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class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-一维稳态导热" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#一维稳态导热"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>一维稳态导热</span> </div> </a> <ul id="toc-一维稳态导热-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-傅立叶定律" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#傅立叶定律"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>傅立叶定律</span> </div> </a> <button aria-controls="toc-傅立叶定律-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关傅立叶定律子章节</span> </button> <ul id="toc-傅立叶定律-sublist" class="vector-toc-list"> <li id="toc-微分形式" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#微分形式"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>微分形式</span> </div> </a> <ul id="toc-微分形式-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-积分形式" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#积分形式"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>积分形式</span> </div> </a> <ul id="toc-积分形式-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-热导" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#热导"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>热导</span> </div> </a> <ul id="toc-热导-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-化工方面的應用" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#化工方面的應用"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>化工方面的应用</span> </div> </a> <ul id="toc-化工方面的應用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-相關條目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#相關條目"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>相关条目</span> </div> </a> <ul id="toc-相關條目-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="zh-Hans-MY" dir="ltr"> <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">开关目录</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading" lang="zh-Hans-MY" dir="ltr"><span class="mw-page-title-main">热传导</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="zh-Hans-MY" dir="ltr"> <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。53种语言可用" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-53" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">53种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Warmtegeleiding" title="Warmtegeleiding – 南非荷兰语" lang="af" hreflang="af" data-title="Warmtegeleiding" data-language-autonym="Afrikaans" data-language-local-name="南非荷兰语" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%88%D8%B5%D9%8A%D9%84_%D8%AD%D8%B1%D8%A7%D8%B1%D9%8A" title="توصيل حراري – 阿拉伯语" lang="ar" hreflang="ar" data-title="توصيل حراري" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0stilikke%C3%A7irm%C9%99" title="İstilikkeçirmə – 阿塞拜疆语" lang="az" hreflang="az" data-title="İstilikkeçirmə" data-language-autonym="Azərbaycanca" data-language-local-name="阿塞拜疆语" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BF%D0%BB%D0%B0%D0%BF%D1%80%D0%B0%D0%B2%D0%BE%D0%B4%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Цеплаправоднасць – 白俄罗斯语" lang="be" hreflang="be" data-title="Цеплаправоднасць" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BF%D0%BB%D0%B0%D0%BF%D1%80%D0%B0%D0%B2%D0%BE%D0%B4%D0%BD%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Цеплаправоднасьць – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Цеплаправоднасьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BF%D0%BB%D0%BE%D0%BF%D1%80%D0%BE%D0%B2%D0%BE%D0%B4%D0%B8%D0%BC%D0%BE%D1%81%D1%82" title="Топлопроводимост – 保加利亚语" lang="bg" hreflang="bg" data-title="Топлопроводимост" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%AC%E0%A6%B9%E0%A6%A3_(%E0%A6%A4%E0%A6%BE%E0%A6%AA)" title="পরিবহণ (তাপ) – 孟加拉语" lang="bn" hreflang="bn" data-title="পরিবহণ (তাপ)" data-language-autonym="বাংলা" data-language-local-name="孟加拉语" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Conducci%C3%B3_t%C3%A8rmica" title="Conducció tèrmica – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Conducció