{"id":156818,"date":"2023-09-02T12:15:32","date_gmt":"2023-09-02T06:45:32","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156818"},"modified":"2023-09-02T12:15:35","modified_gmt":"2023-09-02T06:45:35","slug":"a-thin-vertical-flat-plate-of-height-l-and-infinite-width-perpendicular-to-the-plane-of-the-figure-is-losing-heat-to-the-surroundings-by-natural-convection","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-thin-vertical-flat-plate-of-height-l-and-infinite-width-perpendicular-to-the-plane-of-the-figure-is-losing-heat-to-the-surroundings-by-natural-convection\/","title":{"rendered":"A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection"},"content":{"rendered":"\n<p>Q. <span style=\"color: var(--contrast); text-align: justify; background-color: var(--base-3); font-size: 12pt; line-height: 103%;\">A thin vertical flat plate of height <i>L<\/i>, and infinite width perpendicular to the plane of the<span style=\"letter-spacing:\n.05pt\"> <\/span><span style=\"letter-spacing:-.05pt\">figure,<\/span><span style=\"letter-spacing:-.5pt\"> <\/span>is<span style=\"letter-spacing:-.45pt\"> <\/span>losing<span style=\"letter-spacing:-.6pt\"> <\/span>heat<span style=\"letter-spacing:-.5pt\"> <\/span>to<span style=\"letter-spacing:-.5pt\"> <\/span>the<span style=\"letter-spacing:-.45pt\"> <\/span>surroundings<span style=\"letter-spacing:-.5pt\"> <\/span>by<span style=\"letter-spacing:-.7pt\"> <\/span>natural<span style=\"letter-spacing:-.5pt\"> <\/span>convection.<span style=\"letter-spacing:\n-.5pt\"> <\/span>The<span style=\"letter-spacing:-.55pt\"> <\/span>temperatures<span style=\"letter-spacing:-.5pt\"> <\/span>of<span style=\"letter-spacing:-.55pt\"> <\/span>the<span style=\"letter-spacing:-.5pt\"> <\/span>plate<span style=\"letter-spacing:-2.85pt\"> <\/span>and<span style=\"letter-spacing:.05pt\"> <\/span>the<span style=\"letter-spacing:\n.05pt\"> <\/span>surroundings,<span style=\"letter-spacing:.05pt\"> <\/span>and<span style=\"letter-spacing:.05pt\"> <\/span>the<span style=\"letter-spacing:.05pt\"> <\/span>properties<span style=\"letter-spacing:.05pt\"> <\/span>of<span style=\"letter-spacing:.05pt\"> <\/span>the<span style=\"letter-spacing:.05pt\"> <\/span>surrounding<span style=\"letter-spacing:\n.05pt\"> <\/span>fluid,<span style=\"letter-spacing:.05pt\"> <\/span>are<span style=\"letter-spacing:.05pt\"> <\/span>constant.<span style=\"letter-spacing:.05pt\"> <\/span>The<span style=\"letter-spacing:.05pt\"> <\/span>relationship between the average Nusselt and Rayleigh numbers is given as<span style=\"letter-spacing:.05pt\"> <\/span><\/span><i style=\"font-size: inherit; color: var(--contrast); text-align: justify; background-color: var(--base-3);\"><span style=\"font-size:14.0pt;mso-bidi-font-size:11.0pt;line-height:\n103%;position:relative;top:-1.0pt;mso-text-raise:1.0pt;mso-font-width:95%\">Nu <\/span><\/i><span style=\"color: var(--contrast); text-align: justify; background-color: var(--base-3); font-size: 14pt; line-height: 103%; font-family: Symbol; position: relative; top: -1pt;\">=<\/span><span style=\"color: var(--contrast); text-align: justify; background-color: var(--base-3); font-size: 14pt; line-height: 103%; position: relative; top: -1pt;\">\u00a0<i>K Ra <\/i><sup>1<\/sup> \/<sup>4<\/sup> <\/span><span style=\"color: var(--contrast); text-align: justify; background-color: var(--base-3); font-size: 12pt; line-height: 103%;\">,<span style=\"letter-spacing:.05pt\"> <\/span>where <i>K <\/i>is a constant. The length scales for Nusselt and Rayleigh numbers are the height of<span style=\"letter-spacing:-2.85pt\"> <\/span>the<span style=\"letter-spacing:-.05pt\"> <\/span>plate.<span style=\"letter-spacing:-.05pt\"> <\/span>The<span style=\"letter-spacing:-.1pt\"> <\/span>height<span style=\"letter-spacing:-.05pt\"> <\/span>of the<span style=\"letter-spacing:-.05pt\"> <\/span>plate<span style=\"letter-spacing:-.1pt\"> <\/span>is increased<span style=\"letter-spacing:.1pt\"> <\/span>to 16<i>L<span style=\"letter-spacing:-.05pt\"> <\/span><\/i>keeping all other<span style=\"letter-spacing:-.15pt\"> <\/span>factors constant.<\/span><span style=\"font-size: inherit; color: var(--contrast); background-color: var(--base-3);\"> <\/span><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" width=\"364\" height=\"358\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-703.png\" alt=\"\" class=\"wp-image-156819\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-703.png 364w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-703-300x295.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/figure>\n\n\n\n<p>If the average heat transfer coefficient for the first plate is <em>h<\/em>1 and that for the second plate is<em>h<\/em>2, the value of the ratio <em>h<\/em>1<em>\/h<\/em>2 is\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 .<\/p>\n\n\n\n<p>Ans: 2<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Nu = K(Ra)<sup>1\/4<\/sup><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"171\" height=\"175\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-704.png\" alt=\"\" class=\"wp-image-156820\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings, and the properties of the surrounding fluid, are constant. The relationship between the average Nusselt and Rayleigh numbers is [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":156821,"comment_status":"open","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-4)","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-4)","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-4)","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":[5141],"tags":[5140],"class_list":["post-156818","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156818","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=156818"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156818\/revisions"}],"predecessor-version":[{"id":156822,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156818\/revisions\/156822"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156821"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156818"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156818"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156818"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}