{"id":52203,"date":"2020-02-17T08:51:40","date_gmt":"2020-02-17T07:51:40","guid":{"rendered":"https:\/\/www.thermal-engineering.org\/quest-ce-que-le-nombre-nusselt-definition\/"},"modified":"2021-05-28T20:24:39","modified_gmt":"2021-05-28T19:24:39","slug":"quest-ce-que-le-nombre-nusselt-definition","status":"publish","type":"post","link":"https:\/\/www.thermal-engineering.org\/fr\/quest-ce-que-le-nombre-nusselt-definition\/","title":{"rendered":"Qu&#8217;est-ce que le nombre Nusselt &#8211; D\u00e9finition"},"content":{"rendered":"<div class=\"su-quote su-quote-style-default\">\n<div class=\"su-quote-inner su-clearfix\">Le nombre Nusselt est un nombre sans dimension, nomm\u00e9 d&#8217;apr\u00e8s un ing\u00e9nieur allemand Wilhelm Nusselt.\u00a0le nombre de Nusselt repr\u00e9sente l&#8217;am\u00e9lioration du transfert de chaleur \u00e0 travers une couche fluide \u00e0 la suite de la convection.\u00a0G\u00e9nie thermique<\/div>\n<\/div>\n<div class=\"su-divider su-divider-style-dotted\"><\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Nombre de Nusselt<\/h2>\n<p>Le\u00a0<strong>nombre Nusselt<\/strong>\u00a0est un nombre sans dimension, nomm\u00e9 d&#8217;apr\u00e8s un ing\u00e9nieur allemand Wilhelm Nusselt.\u00a0Le\u00a0<strong>nombre de Nusselt<\/strong>\u00a0est \u00e9troitement li\u00e9 au\u00a0<a title=\"Qu'est-ce que le num\u00e9ro P\u00e9clet\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-peclet-number\/\">nombre de P\u00e9clet<\/a>\u00a0et les deux nombres sont utilis\u00e9s pour d\u00e9crire le rapport de l&#8217;\u00a0<strong>\u00e9nergie thermique convect\u00e9e<\/strong>\u00a0au fluide \u00e0 l&#8217;\u00a0<strong>\u00e9nergie thermique conduite<\/strong>\u00a0dans le fluide.\u00a0<strong>Le nombre de Nusselt<\/strong>\u00a0est \u00e9gal au\u00a0<strong>gradient de temp\u00e9rature<\/strong>\u00a0sans dimension\u00a0\u00e0 la surface, et il fournit une mesure du transfert de chaleur par convection se produisant \u00e0 la surface.\u00a0La composante conductrice est mesur\u00e9e dans les m\u00eames conditions que la convection thermique mais avec un fluide stagnant.\u00a0Le\u00a0<strong>num\u00e9ro de Nusselt<\/strong>est \u00e0 la couche limite thermique ce que le coefficient de frottement est \u00e0 la couche limite de vitesse.\u00a0Ainsi, le nombre de Nusselt est d\u00e9fini comme:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Nusselt-Number-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-20391 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Nusselt-Number-definition-300x270.png\" alt=\"Nombre de Nusselt - d\u00e9finition\" width=\"300\" height=\"270\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Nusselt-Number-definition-300x270.png\" \/><\/a><\/p>\n<p>o\u00f9:<\/p>\n<p><strong><em>k\u00a0<\/em><\/strong><strong><em><sub>f<\/sub><\/em><\/strong>\u00a0est<a href=\"https:\/\/www.thermal-engineering.org\/what-is-thermal-conductivity-definition\/\"><strong>\u00a0la conductivit\u00e9 thermique<\/strong><\/a>\u00a0du fluide [W \/ mK]\n<p><strong><em>L<\/em><\/strong>\u00a0est la<strong>\u00a0longueur caract\u00e9ristique<\/strong><\/p>\n<p><strong><em>h<\/em><\/strong>\u00a0est le<strong>\u00a0coefficient de transfert de chaleur par convection<\/strong>\u00a0[W \/ m<sup>\u00a02<\/sup>\u00a0.K]\n<p>\u00c0 titre d&#8217;illustration, consid\u00e9rons une couche fluide d&#8217;\u00e9paisseur\u00a0<strong>L<\/strong>\u00a0et de diff\u00e9rence de temp\u00e9rature\u00a0<strong>\u0394T<\/strong>\u00a0.\u00a0Le transfert de chaleur \u00e0 travers la couche de fluide se fera par convection lorsque le fluide implique un certain mouvement et par conduction lorsque la couche de fluide est immobile.