tèrmica" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Veden%C3%AD_tepla" title="Vedení tepla – 捷克语" lang="cs" hreflang="cs" data-title="Vedení tepla" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Varmestr%C3%B8m" title="Varmestrøm – 丹麦语" lang="da" hreflang="da" data-title="Varmestrøm" data-language-autonym="Dansk" data-language-local-name="丹麦语" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/W%C3%A4rmeleitung" title="Wärmeleitung – 德语" lang="de" hreflang="de" data-title="Wärmeleitung" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Thermal_conduction" title="Thermal conduction – 英语" lang="en" hreflang="en" data-title="Thermal conduction" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Varmokondukto" title="Varmokondukto – 世界语" lang="eo" hreflang="eo" data-title="Varmokondukto" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Conducci%C3%B3n_de_calor" title="Conducción de calor – 西班牙语" lang="es" hreflang="es" data-title="Conducción de calor" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Soojusjuhtivus" title="Soojusjuhtivus – 爱沙尼亚语" lang="et" hreflang="et" data-title="Soojusjuhtivus" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Beroaren_eroapen" title="Beroaren eroapen – 巴斯克语" lang="eu" hreflang="eu" data-title="Beroaren eroapen" data-language-autonym="Euskara" data-language-local-name="巴斯克语" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%B3%D8%A7%D9%86%D8%B4_%DA%AF%D8%B1%D9%85%D8%A7%DB%8C%DB%8C" title="رسانش گرمایی – 波斯语" lang="fa" hreflang="fa" data-title="رسانش گرمایی" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/L%C3%A4mm%C3%B6njohtuminen" title="Lämmönjohtuminen – 芬兰语" lang="fi" hreflang="fi" data-title="Lämmönjohtuminen" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Conduction_thermique" title="Conduction thermique – 法语" lang="fr" hreflang="fr" data-title="Conduction thermique" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Conduci%C3%B3n_de_calor" title="Condución de calor – 加利西亚语" lang="gl" hreflang="gl" data-title="Condución de calor" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/%C3%87hiass-chondughtaght" title="Çhiass-chondughtaght – 马恩语" lang="gv" hreflang="gv" data-title="Çhiass-chondughtaght" data-language-autonym="Gaelg" data-language-local-name="马恩语" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%95%D7%9C%D7%9B%D7%AA_%D7%97%D7%95%D7%9D" title="הולכת חום – 希伯来语" lang="he" hreflang="he" data-title="הולכת חום" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE_%E0%A4%9A%E0%A4%BE%E0%A4%B2%E0%A4%A8" title="ऊष्मा चालन – 印地语" lang="hi" hreflang="hi" data-title="ऊष्मा चालन" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kondukcija_topline" title="Kondukcija topline – 克罗地亚语" lang="hr" hreflang="hr" data-title="Kondukcija topline" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Kondiksyon" title="Kondiksyon – 海地克里奥尔语" lang="ht" hreflang="ht" data-title="Kondiksyon" data-language-autonym="Kreyòl ayisyen" data-language-local-name="海地克里奥尔语" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8B%D5%A5%D6%80%D5%B4%D5%A1%D5%B0%D5%A1%D5%B2%D5%B8%D6%80%D5%A4%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Ջերմահաղորդականություն – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Ջերմահաղորդականություն" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Konduksi_panas" title="Konduksi panas – 印度尼西亚语" lang="id" hreflang="id" data-title="Konduksi panas" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Varmeso-kondukto" title="Varmeso-kondukto – 伊多语" lang="io" hreflang="io" data-title="Varmeso-kondukto" data-language-autonym="Ido" data-language-local-name="伊多语" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Conduzione_termica" title="Conduzione termica – 意大利语" lang="it" hreflang="it" data-title="Conduzione termica" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%86%B1%E4%BC%9D%E5%B0%8E" title="熱伝導 – 