{"id":710,"date":"2016-08-01T02:13:41","date_gmt":"2016-08-01T02:13:41","guid":{"rendered":"http:\/\/www.heatsinkcalculator.com\/blog\/?p=710"},"modified":"2023-01-20T16:19:17","modified_gmt":"2023-01-20T16:19:17","slug":"performance-of-a-led-flat-plate-heat-sink-in-multiple-orientations","status":"publish","type":"post","link":"https:\/\/www.heatsinkcalculator.com\/blog\/performance-of-a-led-flat-plate-heat-sink-in-multiple-orientations\/","title":{"rendered":"Performance of a LED flat plate heat sink in multiple orientations"},"content":{"rendered":"<p>Heat sinks are used to cool light emitting diodes (LEDs) in a similar manner to many other semi-conductor devices such as MOSFETs, CPUs and simple diodes. However LEDs because of their varied applications can be installed in various orientations unlike other semi-conductor devices which typically have a fixed orientation. The heat sinks to which LEDs\u00a0are attached must be able to maintain the LED junction temperature below the specified limits in any of these orientations. If a sheet of aluminum or copper is used as the LED heat sink the thermal performance of this sheet will change depending on its orientation.<\/p>\n<p><a href=\"http:\/\/www.heatsinkcalculator.com\/blog\/wp-content\/uploads\/2016\/07\/led_flat_plate_heatsink.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-724\" src=\"http:\/\/www.heatsinkcalculator.com\/blog\/wp-content\/uploads\/2016\/07\/led_flat_plate_heatsink.png\" alt=\"led_flat_plate_heatsink\" width=\"378\" height=\"406\" srcset=\"https:\/\/www.heatsinkcalculator.com\/blog\/wp-content\/uploads\/2016\/07\/led_flat_plate_heatsink.png 378w, https:\/\/www.heatsinkcalculator.com\/blog\/wp-content\/uploads\/2016\/07\/led_flat_plate_heatsink-279x300.png 279w\" sizes=\"auto, (max-width: 378px) 100vw, 378px\" \/><\/a><\/p>\n<p>Figure 1. LED flat plate heat sink<br \/>\n<!--more continue&gt;&gt;--><br \/>\nIn the blog article <a href=\"http:\/\/www.heatsinkcalculator.com\/blog\/how-to-design-a-flat-plate-heat-sink\/\">How to design a flat plate heat sink<\/a>\u00a0the analysis of a vertical flat plate heat sink cooled via natural convection and radiation is explained. In this article we&#8217;ll explain the heat sink thermal resistance calculations necessary to estimate the thermal performance of a flat plate heat sinks in the two additional orientations as shown in figure 1.\u00a0Analyses for a flat plate heat sink oriented at incremental angles between the vertical orientation, horizontal orientation with the heated surface facing up and the horizontal orientation with the heated surfacing down will not be provided since the thermal performance will lie some where between these three orientations. The horizontal orientation with hot surface facing down typically has the worst\u00a0performance.<\/p>\n<p>The\u00a0orientation of the flat plate heat sink has no effect on conduction from the LED heat source through the flat plate to the external surface and radiation from the external surface.\u00a0Please refer to the blog article\u00a0<a href=\"http:\/\/www.heatsinkcalculator.com\/blog\/how-to-design-a-flat-plate-heat-sink\/\">How to design a flat plate heat sink<\/a>\u00a0for a detailed explanation of the junction to case resistance, contact\/thermal interface resistance\u00a0and radiation resistance calculations for a flat plate heat sink.<\/p>\n<p>The equation for thermal\u00a0convection resistance R<sub>conv<\/sub> from the surface of a horizontal flat plate with the heated surface facing upward or downward \u00a0is given by equation 6. \u00a0 The corresponding average Nusselt number, Nu<sub>L<\/sub> for each orientation (equations 1 and 2), [1] are used to calculate the convection thermal resistance R<sub>conv<\/sub> of each orientation. Using the procedure and equations described\u00a0in the blog post\u00a0<a href=\"http:\/\/www.heatsinkcalculator.com\/blog\/how-to-design-a-flat-plate-heat-sink\/\">How to design a flat plate heat sink<\/a>\u00a0and replacing the thermal convection resistance equation with equation 6 the performance of the flat plate LED heat sink can be estimated.<\/p>\n<p>horizontal flat plate with the heated surface facing upward<br \/>\n<span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20%5Coverline%7BNu%7D_%7BL%7D%3D%5Cleft%20%5B%5Cleft%20%280.54Ra%7B_%7BL%7D%7D%5E%7B1%2F4%7D%20%5Cright%20%29%5E%7B-4%7D%2B%5Cleft%20%280.15Ra%7B_%7BL%7D%7D%5E%7B1%2F3%7D%20%5Cright%20%29%5E%7B-4%7D%20%5Cright%20%5D%5E%7B-1%2F4%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>1<\/p>\n<p>horizontal flat plate with the heated surface facing downward<br \/>\n<span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20%5Coverline%7BNu%7D_%7BL%7D%3D0.52Ra%7B_%7BL%7D%7D%5E%7B1%2F5%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>2<\/p>\n<p>where:<\/p>\n<p><span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20Ra_%7BL%7D%3D%5Cfrac%7Bg%5Cbeta%20%28T_%7Bs%7D-T_%7Bamb%7D%29%7B%5Cwidehat%7BL%7D%7D%5E%7B3%7D%7D%7B%5Cnu%20%5Calpha%20%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>3<\/p>\n<p><span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20%5Cwidehat%7BL%7D%3D%5Cfrac%7BLW%7D%7B2%5Cleft%20%28L%2BW%20%5Cright%20%29%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>4<\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20T_%7Bs%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>is the surface temperature of the plate<\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20T_%7Bamb%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>is