<\/p>\n<p>En cas de\u00a0<a title=\"Conduction thermique - Conduction thermique\" href=\"https:\/\/www.thermal-engineering.org\/what-is-thermal-conduction-heat-conduction-definition\/\">conduction<\/a>\u00a0, le\u00a0<a title=\"Densit\u00e9 de flux thermique - Flux thermique\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/heat-flux-density-thermal-flux\/\">flux de chaleur<\/a>\u00a0peut \u00eatre calcul\u00e9 en utilisant\u00a0<a title=\"Loi de Fourier de la conduction thermique\" href=\"https:\/\/www.thermal-engineering.org\/what-is-fouriers-law-of-thermal-conduction-definition\/\">la loi de conduction de Fourier<\/a>\u00a0.\u00a0En cas de convection, le flux de chaleur peut \u00eatre calcul\u00e9 en utilisant la loi de Newton du refroidissement.\u00a0Prendre leur rapport donne:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/nusselt-number-convection-to-conduction.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20394 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/nusselt-number-convection-to-conduction.png\" alt=\"nombre de nusselt - convection \u00e0 conduction\" width=\"353\" height=\"227\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/nusselt-number-convection-to-conduction.png\" \/><\/a><\/p>\n<p>L&#8217;\u00e9quation pr\u00e9c\u00e9dente d\u00e9finit le\u00a0<strong>nombre de Nusselt<\/strong>\u00a0.\u00a0Par cons\u00e9quent, le\u00a0<strong>nombre de Nusselt<\/strong>\u00a0repr\u00e9sente l&#8217;am\u00e9lioration du transfert de chaleur \u00e0 travers une couche de fluide en raison de la\u00a0<strong>convection relative \u00e0 la conduction \u00e0<\/strong>\u00a0travers la m\u00eame couche de fluide.\u00a0Un\u00a0<strong>nombre Nusselt<\/strong>\u00a0de\u00a0<strong>Nu = 1<\/strong>\u00a0pour une couche fluide repr\u00e9sente le transfert de chaleur \u00e0 travers la couche par\u00a0<strong>conduction pure<\/strong>\u00a0.\u00a0Plus le\u00a0<strong>nombre de Nusselt est \u00e9lev\u00e9<\/strong>\u00a0, plus la convection est efficace.\u00a0Un nombre de Nusselt plus grand correspond \u00e0 une convection plus efficace, avec un \u00e9coulement turbulent typiquement dans la gamme 100\u20131000.\u00a0Pour un \u00e9coulement turbulent, le\u00a0<strong>nombre de Nusselt<\/strong>\u00a0est g\u00e9n\u00e9ralement fonction du\u00a0<a title=\"Le num\u00e9ro de Reynold\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">nombre de Reynolds<\/a>\u00a0et du<a title=\"Qu'est-ce que le num\u00e9ro Prandtl\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">Num\u00e9ro Prandtl<\/a>\u00a0.<\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Corr\u00e9lations &#8211; D\u00e9bit de fluide monophas\u00e9<\/h2>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-accordion\">\n<div class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\">\n<ul>\n<li class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\">D\u00e9bit laminaire externe<\/li>\n<li class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\">D\u00e9bit laminaire interne<\/li>\n<li class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\">D\u00e9bit turbulent externe<\/li>\n<li class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\">D\u00e9bit turbulent interne &#8211; Dittus-Boelter<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<h2>Nombre de Nusselt pour les r\u00e9acteurs \u00e0 m\u00e9tal liquide<\/h2>\n<p>Voir aussi:\u00a0<a title=\"Nombre de Nusselt pour les r\u00e9acteurs \u00e0 m\u00e9tal liquide\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-nusselt-number\/nusselt-number-for-liquid-metal-reactors\/\">Nombre de Nusselt pour les r\u00e9acteurs \u00e0 m\u00e9tal liquide<\/a><\/p>\n<p>Pour\u00a0<a title=\"M\u00e9taux liquides\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/materials-nuclear-engineering\/liquid-metals\/\"><strong>les m\u00e9taux liquides,<\/strong><\/a>\u00a0le\u00a0<a title=\"Qu'est-ce que le num\u00e9ro Prandtl\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\"><strong>nombre de Prandtl<\/strong>\u00a0<\/a>est tr\u00e8s faible, g\u00e9n\u00e9ralement compris entre\u00a0<strong>0,01 et 0,001.