日语" lang="ja" hreflang="ja" data-title="熱伝導" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D1%8B%D0%BB%D1%83_%D3%A9%D1%82%D0%BA%D1%96%D0%B7%D0%B3%D1%96%D1%88%D1%82%D1%96%D0%BA" title="Жылу өткізгіштік – 哈萨克语" lang="kk" hreflang="kk" data-title="Жылу өткізгіштік" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%B4%EC%A0%84%EB%8F%84" title="열전도 – 韩语" lang="ko" hreflang="ko" data-title="열전도" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Conduzzion_termica" title="Conduzzion termica – 倫巴底文" lang="lmo" hreflang="lmo" data-title="Conduzzion termica" data-language-autonym="Lombard" data-language-local-name="倫巴底文" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/%C5%A0iluminis_laidumas" title="Šiluminis laidumas – 立陶宛语" lang="lt" hreflang="lt" data-title="Šiluminis laidumas" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Siltumvad%C4%AB%C5%A1ana" title="Siltumvadīšana – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Siltumvadīšana" data-language-autonym="Latviešu" data-language-local-name="拉脱维亚语" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A4%E0%B4%BE%E0%B4%AA%E0%B4%9A%E0%B4%BE%E0%B4%B2%E0%B4%95%E0%B4%82" title="താപചാലകം – 马拉雅拉姆语" lang="ml" hreflang="ml" data-title="താപചാലകം" data-language-autonym="മലയാളം" data-language-local-name="马拉雅拉姆语" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%95%E1%80%B0%E1%80%9C%E1%80%BB%E1%80%BE%E1%80%B1%E1%80%AC%E1%80%80%E1%80%BA%E1%80%80%E1%80%B0%E1%80%B8%E1%80%81%E1%80%BC%E1%80%84%E1%80%BA%E1%80%B8" title="အပူလျှောက်ကူးခြင်း – 缅甸语" lang="my" hreflang="my" data-title="အပူလျှောက်ကူးခြင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="缅甸语" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%A4%E0%A4%BE%E0%A4%AA_%E0%A4%B8%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BE%E0%A4%B2%E0%A4%A8" title="ताप सञ्चालन – 尼泊尔语" lang="ne" hreflang="ne" data-title="ताप सञ्चालन" data-language-autonym="नेपाली" data-language-local-name="尼泊尔语" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Varmekonduksjon" title="Varmekonduksjon – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Varmekonduksjon" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Varmeledning" title="Varmeledning – 书面挪威语" lang="nb" hreflang="nb" data-title="Varmeledning" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przewodzenie_ciep%C5%82a" title="Przewodzenie ciepła – 波兰语" lang="pl" hreflang="pl" data-title="Przewodzenie ciepła" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Condu%C3%A7%C3%A3o_t%C3%A9rmica" title="Condução térmica – 葡萄牙语" lang="pt" hreflang="pt" data-title="Condução térmica" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Conduc%C8%9Bie_termic%C4%83" title="Conducție termică – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Conducție termică" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kondukcija" title="Kondukcija – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Kondukcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Heat_conduction" title="Heat conduction – Simple English" lang="en-simple" hreflang="en-simple" data-title="Heat conduction" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Vedenie_tepla" title="Vedenie tepla – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Vedenie tepla" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kondukcija" title="Kondukcija – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Kondukcija" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Konduktion" title="Konduktion – 瑞典语" lang="sv" hreflang="sv" data-title="Konduktion" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AF%86%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AE%9F%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%B2%E0%AF%8D" title="வெப்பக் கடத்தல் – 泰米尔语" lang="ta" hreflang="ta" data-title="வெப்பக் கடத்தல்" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%99%E0%B8%B3%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A3%E0%B9%89%E0%B8%AD%E0%B8%99" title="การนำความร้อน – 泰语" lang="th" hreflang="th" data-title="การนำความร้อน" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Is%C4%B1_iletimi" title="Isı iletimi – 土耳其语" lang="tr" hreflang="tr" data-title="Isı iletimi" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BF%D0%BB%D0%BE%D0%BF%D1%80%D0%BE%D0%B2%D1%96%D0%B4%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Теплопровідність – 乌克兰语" lang="uk" hreflang="uk" data-title="Теплопровідність" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/D%E1%BA%ABn_nhi%E1%BB%87t" title="Dẫn nhiệt – 越南语" lang="vi" hreflang="vi" data-title="Dẫn nhiệt" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li> </ul> 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.ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ambox{border-left-color:#36c!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-Unreferenced plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/File:Tango-nosources.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Tango-nosources.svg/45px-Tango-nosources.svg.png" decoding="async" width="45" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Tango-nosources.svg/68px-Tango-nosources.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Tango-nosources.svg/90px-Tango-nosources.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">此条目<b>没有列出任何<a href="/wiki/Wikipedia:%E5%88%97%E6%98%8E%E6%9D%A5%E6%BA%90" title="Wikipedia:列明来源">参考或来源</a></b>。<span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2019年9月21日</span>)</i></small><span class="hide-when-compact"><br /><small>维基百科所有的内容都应该<a href="/wiki/Wikipedia:%E5%8F%AF%E4%BE%9B%E6%9F%A5%E8%AD%89" title="Wikipedia:可供查证">可供查证</a>。请协助补充<a href="/wiki/Wikipedia:%E5%8F%AF%E9%9D%A0%E6%9D%A5%E6%BA%90" title="Wikipedia:可靠来源">可靠来源</a>以<a class="external text" href="https://zh.wikipedia.org/w/index.php?title=%E7%83%AD%E4%BC%A0%E5%AF%BC&action=edit">改善这篇条目</a>。无法查证的内容可能会因为异议提出而被移除。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <p><b>热传导</b>，是指在物体内部或相互接触的物体表面之间，由于分子、原子及自由电子等微观粒子的热运动，而产生的热量传递现象，是<a href="/wiki/%E7%83%AD%E8%83%BD" title="热能">热能</a>从高温向低温部分转移的过程，是一个<a href="/wiki/%E5%88%86%E5%AD%90" title="分子">分子</a>向另一个分子传递振动<a href="/wiki/%E8%83%BD%E9%87%8F" title="能量">能</a>的结果。各种<a href="/wiki/%E6%9D%90%E6%96%99" title="材料">材料</a>的热传导性能不同，传导性能好的，如<a href="/wiki/%E9%87%91%E5%B1%9E" title="金属">金属</a>，还包括了自由<a href="/wiki/%E7%94%B5%E5%AD%90" title="电子">电子</a>的移动，所以传热速度快，可以做<a href="/wiki/%E7%86%B1%E4%BA%A4%E6%8F%9B%E5%99%A8" class="mw-redirect" title="热交换器">热交换器</a>材料，而金属传导能力依次为银＞铜＞金＞铝；传导性能不好的，如<a href="/wiki/%E7%9F%B3%E6%A3%89" title="石棉">石棉</a>，可以做热绝缘材料。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="一维稳态导热"><span id=".E4.B8.80.E7.BB.B4.E7.A8.B3.E6.80.81.E5.AF.BC.E7.83.AD"></span>一维稳态导热</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%83%AD%E4%BC%A0%E5%AF%BC&action=edit&section=1" title="编辑章节：一维稳态导热"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在工业和日常生活中，大平壁的导热是最简单、最常见的导热问题，例如通过炉墙以及房屋墙壁的导热等。当平壁两表面分别维持均匀恒定的温度时，可以近似地认为平壁内的温度只沿着垂直于壁面的方向发生变化，并且不随时间而变，热量也只沿着垂直于壁面的方向传递，如图1所示，这样的导热称为一维稳态导热。 </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Heat_Conduction_through_3_walls_Series_Example.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Heat_Conduction_through_3_walls_Series_Example.png/139px-Heat_Conduction_through_3_walls_Series_Example.png" decoding="async" width="139" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Heat_Conduction_through_3_walls_Series_Example.png/209px-Heat_Conduction_through_3_walls_Series_Example.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Heat_Conduction_through_3_walls_Series_Example.png/279px-Heat_Conduction_through_3_walls_Series_Example.png 2x" data-file-width="916" data-file-height="815" /></a><figcaption> 三层平壁的稳态导热</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="傅立叶定律"><span id=".E5.82.85.E7.AB.8B.E5.8F.B6.E5.AE.9A.E5.BE.8B"></span>傅立叶定律</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%83%AD%E4%BC%A0%E5%AF%BC&action=edit&section=2" title="编辑章节：傅立叶定律"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>热传导定律，也称为傅立叶定律，描述了热量在介质中的传导规律。