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Page 1: Analytical Heat Transfer

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Page 17: Analytical Heat Transfer

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Page 18: Analytical Heat Transfer

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Page 19: Analytical Heat Transfer

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Page 20: Analytical Heat Transfer

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Page 21: Analytical Heat Transfer

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pqv�� � $ Í þ Û»¼�$[a þ Û©¡ Õ � $ Í þ q ¼D$[a þ q¯¡ � � í ¡ õnò¡ª�eh�qp«gLyzw)mBrSw)thv%sog�moº�w?ª �«sB�¤i g $ji kolpn � � $ Í þ Û»¼�$[a þ qÖ¡�¼ � $ Í þ qh¼D$;a þ Û�¡

pqv�� � $ Í þ Û ¼�$ a þ q ¡ Õ � $ Í þ q ¼D$ a þ Û ¡ � � í ¡ õxóJ¡`<glknv7ª�mu�«sogLsoe�g�g�pqg�¬�g�v%s�wxy+kxmug.k Ë Ê �qv�sog.mo¬�ifwxyDsoe�g�¦;g.mo�q¬�gSsog.mÒÓak)i Ë Ê � Ó Ë2Ì ®,ijw¼sue�k?s$[a � Ì ¡ � $[a þ ÿ b ´ � Ì ¡cê�a F a � í ¡ õ)Ì2¡$ Í � Ì ¡ � $ Í þ ÿh¼ ´ � Ì ¡cê Í F Í � í ¡ õnõ¡

Page 22: Analytical Heat Transfer

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dfeXt�i Ë ´Ë2Ì ¢ ´ � Ó è ícê Í F Í<b ícê a F a é � í ¡ õ%öI¡`J�«soe�soehg� ,wnt�v��hkxmu§Fr�wnv����«so�qwnv ´ � Ë2¡ � Ë�®�soe�glijw)p«t�su�«w)v7�¤i´ " Ì ¡ � $ Í þ ÿ ¼�$ a þ ÿÿrHts�uVs b ÿrHtv\uv2w í ¼<g�´�¦yxô¼ � Ó è ícê Í F Í b ícê�a F a étz|{ � í ¡ õnü¡�I� � �¦¥ ��] �o��ö«�x��� � �h�dfehglø�� gS·9g.rIsu�«¶)g�vhg0ioif�¤i

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¢µiuijt�¬¼�qvh� � sow� ,glk¼r�wnv�ijsuknv%s.®Xsoe�g�v%t�¬° ,g�mBwny#som�kxv;i�yzg.m�thvh�«sui��¤i�ì$ � � Ê �F H Û�� � í ¡ ö?ò¡dfehg�ehg0k?sBr�kn¦�knr��¯s�§!m�k?sug|m�k?su�«w��¤i Fo� � F H Û�� Õ F Ht~ ¶ ¡9h�½ÔX× å Ø : Ô ä Ô ë0ë�� �ì$ � Ó?ÔJ)�Ö å Ø�æ äDë

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Page 23: Analytical Heat Transfer

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� g ¡ È mow%ioijº�w?ª�®X ,wxsoe�º�t��q�hiB¬¼�«´�g.�� y«¡�d#t� ;g�ª��«soe'ªfkxpqp9sog�¬�¦,g�m�k?suthmoglr�wnv�ijsuknv%s¬ � í ¼­gS´�¦ � ¼��ì$ � ¡ � í ¡ ö?ü¡ÒLÓ?Ô ë.ë è#Ó?Ô©çÀÓ?æ?VÁ�sB�¤if�«¬�¦,wnmosukxv%s�suw��hgSsog.mo¬��qvhgLsoe�g�¦hmog0ioiothmug6�hmow)¦Fsuehmow)th�ne'k¼ehg.kxsBgS´hr�e�knvh�ng.m.¡�dfeh�¤if�qi��)�«¶)g�v7 %§g çç ÿ � � å

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Page 24: Analytical Heat Transfer

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Page 25: Analytical Heat Transfer

s teuwvyx{z}| ÇÈ � Ï ` É ÊLb Ñ

�7�jà XN�|Z�Þ��Ë�Ð��ÛÌYBÛ&� �0�-Z�������Í�Û[Zù\;�fÛ;Îy\2Þ�Û��h�Á�y�®hehw?ª£g�¶)g�m0®%soehg ¿ �¤iBiop«�q�ne%sopq§�sug�¬�¦;g.mukxsothmugS¹���g.¦;g.v���g�v%s0®Xsoehg.v�ª£g�e�kM¶)gË ãË ä ¢ � í ¢Ù¬ ã ¡ ã � Ë � Êh¡ í ¡ª�eh�¤r�eNr�kxv� ,glijw)p«¶)g.�! X§Fsoehg�¬�gSsuehw���wxyÀ¦,g�mosot�mo �kxso�qwnv�i.¡5`<glk)ioioth¬�g6soe�kxsã � ä ¡ � ã � � ä ¡B¢Ù¬ ã ÿ � ä ¡B¢0¬ å ã å � ä ¡ ¢Ï,f,�, � Êh¡ Ê2¡