\u00a0<\/strong>Cela signifie que la\u00a0<a href=\"https:\/\/www.thermal-engineering.org\/what-is-thermal-diffusivity-definition\/\"><strong>diffusivit\u00e9 thermique<\/strong><\/a>\u00a0, qui est li\u00e9e au taux de\u00a0<a href=\"https:\/\/www.thermal-engineering.org\/what-is-thermal-conduction-heat-conduction-definition\/\"><strong>transfert<\/strong><\/a>\u00a0de\u00a0<a href=\"https:\/\/www.thermal-engineering.org\/what-is-thermal-conduction-heat-conduction-definition\/\"><strong>chaleur par conduction<\/strong><\/a>\u00a0,\u00a0<strong>domine<\/strong>\u00a0sans ambigu\u00eft\u00e9\u00a0.\u00a0Cette tr\u00e8s grande diffusivit\u00e9 thermique r\u00e9sulte d&#8217;une tr\u00e8s forte conductivit\u00e9 thermique des m\u00e9taux, qui est environ 100 fois sup\u00e9rieure \u00e0 celle de l&#8217;eau.\u00a0Le\u00a0<strong>nombre de Prandtl<\/strong>\u00a0pour le sodium \u00e0 une temp\u00e9rature de fonctionnement typique dans les r\u00e9acteurs rapides refroidis au sodium est d&#8217;environ 0,004.\u00a0Dans ce cas, le d\u00e9veloppement de la couche limite thermique est beaucoup plus rapide que celui de la couche limite de vitesse (\u03b4\u00a0<sub>t<\/sub>\u00a0&gt;&gt; \u03b4), et il est raisonnable de supposer une vitesse uniforme dans toute la couche limite thermique.<\/p>\n<p>Les coefficients de transfert de chaleur pour le d\u00e9bit de sodium \u00e0 travers le canal de carburant sont bas\u00e9s sur le\u00a0<strong>nombre de Prandtl<\/strong>\u00a0et le\u00a0<strong><a title=\"Qu'est-ce que le num\u00e9ro P\u00e9clet\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-peclet-number\/\">nombre de P\u00e9clet<\/a>\u00a0.\u00a0<\/strong>Le pas au diam\u00e8tre (P \/ D) entre \u00e9galement dans de nombreux calculs de transfert de chaleur dans les r\u00e9acteurs \u00e0 m\u00e9tal liquide.\u00a0<strong>Les corr\u00e9lations de transfert de chaleur par convection<\/strong>\u00a0sont g\u00e9n\u00e9ralement pr\u00e9sent\u00e9es en termes de\u00a0<strong>nombre<\/strong>\u00a0de\u00a0<strong>Nusselt par rapport au nombre de P\u00e9clet<\/strong>\u00a0.\u00a0Le nombre typique de P\u00e9clet pour un fonctionnement normal est de 150 \u00e0 300 dans les grappes de combustible.\u00a0Comme pour d&#8217;autres r\u00e9gimes d&#8217;\u00e9coulement, le nombre de Nusselt et une corr\u00e9lation donn\u00e9e peuvent \u00eatre utilis\u00e9s pour d\u00e9terminer le coefficient de transfert de chaleur par convection.<\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\"><\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<h2>Exemple &#8211; Nombre de Nusselt &#8211; Temp\u00e9rature de surface du rev\u00eatement<\/h2>\n<p><strong><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Convection-Convective-Heat-Transfer-example.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20406 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Convection-Convective-Heat-Transfer-example-275x300.png\" alt=\"Convection - Transfert de chaleur par convection\" width=\"275\" height=\"300\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Convection-Convective-Heat-Transfer-example-275x300.png\" \/><\/a>Le rev\u00eatement<\/strong>\u00a0est la couche externe des crayons de combustible, se trouvant entre le\u00a0<strong>liquide de refroidissement<\/strong>\u00a0du\u00a0<strong>r\u00e9acteur<\/strong>\u00a0et le\u00a0<a title=\"Combustible nucl\u00e9aire\" href=\"https:\/\/www.nuclear-power.com\/nuclear-power-plant\/nuclear-fuel\/\"><strong>combustible nucl\u00e9aire<\/strong>\u00a0<\/a>(c&#8217;est-\u00e0-dire\u00a0<strong>les pastilles de combustible<\/strong>\u00a0).