其形式与电传导欧姆定律相似。傅立叶定律可以以两种形式表述：微分形式关注于局部的能量传导率，而积分形式则关注于流入和流出整体一部分介质的能量。 </p> <div class="mw-heading mw-heading3"><h3 id="微分形式"><span id=".E5.BE.AE.E5.88.86.E5.BD.A2.E5.BC.8F"></span>微分形式</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%83%AD%E4%BC%A0%E5%AF%BC&action=edit&section=3" title="编辑章节：微分形式"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>傅立叶定律的微分形式表明了<a href="/wiki/%E7%83%AD%E9%80%9A%E9%87%8F" title="热通量">热通量</a>密度正比于<a href="/wiki/%E7%83%AD%E5%AF%BC%E7%8E%87" class="mw-redirect" title="热导率">热导率</a>乘以负的<a href="/wiki/%E6%BA%AB%E5%BA%A6%E6%A2%AF%E5%BA%A6" title="温度梯度">温度梯度</a>。热通量密度是单位时间内流过单位面积的热量。 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {q}}=-k{\nabla }T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo>→</mo> </mover> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∇</mi> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {q}}=-k{\nabla }T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4f15a7163581466da2c18f26dcaf5aab3a158de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.228ex; height:3.343ex;" alt="{\displaystyle {\overrightarrow {q}}=-k{\nabla }T}"></span></dd></dl> <p>这里（使用<a href="/wiki/%E5%9B%BD%E9%99%85%E5%8D%95%E4%BD%8D%E5%88%B6" title="国际单位制">国际单位制</a>）： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {q}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo>→</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {q}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/150671e22d048dcdc2facf8f40bd49cefc966a03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.538ex; height:3.343ex;" alt="{\displaystyle {\overrightarrow {q}}}"></span> 是热通量密度，单位<a href="/wiki/%E7%93%A6%E7%89%B9_(%E5%8D%95%E4%BD%8D)" class="mw-redirect" title="瓦特 (单位)">W</a>·m<sup>−2</sup>，</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}k{\big .}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}k{\big .}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88cea8823e0b363bd95c5cfbc5979ca790590d41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle {\big .}k{\big .}}"></span> 是这种材料的<a href="/wiki/%E7%83%AD%E5%AF%BC%E7%8E%87" class="mw-redirect" title="热导率">热导率</a>，单位<a href="/wiki/%E7%93%A6%E7%89%B9_(%E5%8D%95%E4%BD%8D)" class="mw-redirect" title="瓦特 (单位)">W</a>·m<sup>−1</sup>·<a href="/wiki/%E5%BC%80%E5%B0%94%E6%96%87_(%E5%8D%95%E4%BD%8D)" class="mw-redirect" title="开尔文 (单位)">K</a><sup>−1</sup>，</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}\nabla T{\big .}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mi mathvariant="normal">∇</mi> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}\nabla T{\big .}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf30b625d8f4e5a9b6f983672ff1d8225c0b210a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.572ex; height:2.176ex;" alt="{\displaystyle {\big .}\nabla T{\big .}}"></span> 是温度梯度，单位<a href="/wiki/%E5%BC%80%E5%B0%94%E6%96%87_(%E5%8D%95%E4%BD%8D)" class="mw-redirect" title="开尔文 (单位)">K</a>·m<sup>−1</sup>。</dd></dl> <p>热导<i>k</i>通常情况下都被当作是常数，但是实际情况是，<i>k</i>的值会随温度而变化。然而在很大的温度范围内，<i>k</i>的变化都可忽略不计。在各向异性介质中，热导率显著地随方向而变化，这时<i>k</i>是一个二阶<a href="/wiki/%E5%BC%A0%E9%87%8F" class="mw-redirect" title="张量">张量</a>。在非均匀介质中，<i>k</i>与空间位置有关。 </p><p>在许多情况下，当我们只需考虑一个方向上的热传递（比如x方向）时，可用一维傅立叶定律： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{x}=-k{\frac {dT}{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>T</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{x}=-k{\frac {dT}{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c24cc3bf87ecafbc9fffdbbe40188f83daa9c4b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.016ex; height:5.509ex;" alt="{\displaystyle q_{x}=-k{\frac {dT}{dx}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="积分形式"><span id=".E7.A7.AF.E5.88.86.E5.BD.A2.E5.BC.8F"></span>积分形式</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%83%AD%E4%BC%A0%E5%AF%BC&action=edit&section=4" title="编辑章节：积分形式"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>通过在部分介质表面<i>S</i>上对微分式进行积分，我们得到了傅立叶定律的积分形式： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {\partial Q}{\partial t}}=-k\oint _{S}{{\overrightarrow {\nabla }}T\cdot \,{\overrightarrow {dA}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>Q</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">∇</mi> <mo>→</mo> </mover> </mrow> <mi>T</mi> <mo>⋅</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>d</mi> <mi>A</mi> </mrow> <mo>→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {\partial Q}{\partial t}}=-k\oint _{S}{{\overrightarrow {\nabla }}T\cdot \,{\overrightarrow {dA}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57e15ff186d23e0c5c5287fcb8e765fad98f01cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.429ex; height:5.843ex;" alt="{\displaystyle P={\frac {\partial Q}{\partial t}}=-k\oint _{S}{{\overrightarrow {\nabla }}T\cdot \,{\overrightarrow {dA}}}}"></span></dd></dl> <p>这里（使用<a href="/wiki/%E5%9B%BD%E9%99%85%E5%8D%95%E4%BD%8D%E5%88%B6" title="国际单位制">国际单位制</a>）： </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}P={\frac {\partial Q}{\partial t}}{\big .}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>Q</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}P={\frac {\partial Q}{\partial t}}{\big .}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e44df882ea26a86702eb54e92ad3756b06f8f5a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.836ex; height:5.509ex;" alt="{\displaystyle {\big .}P={\frac {\partial Q}{\partial t}}{\big .}}"></span> 是热传导功率，即单位时间通过面积<i>S</i>的热量，单位<a href="/wiki/%E7%93%A6%E7%89%B9_(%E5%8D%95%E4%BD%8D)" class="mw-redirect" title="瓦特 (单位)">W</a>，而</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {dA}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>d</mi> <mi>A</mi> </mrow> <mo>→</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {dA}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ace7eb096c93516c185dc9371f07059e2d8dcf2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-top: -0.372ex; width:3.089ex; height:3.843ex;" alt="{\displaystyle {\overrightarrow {dA}}}"></span> 是面元矢量，单位m<sup>2</sup>。</li></ul> <p>当我们所研究的介质是一段两端温度恒定、均匀的一维介质时，积分得到的热传导功率为： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}=-kA{\frac {\Delta T}{\Delta x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}=-kA{\frac {\Delta T}{\Delta x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85d6cb69dc1d1a77f41c45da5134725d7453b8a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.723ex; height:5.509ex;" alt="{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}=-kA{\frac {\Delta T}{\Delta x}}}"></span></dd></dl> <p>这里 </p> <dl><dd><i>A</i> 是介质的截面积，</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e61e7deb9c7c7b7dda762b0935e757add2acc559" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.572ex; height:2.176ex;" alt="{\displaystyle \Delta T}"></span> 是两端温差，</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.266ex; height:2.176ex;" alt="{\displaystyle \Delta x}"></span> 是两端距离。</dd></dl> <p>这一定律是<a href="/wiki/%E7%86%B1%E5%82%B3%E5%B0%8E%E6%96%B9%E7%A8%8B" class="mw-redirect" title="热传导方程">热传导方程式</a>的基础。 </p> <div class="mw-heading mw-heading2"><h2 id="热导"><span id=".E7.83.AD.E5.AF.BC"></span>热导</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%83%AD%E4%BC%A0%E5%AF%BC&action=edit&section=5" title="编辑章节：热导"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>类比于电导，我们可以定义热导<i>U</i>（单位W/K）： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}U={\frac {kA}{\Delta x}},\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mi>U</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>A</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}U={\frac {kA}{\Delta x}},\quad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b979a0fdb494dbf41f3f45e0ef9acbdab8f1a1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.952ex; height:5.509ex;" alt="{\displaystyle {\big .