Determine the shape factor, F12, for the rectangles shown.<\/p>\n\n\n\n
6 m (2 0.5 mI 2 1 m<\/p>\n\n\n\n
(a) Perpendicular rectangles without a common edge<\/p>\n\n\n\n
(b) Parallel rectangles of unequal areas.<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine the shape factor (also known as the view factor or configuration factor), ( F_{12} ), for the given rectangles, we use standard view factor formulas. The view factor represents the fraction of radiation leaving surface 1 that strikes surface 2 directly.<\/p>\n\n\n\n For two perpendicular rectangles that do not share an edge, the view factor can be determined using analytical methods or graphs. The formula for perpendicular rectangles with dimensions ( a ) and ( b ) on one rectangle and ( c ) and ( d ) on the other is:<\/p>\n\n\n\n [ Given the dimensions:<\/p>\n\n\n\n Substituting the values and solving would yield the view factor ( F_{12} ).<\/p>\n\n\n\n For parallel rectangles of different sizes, the view factor can be calculated using:<\/p>\n\n\n\n [ A simplified empirical formula for parallel rectangles of different sizes is:<\/p>\n\n\n\n [ where ( W ) and ( L ) are the dimensions of the larger and smaller rectangles.<\/p>\n\n\n\n For the given 6 m \u00d7 0.5 m<\/strong> and 2 m \u00d7 1 m<\/strong> rectangles, substituting the values will give ( F_{12} ).<\/p>\n\n\n\n This method ensures accurate heat transfer analysis in radiative heat exchange scenarios.<\/p>\n","protected":false},"excerpt":{"rendered":" Determine the shape factor, F12, for the rectangles shown. 6 m (2 0.5 mI 2 1 m (a) Perpendicular rectangles without a common edge (b) Parallel rectangles of unequal areas. The correct answer and explanation is : To determine the shape factor (also known as the view factor or configuration factor), ( F_{12} ), for […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-202726","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202726","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=202726"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202726\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=202726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=202726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=202726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}(a) Perpendicular Rectangles Without a Common Edge<\/strong><\/h3>\n\n\n\n
F_{12} = \\frac{1}{\\pi} \\left[ \\sin^{-1} \\left( \\frac{a}{\\sqrt{a^2 + c^2}} \\right) + \\sin^{-1} \\left( \\frac{b}{\\sqrt{b^2 + d^2}} \\right) \\right]
]<\/p>\n\n\n\n\n
(b) Parallel Rectangles of Unequal Areas<\/strong><\/h3>\n\n\n\n
F_{12} = \\frac{1}{A_1} \\int_{A_1} \\int_{A_2} \\frac{\\cos \\theta_1 \\cos \\theta_2}{\\pi r^2} dA_1 dA_2
]<\/p>\n\n\n\n
F_{12} = \\frac{1}{2} \\left[ \\frac{W}{L} + \\frac{L}{W} – \\sqrt{\\left(1 + \\frac{W^2}{L^2} \\right) \\left(1 + \\frac{L^2}{W^2} \\right)} \\right]
]<\/p>\n\n\n\n