{"id":156505,"date":"2023-08-31T13:45:10","date_gmt":"2023-08-31T08:15:10","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156505"},"modified":"2023-08-31T13:45:10","modified_gmt":"2023-08-31T08:15:10","slug":"the-wall-of-a-constant-diameter-pipe-of-length-1-m-is-heated-uniformly-with-flux-%f0%9d%91%9e-by-wrapping-a-heater-coil-around-it-the-flow-at-the","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/the-wall-of-a-constant-diameter-pipe-of-length-1-m-is-heated-uniformly-with-flux-%f0%9d%91%9e-by-wrapping-a-heater-coil-around-it-the-flow-at-the\/","title":{"rendered":"The wall of a constant diameter pipe of length 1 m is heated uniformly with flux \ud835\udc5e\u201d by wrapping a heater coil around it. The flow at the"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Q. <span style=\"font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:\nEN-US;mso-bidi-language:AR-SA\">The wall of a constant diameter pipe of length 1 m is heated uniformly with flux <\/span><span style=\"font-size:11.0pt;\nfont-family:&quot;Cambria Math&quot;,serif;mso-fareast-font-family:&quot;Cambria Math&quot;;\nmso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:\nEN-US;mso-bidi-language:AR-SA\">\ud835\udc5e\u201d <\/span><span style=\"font-size:11.0pt;\nfont-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\">by<span style=\"letter-spacing:.05pt\"> <\/span>wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully<span style=\"letter-spacing:\n.05pt\"> <\/span>developed. The fluid is incompressible and the flow is assumed to be laminar and steady all<span style=\"letter-spacing:-2.85pt\"> <\/span>through the pipe. The bulk temperature of the fluid is equal to 0 \u00baC at the inlet and 50 \u00baC at<span style=\"letter-spacing:.05pt\"> <\/span>the exit. The wall temperatures are measured at three locations, P, Q and R, as shown in the<span style=\"letter-spacing:-2.85pt\"> <\/span>figure. The flow thermally develops after some distance from the inlet. The following<span style=\"letter-spacing:\n.05pt\"> <\/span>measurements<span style=\"letter-spacing:-.05pt\"> <\/span>are<span style=\"letter-spacing:-.1pt\"> <\/span>made:<\/span><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Point<\/td><td>P<\/td><td>Q<\/td><td>R<\/td><\/tr><tr><td>Wall Temp (\u00baC)<\/td><td>50<\/td><td>80<\/td><td>90<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"859\" height=\"449\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-663.png\" alt=\"\" class=\"wp-image-156507\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-663.png 859w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-663-300x157.png 300w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-663-768x401.png 768w\" sizes=\"(max-width: 859px) 100vw, 859px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ans: Q\u00a0and\u00a0R\u00a0only<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sol:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q\u00a0and\u00a0R\u00a0only<br>Internal forced convection<br>Boundary condition: Constant Heat Flux Case<br>T<sub>m<\/sub>(Bulk mean temperature of fluid)<br>At inlet,\u00a0T<sub>m.i<\/sub>=0\u2218 C<br>At outlet,\u00a0T<sub>m.\u03b8<\/sub>=50\u2218 C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In case of uniform heat bulk mean temperature varies linearly. The difference between bulk mean temperature and wall temperature is constant in thermally developed region. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">so bulk temperature.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">T(x) = A + Bx (I) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At x = 0, T = 0\u00b0C <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A = 0\u00b0C\u00a0 \u00a0 \u00a0 \u00a0(ii) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At x = 1, T = 50\u00b0C <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B = 50\u00b0C\u00a0 \u00a0 (iii) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">from (i), (ii) &amp; (iii) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">bulk temperature T(x) = 50x<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"309\" height=\"141\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-664.png\" alt=\"\" class=\"wp-image-156516\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-664.png 309w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-664-300x137.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. The wall of a constant diameter pipe of length 1 m is heated uniformly with flux \ud835\udc5e\u201d by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady all through the pipe. [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":156523,"comment_status":"open","ping_status":"","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-156505","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\/156505","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=156505"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156505\/revisions"}],"predecessor-version":[{"id":156524,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156505\/revisions\/156524"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156523"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}