فهرست:
فصل اول: مقدمه
1.1 مقدمه.......................................................................................................................................................... 2
2.1 مروری بر کارهای گذشته...................................................................................................................... 4
3.1 اهداف پایاننامه..................................................................................................................................... 15
فصل دوم:
روش مربعات دیفرانسیل و روش مربعات دیفرانسیل تکهای
1.2- مقدمه....................................................................................................................................................... 17
2.2- انتگرالگیری مربعی............................................................................................................................. 18
3.2- مربعات دیفرانسیلی............................................................................................................................ 19
4.2- محاسبهی ضرایب وزنی مشتق مرتبهی اول................................................................................. 19
1.4.2- تقریب بلمن......................................................................................................................................... 19
1.1.4.2- تقریب اول بلمن.............................................................................................................................. 19
2.1.4.2- تقریب دوم بلمن.............................................................................................................................. 20
2.4.2- تقریب کلی شو.................................................................................................................................. 21
5.2- محاسبهی ضرایب وزنی مشتقات مرتبهی دوم و بالاتر............................................................. 23
1.5.2-ضرایب وزنی مشتق مرتبهی دوم.................................................................................................... 23
1.1.5.2- تقریب کلی شو.............................................................................................................................. 23
2.5.2- رابطهی بازگشتی شو برای محاسبهی مشتق مراتب بالاتر............................................... 24
3.5.2- تقریب ضرب ماتریسی..................................................................................................................... 26
6.2- اعمال شرایط مرزی.............................................................................................................................. 27
7.2- انواع انتخاب فواصل بین نقاط......................................................................................................... 29
8.2- مربعات دیفرانسیل تکهای................................................................................................................. 31
9.2- بررسی کارایی روش مربعات دیفرانسیل....................................................................................... 32
1.9.2- جریان جابجایی آزاد دایم بر روی کره دما ثابت............................................................................ 32
1.1.9.2- مدلسازی ریاضی جریان............................................................................................................... 32
2.1.9.2- گسستهسازی معادلات با استفاده از روش مربعات دیفرانسیل.................................. 35
3.1.9.2- نتایج................................................................................................................................................... 36
فصل سوم:
جریان جابجایی آزاد گذرا بر روی کره دما ثابت
1.3- بررسی جریان جابجایی آزادگذرا اطراف کرهی همدما.............................................................. 40
1.1.3- مدلسازی ریاضی جریان.................................................................................................................. 40
2.1.3- گسستهسازی معادلات با استفاده از روش مربعات دیفرانسیل...................................... 43
3.1.3- نتایج...................................................................................................................................................... 44
2.3- بررسی جریان جابجایی آزاد گذرا بر روی کره دما ثابت در حضور میدان مغناطیسی.... 44
1.2.3- مدلسازی ریاضی جریان.................................................................................................................. 47
2.2.3- نتایج...................................................................................................................................................... 49
3.3- بررسی اثر تولیدو جذب حرارت بر جریان جابجایی آزاد گذرا بر روی کره دما ثابت........... 50
1.3.3- مدلسازی ریاضی جریان.................................................................................................................. 50
2.3.3- نتایج...................................................................................................................................................... 51
4.3- بررسی اثر لزجت متغیر با دما بر جریان جابجایی آزاد گذرا بر روی کره دما ثابت............ 53
1.4.3- مدلسازی ریاضی جریان.................................................................................................................. 54
2.4.3- نتایج..................................................................................................................................................... 55
5.3- بررسی اثر هدایت حرارتی متغیر با دما بر جریان جابجایی آزاد گذرا بر روی کره دما ثابت......... 56
1.5.3- مدلسازی ریاضی جریان................................................................................................................. 57
2.5.3- نتایج..................................................................................................................................................... 59
6.3- بررسی اثر لزجت و هدایت حرارتی متغیر با دما بر جریان جابجایی آزاد گذرا بر روی کره دما ثابت 60
1.6.3- مدلسازی ریاضی جریان.................................................................................................................. 60
2.6.3- نتایج..................................................................................................................................................... 63
7.3- بررسی اثر لزجت و هدایت حرارتی متغیر با دما بر جریان جابجایی آزاد گذرا بر روی کره دما ثابت تحت میدان مغناطیسی با در نظر گرفتن تولید و جذب حرارت........................................................................................................ 63
1.7.3- مدلسازی ریاضی جریان.................................................................................................................. 63
2.7.3- نتایج..................................................................................................................................................... 67
فصل چهارم:
بحث و نتیجهگیری و پیشنهادات
1.4- بحث و نتیجهگیری.............................................................................................................................. 69
2.4- پیشنهادات.............................................................................................................................................. 70
فهرست مراجع................................................................................................................................................ 72
پیوستها
جداول.................................................................................................................................................................. 89
اشکال و نمودارها............................................................................................................................................. 96
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