{"id":20317,"date":"2018-11-12T18:33:44","date_gmt":"2018-11-12T18:33:44","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=20317"},"modified":"2023-02-14T12:23:12","modified_gmt":"2023-02-14T12:23:12","slug":"what-is-schmidt-number","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-schmidt-number\/","title":{"rendered":"What is Schmidt Number"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\">The <strong>Schmidt number<\/strong> is a dimensionless number, named after the German engineer Ernst Heinrich Wilhelm Schmidt (1892\u20131975). The <strong>Schmidt number<\/strong> is defined as the <strong>ratio<\/strong> of <strong>momentum diffusivity<\/strong> (kinematic viscosity) and <strong>mass diffusivity<\/strong>. It is\u00a0used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes.<\/div><\/div>\n<p>The <strong>Schmidt number<\/strong> describes the mass momentum transfer, and the equations can be seen below:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Schmidt-number-definition-formula.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20315\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Schmidt-number-definition-formula.png\" alt=\"Schmidt number - definition - formula\" width=\"577\" height=\"395\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Schmidt-number-definition-formula.png 577w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Schmidt-number-definition-formula-300x205.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/a><\/p>\n<p>where:<\/p>\n<ul>\n<li>\u03bd is the momentum diffusivity (kinematic viscosity) [m<sup>2<\/sup>\/s]<\/li>\n<li>\u03bc is the dynamic viscosity [N.s\/m<sup>2<\/sup>]<\/li>\n<li>D is the mass diffusivity [m<sup>2<\/sup>\/s]<\/li>\n<li>\u03c1 is the density [kg\/m<sup>3<\/sup>]<\/li>\n<\/ul>\n<p>It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. The <strong>Schmidt number<\/strong> corresponds to the Prandtl number in heat transfer. A Schmidt number of unity indicates that momentum and mass transfer by diffusion are comparable, and velocity and concentration boundary layers almost coincide with each other. Mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion).\u00a0Mass diffusion in liquids grows with temperature, roughly inversely proportional viscosity-variation with temperature, so that the Schmidt number, <strong>Sc=\u03bd\/D<\/strong>, quickly decreases with temperature. For example, the diffusion coefficient for ethanol in water is D<sub>ethanol,water<\/sub>=1.6\u22c510<sup>\u2212<\/sup><sup>9 <\/sup>\u00a0and gives the Schmidt number Sc = 540, which is typical for liquids.<\/p>\n<p>Diffusivity is encountered in Fick&#8217;s law, which states:<\/p>\n<p><em>If the concentration of a solute in one region is greater than in another of a solution, the solute diffuses from the region of higher concentration to the region of lower concentration, with a magnitude that is proportional to the concentration gradient.<\/em><\/p>\n<p>In one (spatial) dimension, the law is:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/Ficks-Law-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15177\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/Ficks-Law-equation.png\" alt=\"Ficks Law - equation\" width=\"133\" height=\"66\" \/><\/a><\/p>\n<p>where:<\/p>\n<ul>\n<li><em>J<\/em> is the diffusion flux,<\/li>\n<li><em>D<\/em> is the <strong>diffusion coefficient,<\/strong><\/li>\n<li><em>\u03c6<\/em> (for ideal mixtures) is the concentration.<\/li>\n<\/ul>\n<p>This law in <strong>nuclear reactor theory<\/strong> leads to the <a title=\"Neutron Diffusion Theory\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/\"><strong>diffusion approximation<\/strong><\/a>.<\/p>\n<h2>Turbulent Schmidt Number<\/h2>\n<p>Similarly, as for the Prandtl number, also <strong>Schmidt number<\/strong> has a special formula for <a title=\"Turbulent Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/turbulent-flow\/\"><strong>turbulent flow<\/strong><\/a>. The <strong>turbulent Schmidt number<\/strong> describes the ratio between the rates of turbulent transport of momentum and the turbulent transport of mass. The turbulent Schmidt number is commonly used in turbulence research and is defined as:<\/p>\n<p><strong><span style=\"font-size: 25px;\">Sc = \u03bd<sub>t<\/sub>\/K<\/span><\/strong><\/p>\n<p>where:<\/p>\n<ul>\n<li>\u03bd<sub>t <\/sub>is the eddy viscosity [m2\/s]<\/li>\n<li>K is the eddy diffusivity [m2\/s]<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Heat Transfer:<\/strong>\n<ol>\n<li>Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley &amp; Sons, Incorporated, 2011. ISBN: 9781118137253.<\/li>\n<li>Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866.<\/li>\n<li>Fundamentals of Heat and Mass Transfer.\u00a0C. P. Kothandaraman.\u00a0New Age International, 2006, ISBN:\u00a09788122417722.<\/li>\n<li>U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow.\u00a0DOE Fundamentals Handbook,\u00a0Volume\u00a02\u00a0of\u00a03.\u00a0May\u00a02016.<\/li>\n<\/ol>\n<p><strong>Nuclear and Reactor Physics:<\/strong><\/p>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics.\u00a0Clarendon Press; 1 edition, 1991, ISBN:\u00a0978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics.\u00a0Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory.\u00a0DOE Fundamentals Handbook,\u00a0Volume 1 and 2.\u00a0January\u00a01993.<\/li>\n<li>Paul Reuss, Neutron Physics.\u00a0EDP Sciences, 2008.\u00a0ISBN: 978-2759800414.<\/li>\n<\/ol>\n<p><strong><\/strong><strong>Advanced Reactor Physics:<\/strong><\/p>\n<ol>\n<li>K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/li>\n<li>K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.<\/li>\n<li><span style=\"font-weight: 400;\">D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.\u00a0<\/span><\/li>\n<li>E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Introduction to Heat Transfer<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>The Schmidt number describes the mass momentum transfer, and the equations can be seen below: where: \u03bd is the momentum diffusivity (kinematic viscosity) [m2\/s] \u03bc is the dynamic viscosity [N.s\/m2] D is the mass diffusivity [m2\/s] \u03c1 is the density [kg\/m3] It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. &#8230; <a title=\"What is Schmidt Number\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-schmidt-number\/\" aria-label=\"More on What is Schmidt Number\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":20296,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20317"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=20317"}],"version-history":[{"count":3,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20317\/revisions"}],"predecessor-version":[{"id":37248,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20317\/revisions\/37248"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20296"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=20317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}