{"id":388076,"date":"2024-10-04T04:35:26","date_gmt":"2024-10-04T04:35:26","guid":{"rendered":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/"},"modified":"2024-10-28T06:56:33","modified_gmt":"2024-10-28T06:56:33","slug":"question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide","status":"answered","type":"topic","link":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/","title":{"rendered":"Question about the maxwell-stefan equations written in fluent theory guide"},"content":{"rendered":"<p>&lt;p&gt;Hi, I have question about maxwell-stefan equations written in the fluent theory guide Fluent 2024 R2.&lt;\/p&gt;&lt;p&gt;In chapter 7.1.1.3.2, there are definitions and equations related to Maxwell-Stefan equations.&nbsp;&lt;\/p&gt;&lt;p&gt;My question is the formula $M_{w,m}$ which is defined as $\\sum_{i=1}^N\\frac{Y_i}{M_{w,i}}$, where $Y_i$ is a mass fraction of $i$th species, and $M_{w,i}$ is a molecular weight of $i$th species.&lt;\/p&gt;&lt;p&gt;Also, there is a remark related to the formula; &#8216;a subscript used to define a mean molecular weight in the mixture&#8217;.&lt;\/p&gt;&lt;p&gt;I wonder if the expression is defined properly.&lt;\/p&gt;&lt;p&gt;In my thought, $M_{w,m}$ should be inverse of $\\sum_{i=1}^N\\frac{Y_i}{M_{w,i}}$.&nbsp;&lt;\/p&gt;&lt;p&gt;The proof is as follows. By using the related quantities between mass fraction $Y_i$ and mole fraction $X_i$, $\\sum_{i=1}^N\\frac{Y_i}{M_{w,i}}$ is equal to $\\sum_{i=1}^N\\frac{X_iM_{w,i}}{\\sum_{j=1}^N X_jM_{w,j}}\\frac{1}{M_{w,i}}$.&lt;\/p&gt;&lt;p&gt;Since $\\sum_{i=1}^N X_i=1$ by definition of the mole fraction, we can further simplify the expression. As a result, $\\sum_{i=1}^N\\frac{Y_i}{M_{w,i}}$ is equal to $\\frac{1}{\\sum_{j=1}^N\\frac{X_j}{M_{w,j}}}$, which is inverse of the mean molecular weight in the mixture.&nbsp;&lt;\/p&gt;&lt;p&gt;Thank you.&nbsp;&lt;\/p&gt;<\/p>\n","protected":false},"template":"","class_list":["post-388076","topic","type-topic","status-answered","hentry","topic-tag-fluent","topic-tag-multicomponent","topic-tag-multicomponentdiffusion-1"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"description\" content=\"Hi, I have question about maxwell-stefan equations written in the fluent theory guide Fluent 2024 R2.In chapter 7.1.1.3.2, there are definitions and equations related to Maxwell-Stefan equations. 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My question is the formula $M_{w,m}$ which is defined as $\\sum_{i=1}^N\\frac{Y_i}{M_{w,i}}$, where $Y_i$ is a mass fraction of $i$th species, and $M_{w,i}$ is a molecular weight of $i$th species.Also,\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2024-10-04T04:35:26+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2024-10-28T06:56:33+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Question about the maxwell-stefan equations written in fluent theory guide | Ansys Learning Forum\" \/>\n\t\t<meta name=\"twitter:description\" content=\"Hi, I have question about maxwell-stefan equations written in the fluent theory guide Fluent 2024 R2.In chapter 7.1.1.3.2, there are definitions and equations related to Maxwell-Stefan equations. 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My question is the formula $M_{w,m}$ which is defined as $\\sum_{i=1}^N\\frac{Y_i}{M_{w,i}}$, where $Y_i$ is a mass fraction of $i$th species, and $M_{w,i}$ is a molecular weight of $i$th species.Also,","canonical_url":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"BreadcrumbList","@id":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/#breadcrumblist","itemListElement":[{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum#listItem","position":1,"name":"Home","item":"https:\/\/innovationspace.ansys.com\/forum","nextItem":{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum\/topics\/#listItem","name":"Topics"}},{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum\/topics\/#listItem","position":2,"name":"Topics","item":"https:\/\/innovationspace.ansys.com\/forum\/topics\/","nextItem":{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic-tag\/fluent\/#listItem","name":"fluent"},"previousItem":{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum#listItem","name":"Home"}},{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic-tag\/fluent\/#listItem","position":3,"name":"fluent","item":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic-tag\/fluent\/","nextItem":{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/#listItem","name":"Question about the maxwell-stefan equations written in fluent theory guide"},"previousItem":{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum\/topics\/#listItem","name":"Topics"}},{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/#listItem","position":4,"name":"Question about the maxwell-stefan equations written in fluent theory guide","previousItem":{"@type":"ListItem","@id":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic-tag\/fluent\/#listItem","name":"fluent"}}]},{"@type":"Organization","@id":"https:\/\/innovationspace.ansys.com\/forum\/#organization","name":"Ansys Learning Forum","description":"Ansys Innovation Space","url":"https:\/\/innovationspace.ansys.com\/forum\/"},{"@type":"WebPage","@id":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/#webpage","url":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/question-about-the-maxwell-stefan-equations-written-in-fluent-theory-guide\/","name":"Question about the maxwell-stefan equations written in fluent theory guide | Ansys Learning Forum","description":"Hi, I have question about maxwell-stefan equations written in the fluent theory guide Fluent 2024 R2.In chapter 7.1.1.3.2, there are definitions and equations related to Maxwell-Stefan equations. 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