d#w�w)mu��g.m!¬ � ®hª£g6e;kM¶ng Ë ã �Ë ä ¢ ã � � Ë � Êh¡ ò¡ã � � Ë2¡ � í � Êh¡ óJ¡ª�eh�¤r�e'e�kni£suehglijw)p«thso�qwnv ã � � � �V � Êh¡ Ì2¡dÀw�suehg�vhg�´%sBw)mu�hg�m!¬ ÿ ®hª£gL�ngSs Ë ã ÿË ä ¢ ã ÿ � ¼ ã å� � Êh¡ õ¡� ¼ ��� å � Êh¡ïöI¡ã ÿ � Ë2¡ � Ë � Êh¡ ü¡soe�glijw)p«t�su�«w)vFsuw�ª�eh�¤r�e7�¤i ã ÿ � ¼ �0� ¾ ¢ ��� å � Êh¡ " ¡dDkx¨X�«v���suehg�gS´�¦�knv�io�«w)v!sow�w)mu�hg�m!¬ å Ë ã åË ä ¢ ã å � ¼µÊ ã � ã ÿ � Ê�¡ í Ë¡� ¼µÊ � � å ¾ ¼»Ê � � ï � Ê�¡ íní ¡ã å � Ë¡ � í � Ê�¡ í Ê2¡

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Page 26: Analytical Heat Transfer

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ª��«soe�soehgliownpqt�su�«w)v ã å � ��� ¼�Ê ��� å ¢ ��� ï � Ê�¡ í ò¡¢Bv;��iow�wnv±¡ È w)¬° h�qvh�qvh��®�ª£gL�ng�sã � � � ¼¤¬ � � � ¼ � � å ¡�¢Ù¬ å � � � ¼�Ê � � å ¢ � � ï ¡&¢7,�,f, � Ê�¡ í óJ¡

¢Bp«sog.mov�kxso�q¶ng.p«§)®�ª³g�r�knvQ-�v��'kxv�gS´hknrSsBijw)p«t�su�«w)vFsuw�g.¸%t�kxso�qwnv � Ê�¡ í ¡S¡²ÃXg�¦�knmukxso�qvh��¶?kxmu�qkn hp«g0i�®Xª£gL�ngSsË ã� í ¢0¬ ã ¡ ã � Ë ä � Ê�¡ í Ì2¡Á�v%sog.�nm�k?so�qvh�

pqv 㬠㠢 í � ¼ ä ¢ F � Ê�¡ í õ¡dfehglr�wnv����«so�qwnv ã � Ë2¡ � í �)�«¶)g.i F � ¼'pqv � í ¢T¬¯¡I®hiow¼soe�kxs

pqv ã � í ¢Ù¬¯¡í ¢0¬ ã � ¼ ä � Ê�¡ í öI¡dfeh�¤iBr�knv7 ,g�mug.kxmum�kxvh�)g.��suw¼�)�«¶)g ã � � �í ¢Ù¬ � í ¼ � � ¡ � Ê�¡ í ü¡¢ dDkM§%pqwnmo¹�ijg.mo�qg.i½gS´�¦�kxv;ij�qwnv�wxyÀsoehg�g�´�k)rIsµiownpqt�so�qwnv��n�q¶ng0iã � � � ë í ¢0¬ � í ¼ � �V î � ÿ � Ê�¡ í�" ¡� ��� ë í ¼¤¬ � í ¼ ���V ¡�¢0¬ å � í ¼ ��� ¡ å ¢Ï,f,�, î � Ê�¡ïÊxË¡� ��� ¼¤¬ � ��� ¼ �0� å ¡�¢Ù¬ å � ��� ¼�Ê ��� å ¢ ��� ï ¡&¢7,�,f, � Ê�¡ïÊ í ¡¥���2���ÑÐ �n�x���?��� � �¸ª �#� ö � �J�Á�yDsoehg�ehg0k?s�pqw)iuif�qiB�hthgLsow�m�kn���¤k?su�«w)v±®Xª³glr.kxv�ª�mo�«sog� Ø Ë $Ë � ¢ Ï Ê � $ Ñ ¼D$ Ñ% ¡ � Ë � Ê�¡ïÊnÊ2¡dDkx¨X�«v���suehgl���q¬�g�v�io�«w)vhpqg.iui£sog�¬�¦,g�m�k?suthmog6suw¼ ,gl��g�-�vhg.���qv'g.¸%t�k?su�«w)v � í ¡ ònË¡I®hkxv;�Fsu�«¬�gLsuw¼ ,g

ä � Ï Ê � $ Û ¼D$ % ¡�ï �� Ø � Ê�¡ïÊxò¡kxv;�F�qv%somuwX�ht�rS�qvh�¼soehg�¦;kxm�kx¬�gSsug�m í � $&%$ Û ¼D$ % � Ê�¡ïÊ?óJ¡ª£g6�)gSs ËAÒË ä ¢ Ò Ñ � í Ñ � Ê�¡ïÊnÌ2¡ª�ehg.mog Ò � ã ¢Wí � Ê�¡ïÊxõ¡

Page 27: Analytical Heat Transfer

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Page 29: Analytical Heat Transfer

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Page 32: Analytical Heat Transfer

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Page 36: Analytical Heat Transfer

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Page 53: Analytical Heat Transfer

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Page 56: Analytical Heat Transfer

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