the ambient air temperature<\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20g&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>acceleration due to gravity<\/p>\n<p><span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20T_%7Bavg%7D%3D%28T_%7Bs%7D%2BT_%7Bamb%7D%29%2F2&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>5<\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20%5Cnu&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>is the kinematic viscosity of air evaluated at T<sub>avg<\/sub><\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20%5Calpha&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>is the thermal diffusivity of air evaluated at T<sub>avg<\/sub><\/p>\n<p><span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20%5Coverline%7Bh%7D%3D%5Coverline%7BNu%7D_%7BL%7D%5Ctimes%20k_%7Bair%7D%2FL&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>6<\/p>\n<p>where:<\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20k_%7Bair%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>is the thermal conductivity of air evaluated at T<sub>avg<\/sub><\/p>\n<p><span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20R_%7Bconv%7D%3D%5Cfrac%7B1%7D%7B%5Coverline%7Bh%7DA_%7Bp%7D%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>7<\/p>\n<p><strong><span style=\"font-size: 16pt;\">Accounting for multiple LEDs<br \/>\n<\/span><\/strong>If multiple identical LEDs are being cooled by the heat sink and they are spaced very close to one another then a reasonable approximation is to assume that the LEDs are equivalent to one single large heat source as shown if figure 2. The heat source should have an area that is equivalent to the sum of the areas of the LEDs that are in contact with the heat sink. \u00a0The equivalent interface (R<sub>int-eqv<\/sub>) and junction to case thermal (R<sub>th-jc-eqv<\/sub>) resistances for the single equivalent heat source need to be calculated as shown in equations 8 and 9.<\/p>\n<p><a href=\"http:\/\/www.heatsinkcalculator.com\/blog\/wp-content\/uploads\/2016\/07\/multiple_leds_on_heat_sink.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-732\" src=\"http:\/\/www.heatsinkcalculator.com\/blog\/wp-content\/uploads\/2016\/07\/multiple_leds_on_heat_sink.png\" alt=\"multiple_leds_on_heat_sink\" width=\"397\" height=\"289\" srcset=\"https:\/\/www.heatsinkcalculator.com\/blog\/wp-content\/uploads\/2016\/07\/multiple_leds_on_heat_sink.png 397w, https:\/\/www.heatsinkcalculator.com\/blog\/wp-content\/uploads\/2016\/07\/multiple_leds_on_heat_sink-300x218.png 300w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><\/a><\/p>\n<p>Figure 2. Multiple closely spaced LEDs modeled as a single LED<\/p>\n<p><span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20R_%7Bint-eqv%7D%3D%5Cfrac%7BR_%7Bint-single%7D%7D%7BN%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>8<\/p>\n<p><span style=\"display: inline-block; width: 500px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20R_%7Bth-jc-eqv%7D%3D%5Cfrac%7BR_%7Bth-jc-single%7D%7D%7BN%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>9<\/p>\n<p>where:<\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20R_%7Bint-single%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>is the thermal interface resistance of single LED<\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20R_%7Bth-jc-single%7D&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>is the junction to case thermal resistance of single LED<\/p>\n<p><span style=\"display: inline-block; width: 140px;\"><img src='http:\/\/s.wordpress.com\/latex.php?latex=%5Cdisplaystyle%20N&bg=ffffff&fg=000000&s=0' alt='Latex formula' title='Latex formula' class='latex' \/><\/span>is the number of LEDs<\/p>\n<div style=\"background-color: #ffff99; padding: 7px;\">\n<p style=\"margin: 0px;\">An online heat sink calculator based on the calculation methodology described in this blog post is available free of cost. Click the following link to access the calculator: <a href=\"https:\/\/www.heatsinkcalculator.com\/flat-plate-heat-sink-calculator.html\">Flat Plate Heat Sink Calculator<\/a><\/p>\n<\/div>\n<p>[1] F. <span class=\"reference-text\"><span class=\"citation book\">Incropera, D. DeWitt,\u00a0 (2011). <i>Fundamentals of Heat and Mass Transfer<\/i> (7th ed.). Hoboken: Wiley. pp. 610<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Heat sinks are used to cool light emitting diodes (LEDs) in a similar manner to many other semi-conductor devices such [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","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":"","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":"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":"","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":[1],"tags":[],"class_list":["post-710","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/posts\/710","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/comments?post=710"}],"version-history":[{"count":27,"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/posts\/710\/revisions"}],"predecessor-version":[{"id":1605,"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/posts\/710\/revisions\/1605"}],"wp:attachment":[{"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/media?parent=710"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/categories?post=710"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.heatsinkcalculator.com\/blog\/wp-json\/wp\/v2\/tags?post=710"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}