\u00a0Il est fait d&#8217;un mat\u00e9riau r\u00e9sistant \u00e0 la corrosion avec une faible section d&#8217;absorption pour\u00a0<a title=\"Neutron thermique\" href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">les neutrons thermiques<\/a>\u00a0, g\u00e9n\u00e9ralement en\u00a0<strong>alliage de zirconium<\/strong>\u00a0.\u00a0<strong>Le rev\u00eatement<\/strong>\u00a0emp\u00eache les produits de fission radioactifs de s&#8217;\u00e9chapper de la matrice de combustible dans le liquide de refroidissement du r\u00e9acteur et de le contaminer.\u00a0Le rev\u00eatement constitue l&#8217;un des obstacles \u00e0 l&#8217;\u00a0approche de\u00a0\u00ab\u00a0<strong>d\u00e9fense en profondeur<\/strong>\u00a0\u00bb, donc sa\u00a0<strong>refroidissabilit\u00e9<\/strong>\u00a0est l&#8217;un des aspects cl\u00e9s de la s\u00e9curit\u00e9.<\/p>\n<p>Consid\u00e9rons la gaine de combustible du rayon int\u00e9rieur\u00a0<strong>r\u00a0<\/strong><strong><sub>Zr, 2<\/sub><\/strong><strong>\u00a0= 0,408 cm<\/strong>\u00a0et du rayon ext\u00e9rieur\u00a0<strong>r\u00a0<\/strong><strong><sub>Zr, 1<\/sub><\/strong><strong>\u00a0= 0,465 cm<\/strong>\u00a0.\u00a0Par rapport \u00e0 la pastille de combustible, il n&#8217;y a presque pas de g\u00e9n\u00e9ration de chaleur dans la gaine de combustible (la gaine est\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/fission\/energy-release-from-fission\/\">l\u00e9g\u00e8rement chauff\u00e9e par rayonnement<\/a>\u00a0).\u00a0Toute la chaleur g\u00e9n\u00e9r\u00e9e dans le carburant doit \u00eatre transf\u00e9r\u00e9e par\u00a0<a title=\"Conduction thermique - Conduction thermique\" href=\"https:\/\/www.thermal-engineering.org\/what-is-thermal-conduction-heat-conduction-definition\/\"><strong>conduction \u00e0<\/strong><\/a>\u00a0travers le rev\u00eatement et, par cons\u00e9quent, la surface int\u00e9rieure est plus chaude que la surface ext\u00e9rieure.<\/p>\n<p>Suppose que:<\/p>\n<ul>\n<li>le diam\u00e8tre ext\u00e9rieur du rev\u00eatement est:\u00a0<strong>d = 2 xr\u00a0<sub>Zr, 1<\/sub>\u00a0= 9,3 mm<\/strong><\/li>\n<li>le pas des goupilles de combustible est:\u00a0<strong>p = 13 mm<\/strong><\/li>\n<li>la\u00a0<a title=\"Conductivit\u00e9 thermique\" href=\"https:\/\/www.thermal-engineering.org\/what-is-thermal-conductivity-definition\/\">conductivit\u00e9 thermique<\/a>\u00a0de l&#8217;\u00a0<a title=\"Liquide satur\u00e9 et sous-refroidi\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturated-and-subcooled-liquid\/\">eau satur\u00e9e<\/a>\u00a0\u00e0 300 \u00b0 C est:\u00a0<strong>k\u00a0<\/strong><strong><sub>H2O<\/sub><\/strong><strong>\u00a0= 0,545 W \/ mK<\/strong><\/li>\n<li>la viscosit\u00e9 dynamique de l&#8217;eau satur\u00e9e \u00e0 300 \u00b0 C est:\u00a0<strong>\u03bc = 0,0000859 Ns \/ m\u00a0<\/strong><strong><sup>2<\/sup><\/strong><\/li>\n<li>la\u00a0<a title=\"Qu'est-ce que la densit\u00e9 - Physique\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-density-physics\/\">densit\u00e9<\/a>\u00a0du fluide\u00a0est:\u00a0<strong>\u03c1 = 714 kg \/ m\u00a0<\/strong><strong><sup>3<\/sup><\/strong><\/li>\n<li>la\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-capacity\/\"><strong>chaleur sp\u00e9cifique<\/strong><\/a>\u00a0est:\u00a0<strong>c\u00a0<\/strong><strong><sub>p<\/sub><\/strong><strong>\u00a0= 5,65 kJ \/ kg.K<\/strong><\/li>\n<li>la vitesse d&#8217;\u00e9coulement du c\u0153ur est constante et \u00e9gale \u00e0\u00a0<strong>V\u00a0<\/strong><strong><sub>c\u0153ur<\/sub><\/strong><strong>\u00a0= 5 m \/ s<\/strong><\/li>\n<li>la temp\u00e9rature du liquide de refroidissement du r\u00e9acteur \u00e0 cette coordonn\u00e9e axiale est:\u00a0<strong>T en\u00a0<\/strong><strong><sub>vrac<\/sub><\/strong><strong>\u00a0= 296 \u00b0 C<\/strong><\/li>\n<li>le taux de chaleur lin\u00e9aire du combustible est\u00a0<strong>q\u00a0<\/strong><strong><sub>L<\/sub><\/strong><strong>\u00a0= 300 W \/ cm<\/strong>\u00a0(F\u00a0<sub>Q<\/sub>\u00a0\u2248 2.0) et donc le taux de chaleur volum\u00e9trique est q\u00a0<sub>V<\/sub>\u00a0= 597 x 10\u00a0<sup>6<\/sup>\u00a0W \/ m\u00a0<sup>3<\/sup><\/li>\n<\/ul>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Hydraulic-Diameter-Fuel-Channel.