{"id":1955,"date":"2024-07-30T21:36:45","date_gmt":"2024-07-30T21:36:45","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=1955"},"modified":"2024-07-30T21:36:45","modified_gmt":"2024-07-30T21:36:45","slug":"heat-transfer-through-sphere","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/07\/30\/heat-transfer-through-sphere\/","title":{"rendered":"Heat Transfer Through Sphere"},"content":{"rendered":"\n<p id=\"para-057\">Consider a hollow sphere of internal radius&nbsp;<em>r<\/em><sub>1<\/sub>&nbsp;and external radius&nbsp;<em>r<\/em><sub>2<\/sub>&nbsp;as shown in&nbsp;<a href=\"https:\/\/learning.oreilly.com\/library\/view\/basic-mechanical-engineering\/9789332524415\/xhtml\/chapter007.xhtml#img-037\">Figure 7.8.<\/a>&nbsp;Let the inside and outside surface temperature be&nbsp;<em>t<\/em><sub>1<\/sub>&nbsp;and&nbsp;<em>t<\/em><sub>2<\/sub>; and let the thermal conductivity be&nbsp;<em>k<\/em>. Consider a small element of thickness&nbsp;<em>dr<\/em>&nbsp;at any radius&nbsp;<em>r<\/em>. It can be shown that the surface area of this spherical element is given by 4<em>\u03c0r<\/em><sup>2<\/sup>. The heat transfer rate<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page177d.png\" alt=\"Figure 7.8\"\/><\/figure>\n\n\n\n<p id=\"para-058\"><strong>Figure 7.8<\/strong>&nbsp;Heat Transfer through Sphere<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page177e.png\" alt=\"equation\"\/><\/figure>\n\n\n\n<p id=\"para-060\">On integrating, we get<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page177h.png\" alt=\"equation\"\/><\/figure>\n\n\n\n<p id=\"para-063\">Applying electrical analogy, we get<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page177j.png\" alt=\"equation\"\/><\/figure>\n\n\n\n<p id=\"para-064\">If the concept of mean area,&nbsp;<em>A<\/em><sub>m<\/sub>&nbsp;and mean radius,&nbsp;<em>r<\/em><sub>m<\/sub>&nbsp;are applied<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page177k.png\" alt=\"equation\"\/><\/figure>\n\n\n\n<p id=\"para-065\"><a><\/a>where<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page178a.png\" alt=\"equation\"\/><\/figure>\n\n\n\n<p id=\"para-067\"><em>r<\/em><sub>m<\/sub>&nbsp;is geometric mean.<\/p>\n\n\n\n<p id=\"para-068\"><strong>Example 7.6:<\/strong>&nbsp;A small hemispherical oven is built of an inner layer of insulating firebrick 120 mm thick and an outer covering 80% magnesia 40 mm thick. The inner surface of the oven is 820\u00b0C and the heat transfer coefficient for the outside surface is 10 W\/m<sup>2<\/sup>K; the room temperature is 22\u00b0C. Calculate the heat loss through the hemisphere, if the inside radius is 0.8 m. Take the thermal conductivities of firebrick and 80% magnesia as 0.31 and 0.05 W\/m K.<\/p>\n\n\n\n<p id=\"para-069\">Solution:<\/p>\n\n\n\n<p id=\"para-070\">Given:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page178.png\" alt=\"equation\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Consider a hollow sphere of internal radius&nbsp;r1&nbsp;and external radius&nbsp;r2&nbsp;as shown in&nbsp;Figure 7.8.&nbsp;Let the inside and outside surface temperature be&nbsp;t1&nbsp;and&nbsp;t2; and let the thermal conductivity be&nbsp;k. Consider a small element of thickness&nbsp;dr&nbsp;at any radius&nbsp;r. It can be shown that the surface area of this spherical element is given by 4\u03c0r2. The heat transfer rate Figure 7.8&nbsp;Heat [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1956,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[338],"tags":[],"class_list":["post-1955","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-heat-transfer"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/07\/download-10.jpeg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1955","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=1955"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1955\/revisions"}],"predecessor-version":[{"id":1957,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1955\/revisions\/1957"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/1956"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=1955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=1955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=1955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}