to be non-linear, incompressible, and fully developed. Moreover, due to the pulsatile pressure gradient arising from systematic functioning of the heart and the body acceleration, the blood flow has been assumed unsteady. To facilitate the application of the finite difference scheme in solving the governing equations, a coordinate transformation is employed, transforming the stenosed artery into a rectangular artery. The nonlinear momentum and the continuity equations under suitable initial and boundary conditions can be numerically solved using the Crank-Nicolson scheme. The blood flow characteristics such as the velocity profile, the volumetric flow rate, and the resistance to flow are obtained and the effects of the severity of the stenosis and the magnetic field on these flow characteristics are discussed. Besides the blood flow characteristics through elastic arteries have been compared with the rigid ones.

کلیدواژه‌ها English

Blood flow pulsatile
Magnetic field
Body acceleration
Crank-Nicolson scheme
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دوره 22، ویژه نامه
علوم انسانی
پاییز 1404
صفحه 553-575

  • تاریخ دریافت 23 اسفند 1402
  • تاریخ بازنگری 15 خرداد 1403
  • تاریخ پذیرش 24 مرداد 1403