}U={\frac {kA}{\Delta x}},\quad }"></span></dd></dl> <p>这样傅立叶定律可以写为 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}=U\,(-\Delta T).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>U</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}=U\,(-\Delta T).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d19c729b2134023a66984578c3d03cfb788d651" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:22.559ex; height:5.509ex;" alt="{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}=U\,(-\Delta T).}"></span></dd></dl> <p>热导的倒数是热阻： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}R={\frac {1}{U}}={\frac {\Delta x}{kA}}={\frac {-\Delta T}{P}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>U</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> <mrow> <mi>k</mi> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mrow> <mi>P</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}R={\frac {1}{U}}={\frac {\Delta x}{kA}}={\frac {-\Delta T}{P}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa01a035f0809679fb0fd7e0c10004565e8a3503" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:24.643ex; height:5.509ex;" alt="{\displaystyle {\big .}R={\frac {1}{U}}={\frac {\Delta x}{kA}}={\frac {-\Delta T}{P}}.}"></span></dd></dl> <p>对于由多层不同热阻组成的介质，其总热阻为各层热阻之和，因为通过每层的热传递功率都是相同的。因而总热导与各层热导满足： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}{\frac {1}{U}}={\frac {1}{U_{1}}}+{\frac {1}{U_{2}}}+{\frac {1}{U_{3}}}+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>U</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}{\frac {1}{U}}={\frac {1}{U_{1}}}+{\frac {1}{U_{2}}}+{\frac {1}{U_{3}}}+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e78bf10c738966c0ba4d95c2e8a07e8d530bfd74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.395ex; height:5.676ex;" alt="{\displaystyle {\big .}{\frac {1}{U}}={\frac {1}{U_{1}}}+{\frac {1}{U_{2}}}+{\frac {1}{U_{3}}}+\cdots }"></span></dd></dl> <p>所以对于多层介质： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}={\frac {A\,(-\Delta T)}{{\frac {\Delta x_{1}}{k_{1}}}+{\frac {\Delta x_{2}}{k_{2}}}+{\frac {\Delta x_{3}}{k_{3}}}+\cdots }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em"></mo> </mrow> </mrow> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}={\frac {A\,(-\Delta T)}{{\frac {\Delta x_{1}}{k_{1}}}+{\frac {\Delta x_{2}}{k_{2}}}+{\frac {\Delta x_{3}}{k_{3}}}+\cdots }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60f1d5104d8271d427c95dedb58079af49815d11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:37.21ex; height:8.009ex;" alt="{\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}={\frac {A\,(-\Delta T)}{{\frac {\Delta x_{1}}{k_{1}}}+{\frac {\Delta x_{2}}{k_{2}}}+{\frac {\Delta x_{3}}{k_{3}}}+\cdots }}.}"></span></dd></dl> <p>对于隔着夹层的两种流体之间的热传递，有时必须要考虑到附着与夹层上的流体<a href="/wiki/%E8%96%84%E8%86%9C" title="薄膜">薄膜</a>的热阻，由于其性质与<a href="/wiki/%E6%B9%8D%E6%B5%81" title="湍流">湍流</a>和<a href="/wiki/%E9%BB%8F%E5%BA%A6" title="黏度">粘滞</a>等复杂情况有关，这一流体薄膜非常难于界定。但是当我们考虑薄高热导夹层时，这一影响因素还是很重要的。 </p> <div class="mw-heading mw-heading2"><h2 id="化工方面的應用"><span id=".E5.8C.96.E5.B7.A5.E6.96.B9.E9.9D.A2.E7.9A.84.E6.87.89.E7.94.A8"></span>化工方面的应用</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%83%AD%E4%BC%A0%E5%AF%BC&action=edit&section=6" title="编辑章节：化工方面的应用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>几乎各种<a href="/wiki/%E5%8C%96%E5%AD%A6%E5%B7%A5%E4%B8%9A" title="化学工业">化学工业</a>都有热交换过程，需要热交换器，而根据热传导的方式和工艺要求，设计各种热交换器。 </p> <div class="mw-heading mw-heading2"><h2 id="相關條目"><span id=".E7.9B.B8.E9.97.9C.E6.A2.9D.E7.9B.AE"></span>相关条目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%83%AD%E4%BC%A0%E5%AF%BC&action=edit&section=7" title="编辑章节：相关条目"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a 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