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20407 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Hydraulic-Diameter-Fuel-Channel-254x300.png\" alt=\"Diam\u00e8tre hydraulique - Canal de carburant\" width=\"254\" height=\"300\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Hydraulic-Diameter-Fuel-Channel-254x300.png\" \/><\/a>Calculez le nombre de\u00a0<a title=\"Qu'est-ce que le num\u00e9ro Prandtl\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">Prandtl<\/a>\u00a0,\u00a0<a title=\"Le num\u00e9ro de Reynold\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">Reynolds<\/a>\u00a0et Nusselt pour ce r\u00e9gime d&#8217;\u00e9coulement (\u00e9coulement turbulent forc\u00e9 interne) \u00e0 l&#8217;int\u00e9rieur du r\u00e9seau rectangulaire de combustible (canal de combustible), puis calculez le\u00a0<strong>coefficient de transfert de chaleur<\/strong>\u00a0et enfin la\u00a0<strong>temp\u00e9rature de surface de<\/strong>\u00a0la\u00a0<strong>gaine<\/strong>\u00a0,\u00a0<strong>T\u00a0<sub>Zr, 1<\/sub><\/strong>\u00a0.<\/p>\n<p>Pour calculer la\u00a0<strong>temp\u00e9rature de surface de<\/strong>\u00a0la\u00a0<strong>gaine<\/strong>\u00a0, nous devons calculer le nombre de\u00a0<strong>Prandtl<\/strong>\u00a0,\u00a0<strong>Reynolds<\/strong>\u00a0et\u00a0<strong>Nusselt<\/strong>\u00a0, car le transfert de chaleur pour ce r\u00e9gime d&#8217;\u00e9coulement peut \u00eatre d\u00e9crit par l&#8217;\u00a0<strong>\u00e9quation de Dittus-Boelter<\/strong>\u00a0, qui est:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Dittus-Boelter-Equation-Formula.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20409 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Dittus-Boelter-Equation-Formula.png\" alt=\"\u00c9quation Dittus-Boelter - Formule\" width=\"556\" height=\"278\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Dittus-Boelter-Equation-Formula.png\" \/><\/a><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Calcul du nombre de Prandtl<\/h2>\n<p>Pour calculer le\u00a0<a title=\"Qu'est-ce que le num\u00e9ro Prandtl\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">nombre de Prandtl<\/a>\u00a0, nous devons savoir:<\/p>\n<ul>\n<li>la conductivit\u00e9 thermique de l&#8217;eau satur\u00e9e \u00e0 300 \u00b0 C est:\u00a0<strong>k\u00a0<\/strong><strong><sub>H2O<\/sub><\/strong><strong>\u00a0= 0,545 W \/ mK<\/strong><\/li>\n<li>la viscosit\u00e9 dynamique de l&#8217;eau satur\u00e9e \u00e0 300 \u00b0 C est:\u00a0<strong>\u03bc = 0,0000859 Ns \/ m\u00a0<\/strong><strong><sup>2<\/sup><\/strong><\/li>\n<li>la\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-capacity\/\"><strong>chaleur sp\u00e9cifique<\/strong><\/a>\u00a0est:\u00a0<strong>c\u00a0<\/strong><strong><sub>p<\/sub><\/strong><strong>\u00a0= 5,65 kJ \/ kg.K<\/strong><\/li>\n<\/ul>\n<p>Notez que tous ces param\u00e8tres diff\u00e8rent de mani\u00e8re significative pour l&#8217;eau \u00e0 300 \u00b0 C de ceux \u00e0 20 \u00b0 C.\u00a0Le nombre de Prandtl pour l&#8217;\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/\">eau<\/a>\u00a0\u00e0 20 \u00b0 C est d&#8217;environ\u00a0<strong>6,91.\u00a0<\/strong>Le nombre de Prandtl pour le liquide de refroidissement du r\u00e9acteur \u00e0 300 \u00b0 C est alors:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/prandtl-number-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20411 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/prandtl-number-example.png\" alt=\"num\u00e9ro prandtl - exemple\" width=\"469\" height=\"80\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/prandtl-number-example.png\" \/><\/a><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Calcul du nombre de Reynolds<\/h2>\n<p>Pour calculer le nombre de Reynolds, nous devons savoir:<\/p>\n<ul>\n<li>le diam\u00e8tre ext\u00e9rieur du rev\u00eatement est:\u00a0<strong>d = 2 xr\u00a0<sub>Zr, 1<\/sub>\u00a0= 9,3 mm<\/strong>\u00a0(pour calculer le diam\u00e8tre hydraulique)<\/li>\n<li>le pas des goupilles de combustible est:\u00a0<strong>p = 13 mm<\/strong>\u00a0\u00a0(pour calculer le diam\u00e8tre hydraulique)<\/li>\n<li>la viscosit\u00e9 dynamique de l&#8217;eau satur\u00e9e \u00e0 300 \u00b0 C est:\u00a0<strong>\u03bc = 0,0000859 Ns \/ m\u00a0<\/strong><strong><sup>2<\/sup><\/strong><\/li>\n<li>la densit\u00e9 du fluide est:\u00a0<strong>\u03c1 = 714 kg \/ m\u00a0<\/strong><strong><sup>3<\/sup><\/strong><\/li>\n<\/ul>\n<p><strong>Le diam\u00e8tre hydraulique, D\u00a0<\/strong><strong><sub>h<\/sub><\/strong>\u00a0, est un terme couramment utilis\u00e9 pour g\u00e9rer le d\u00e9bit dans\u00a0<strong>des tubes et canaux non circulaires<\/strong>\u00a0.\u00a0Le\u00a0<strong>diam\u00e8tre hydraulique du canal de carburant<\/strong>\u00a0,\u00a0<em>D\u00a0<\/em><em><sub>h<\/sub><\/em>\u00a0, est \u00e9gal \u00e0 13,85 mm.<\/p>\n<p>Voir aussi:\u00a0<a title=\"Diam\u00e8tre hydraulique\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/fluid-dynamics\/internal-flow\/hydraulic-diameter-2\/\">Diam\u00e8tre hydraulique<\/a><\/p>\n<p>Le\u00a0<strong>nombre de Reynolds<\/strong>\u00a0\u00e0 l&#8217;int\u00e9rieur du canal de carburant est alors \u00e9gal \u00e0:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/reynolds-number-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20412 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/reynolds-number-example.png\" alt=\"nombre de reynolds - exemple\" width=\"593\" height=\"78\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/reynolds-number-example.png\" \/><\/a><\/p>\n<p>Cela satisfait pleinement les\u00a0<a title=\"\u00c9coulement turbulent\" href=\"https:\/\/www.thermal-engineering.org\/what-is-turbulent-flow-definition\/\"><strong>conditions turbulentes<\/strong><\/a>\u00a0.<\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Calcul du nombre de Nusselt \u00e0 l&#8217;aide de l&#8217;\u00e9quation de Dittus-Boelter<\/h2>\n<p>Pour un \u00e9coulement turbulent pleinement d\u00e9velopp\u00e9 (hydrodynamiquement et thermiquement) dans un tube circulaire lisse, le\u00a0<strong>nombre de Nusselt<\/strong>\u00a0local\u00a0peut \u00eatre obtenu \u00e0 partir de l&#8217;\u00a0<strong>\u00e9quation<\/strong>\u00a0bien connue de\u00a0<strong>Dittus ?? Boelter<\/strong>\u00a0.<\/p>\n<p>Pour calculer le\u00a0<strong>nombre de Nusselt<\/strong>\u00a0, nous devons savoir:<\/p>\n<ul>\n<li>le\u00a0<a title=\"Le num\u00e9ro de Reynold\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">nombre de Reynolds<\/a>\u00a0, qui est\u00a0<strong>Re\u00a0<sub>Dh<\/sub>\u00a0= 575600<\/strong><\/li>\n<li>le\u00a0<a title=\"Qu'est-ce que le num\u00e9ro Prandtl\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">nombre de Prandtl<\/a>\u00a0, qui est\u00a0<strong>Pr = 0,89<\/strong><\/li>\n<\/ul>\n<p>Le\u00a0<strong>nombre de Nusselt<\/strong>\u00a0pour la convection forc\u00e9e \u00e0 l&#8217;int\u00e9rieur du canal de carburant est alors \u00e9gal \u00e0:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/nusselt-number-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20413 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/nusselt-number-example.png\" alt=\"num\u00e9ro nusselt - exemple\" width=\"387\" height=\"58\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/nusselt-number-example.png\" \/><\/a><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Calcul du coefficient de transfert de chaleur et de la temp\u00e9rature de surface du rev\u00eatement, T\u00a0<sub>Zr, 1<\/sub><\/h2>\n<p>Une connaissance d\u00e9taill\u00e9e de la g\u00e9om\u00e9trie, des param\u00e8tres des fluides, du rayon ext\u00e9rieur du rev\u00eatement, du taux de chaleur lin\u00e9aire, du coefficient de transfert de chaleur par convection nous permet de calculer la diff\u00e9rence de temp\u00e9rature\u00a0<strong>\u2206T<\/strong>\u00a0entre le liquide de refroidissement (T en\u00a0<sub>vrac<\/sub>\u00a0) et la surface du rev\u00eatement (T\u00a0<sub>Zr, 1<\/sub>\u00a0).<\/p>\n<p>Pour calculer la temp\u00e9rature de surface de la gaine, il faut savoir:<\/p>\n<ul>\n<li>le diam\u00e8tre ext\u00e9rieur du rev\u00eatement est: d = 2 x\u00a0<strong>r\u00a0<\/strong><strong><sub>Zr, 1<\/sub><\/strong><strong>\u00a0= 9,3 mm<\/strong><\/li>\n<li>le nombre de Nusselt, qui est\u00a0<strong>Nu\u00a0<\/strong><strong><sub>Dh<\/sub><\/strong><strong>\u00a0= 890<\/strong><\/li>\n<li>le diam\u00e8tre hydraulique du canal de carburant est:\u00a0<strong><em>D\u00a0<\/em><\/strong><strong><em><sub>h<\/sub><\/em><\/strong><strong>\u00a0= 13,85 mm<\/strong><\/li>\n<li>la conductivit\u00e9 thermique du liquide de refroidissement du r\u00e9acteur (300 \u00b0 C) est:\u00a0<strong>k\u00a0<\/strong><strong><sub>H2O<\/sub><\/strong><strong>\u00a0= 0,545 W \/ mK<\/strong><\/li>\n<li>la temp\u00e9rature en vrac du liquide de refroidissement du r\u00e9acteur \u00e0 cette coordonn\u00e9e axiale est:\u00a0<strong>T en\u00a0<\/strong><strong><sub>vrac<\/sub><\/strong><strong>\u00a0= 296 \u00b0 C<\/strong><\/li>\n<li>le taux de chaleur lin\u00e9aire du combustible est:\u00a0<strong>q\u00a0<\/strong><strong><sub>L<\/sub><\/strong><strong>\u00a0= 300 W \/ cm<\/strong>\u00a0(F\u00a0<sub>Q<\/sub>\u00a0\u2248 2.0)<\/li>\n<\/ul>\n<p>Le coefficient de transfert de chaleur par convection,\u00a0<strong>h<\/strong>\u00a0, est donn\u00e9 directement par la d\u00e9finition du nombre de Nusselt:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/convective-heat-transfer-coefficient-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20410 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/convective-heat-transfer-coefficient-example.png\" alt=\"coefficient de transfert de chaleur par convection - exemple\" width=\"619\" height=\"92\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/convective-heat-transfer-coefficient-example.png\" \/><\/a><\/p>\n<p>Enfin, nous pouvons calculer la temp\u00e9rature de surface de la gaine (T\u00a0<sub>Zr, 1<\/sub>\u00a0) simplement en utilisant la\u00a0<strong>loi de Newton du refroidissement<\/strong>\u00a0:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Newton-law-of-cooling-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20408 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Newton-law-of-cooling-example.png\" alt=\"Loi de Newton du refroidissement - exemple\" width=\"377\" height=\"369\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Newton-law-of-cooling-example.png\" \/><\/a><\/p>\n<p>Pour les REP en fonctionnement normal, il y a une\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturated-and-subcooled-liquid\/\">eau liquide comprim\u00e9e \u00e0 l&#8217;<\/a>\u00a0int\u00e9rieur du c\u0153ur du r\u00e9acteur, des boucles et des g\u00e9n\u00e9rateurs de vapeur.\u00a0La pression est maintenue \u00e0 environ\u00a0<strong>16 MPa<\/strong>\u00a0.\u00a0\u00c0 cette pression, l&#8217;eau bout \u00e0 environ\u00a0<strong>350 \u00b0 C<\/strong>\u00a0(662 \u00b0 F).\u00a0Comme on peut le voir, la temp\u00e9rature de surface T\u00a0<sub>Zr, 1<\/sub>\u00a0= 325 \u00b0 C garantit que m\u00eame une \u00e9bullition sous-refroidie ne se produit pas.\u00a0Notez que l&#8217;\u00e9bullition sous-refroidie n\u00e9cessite T\u00a0<sub>Zr, 1<\/sub>\u00a0= T\u00a0<sub>sat<\/sub>\u00a0.\u00a0\u00c9tant donn\u00e9 que les temp\u00e9ratures d&#8217;entr\u00e9e de l&#8217;eau sont g\u00e9n\u00e9ralement d&#8217;environ\u00a0<strong>290 \u00b0 C<\/strong>(554 \u00b0 F), il est \u00e9vident que cet exemple correspond \u00e0 la partie inf\u00e9rieure du noyau.\u00a0Aux altitudes plus \u00e9lev\u00e9es du c\u0153ur, la temp\u00e9rature globale peut atteindre jusqu&#8217;\u00e0 330 \u00b0 C.\u00a0La diff\u00e9rence de temp\u00e9rature de 29 \u00b0 C peut entra\u00eener une \u00e9bullition sous-refroidie (330 \u00b0 C + 29 \u00b0 C&gt; 350 \u00b0 C).\u00a0D&#8217;autre part, l&#8217;\u00a0<strong>\u00e9bullition nucl\u00e9\u00e9e<\/strong>\u00a0\u00e0 la surface perturbe efficacement la couche stagnante et, par cons\u00e9quent, l&#8217;\u00e9bullition nucl\u00e9\u00e9e augmente consid\u00e9rablement la capacit\u00e9 d&#8217;une surface \u00e0 transf\u00e9rer l&#8217;\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/\">\u00e9nergie thermique<\/a>\u00a0au fluide en vrac.\u00a0En cons\u00e9quence, le coefficient de transfert de chaleur convectif augmente consid\u00e9rablement et donc \u00e0 des altitudes plus \u00e9lev\u00e9es, la diff\u00e9rence de temp\u00e9rature (T\u00a0<sub>Zr, 1<\/sub>\u00a0&#8211; T en\u00a0<sub>vrac<\/sub>\u00a0) diminue consid\u00e9rablement.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;.<\/p>\n<p>Cet article est bas\u00e9 sur la traduction automatique de l&#8217;article original en anglais. Pour plus d&#8217;informations, voir l&#8217;article en anglais. Pouvez vous nous aider Si vous souhaitez corriger la traduction, envoyez-la \u00e0 l&#8217;adresse: translations@nuclear-power.com ou remplissez le formulaire de traduction en ligne. Nous appr\u00e9cions votre aide, nous mettrons \u00e0 jour la traduction le plus rapidement possible. Merci<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Le nombre Nusselt est un nombre sans dimension, nomm\u00e9 d&#8217;apr\u00e8s un ing\u00e9nieur allemand Wilhelm Nusselt.\u00a0le nombre de Nusselt repr\u00e9sente l&#8217;am\u00e9lioration du transfert de chaleur \u00e0 travers une couche fluide \u00e0 la suite de la convection.\u00a0G\u00e9nie thermique Nombre de Nusselt Le\u00a0nombre Nusselt\u00a0est un nombre sans dimension, nomm\u00e9 d&#8217;apr\u00e8s un ing\u00e9nieur allemand Wilhelm Nusselt.\u00a0Le\u00a0nombre de Nusselt\u00a0est \u00e9troitement &#8230; <a title=\"Qu&#8217;est-ce que le nombre Nusselt &#8211; D\u00e9finition\" class=\"read-more\" href=\"https:\/\/www.thermal-engineering.org\/fr\/quest-ce-que-le-nombre-nusselt-definition\/\" aria-label=\"En savoir plus sur Qu&#8217;est-ce que le nombre Nusselt &#8211; D\u00e9finition\">Lire la suite<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[8],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v15.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Qu&#039;est-ce que le nombre de Nusselt - D\u00e9finition<\/title>\n<meta name=\"description\" content=\"Le nombre de Nusselt est un nombre sans dimension, nomm\u00e9 d&#039;apr\u00e8s l&#039;ing\u00e9nieur allemand Wilhelm Nusselt. le nombre de Nusselt repr\u00e9sente l&#039;am\u00e9lioration du transfert de chaleur \u00e0 travers une couche de fluide r\u00e9sultant de la convection. 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