{"id":6223,"date":"2021-10-01T09:53:45","date_gmt":"2021-10-01T08:53:45","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=6223"},"modified":"2024-05-14T13:32:03","modified_gmt":"2024-05-14T12:32:03","slug":"how-to-calculate-and-solve-for-chapman-enskog-theory-integral-transport-phenomena","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2021\/10\/01\/how-to-calculate-and-solve-for-chapman-enskog-theory-integral-transport-phenomena\/","title":{"rendered":"How to Calculate and Solve for Chapman Enskog Theory Integral | Transport Phenomena"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents Chapman Enskog theory integral. To calculate Chapman Enskog theory integral, three essential parameters are needed and these parameters are Boltzmann’s Constant (KB<\/sub>), Temperature (T)<\/strong> and Enskog Constant (Energy Parameter) (\u03b5).<\/strong><\/p>\n

The formula for calculating Chapman Enskog theory integral:<\/strong><\/h3>\n

\u03b7n<\/sub> = KB<\/sub>T<\/sup> \/ \u03b5<\/sub><\/p>\n

Where:<\/p>\n

\u03b7n<\/sub> = Chapman Enskog Theory Integral
\nKB<\/sub> = Boltzmann’s Constant
\nT = Temperature
\n\u03b5 = Enskog Constant (Energy Parameter)<\/p>\n

Let’s solve an example;
\nFind the Chapman Enskog theory integral when the Boltzmann constant is 1.380e-23, the temperature is 20, and the Enskog constant (energy parameter) is 10.<\/p>\n

This implies that;<\/p>\n

KB<\/sub> = Boltzmann’s Constant = 1.380e-23
\nT = Temperature = 20
\n\u03b5 = Enskog Constant (Energy Parameter) = 10<\/p>\n

\u03b7n<\/sub> = KB<\/sub>T<\/sup> \/ \u03b5<\/sub>
\nSo, \u03b7n<\/sub> = (1.380e-23)(20)<\/sup> \/ 10<\/sub>
\n\u03b7n<\/sub> = 2.76129e-22<\/sup> \/ 10<\/sub>
\n\u03b7n<\/sub> = 2.76e-23<\/p>\n

Therefore, the Chapman Enskog theory integral <\/strong>is 2.76e-23.<\/strong><\/p>\n

Calculating the Temperature when the Chapman Enskog Theory Integral, the Boltzmann’s Constant and the Enskog Constant (Energy Parameter) are Given<\/strong><\/h3>\n

T = \u03b7n<\/sub> x \u03b5<\/sup> \/ KB<\/sub><\/sub><\/p>\n

Where:<\/p>\n

T = Temperature
\n\u03b7n<\/sub> = Chapman Enskog Theory Integral
\nKB<\/sub> = Boltzmann’s Constant
\n\u03b5 = Enskog Constant (Energy Parameter)<\/p>\n

Let’s solve an example;
\nFind the temperature when the Chapman Enskog theory integral is 10, the Boltzmann’s constant is 1.380e-23 and the Enskog constant (energy parameter) is 8.<\/p>\n

This implies that;<\/p>\n

\u03b7n<\/sub> = Chapman Enskog Theory Integral = 10
\nKB<\/sub> = Boltzmann’s Constant = 1.380e-23
\n\u03b5 = Enskog Constant (Energy Parameter) = 8<\/p>\n

T = \u03b7n<\/sub> x \u03b5<\/sup> \/ KB<\/sub><\/sub>
\nT = 10 x 8<\/sup> \/ 1.380e-23<\/sub>
\nSo, T = 80<\/sup> \/ 1.380e-23<\/sub>
\nT = 5.79e+24<\/p>\n

Therefore, the temperature <\/strong>is 5.79e+24.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Stefan Boltzmann’s Constant | Radiation Heat Transfer<\/a><\/p>\n

Calculating the Enskog Constant (Energy Parameter) when the Chapman Enskog Theory Integral, the Temperature and the Boltzmann’s Constant are Given<\/strong><\/h3>\n

\u03b5 = \u03b7n<\/sub> x T<\/sup> \/ KB<\/sub><\/sub><\/p>\n

Where:<\/p>\n

\u03b5 = Enskog Constant (Energy Parameter)
\n\u03b7n<\/sub> = Chapman Enskog Theory Integral
\nKB<\/sub> = Boltzmann’s Constant
\nT = Temperature<\/p>\n

Let’s solve an example;
\nFind the Enskog constant (energy parameter) when the Chapman Enskog theory integral is 20, the Boltzmann’s constant is 1.380e-23 and the temperature is 10.<\/p>\n

This implies that;<\/p>\n

\u03b7n<\/sub> = Chapman Enskog Theory Integral = 20
\nKB<\/sub> = Boltzmann’s Constant = 1.380e-23
\nT = Temperature = 10<\/p>\n

\u03b5 = \u03b7n<\/sub> x T<\/sup> \/ KB<\/sub><\/sub>
\nThat is, \u03b5 = 20 x 10<\/sup> \/ 1.380e-23<\/sub>
\n\u03b5 = 200<\/sup> \/ 1.380e-23<\/sub>
\n\u03b5 = 1.44e+25<\/p>\n

Therefore, the enskog constant <\/strong>is 1.44e+25.<\/strong><\/p>\n

How to Calculate Chapman Enskog Theory Integral Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the Chapman Enskog theory integral.<\/p>\n

\n

To get the answer and workings of the Chapman Enskog theory integral, use the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe <\/strong>to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a><\/p>\n

Apple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Materials and Metallurgical\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n<\/div>\n

<\/p>\n

Now, Click on Transport Phenomena <\/b>under\u00a0Materials and Metallurgical<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on Chapman Enskog Theory Integral <\/strong>under Transport Phenomena
\n<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the chapman enskog theory integral according to the respective parameter which is the Boltzmann’s Constant (KB<\/sub>), Temperature (T) and Enskog Constant (Energy Parameter) (\u03b5).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the\u00a0Boltzmann’s Constant (KB<\/sub>)<\/strong> is 1.380e-23<\/strong>, Temperature (T)\u00a0<\/strong>is\u00a020<\/strong> and Enskog Constant (Energy Parameter) (\u03b5)<\/strong> is 10<\/strong>.<\/p>\n

\"How<\/p>\n

Finally, Click on Calculate<\/p>\n

\"How
\n\"\"<\/p>\n

As you can see from\u00a0the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the chapman enskog theory integral and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents Chapman Enskog theory integral. To calculate Chapman Enskog theory integral, three essential parameters are…","protected":false},"author":5,"featured_media":15212,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"categories":[47],"tags":[873,1785,60,1784,543,75,1775],"class_list":["post-6223","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-boltzmanns-constant","tag-chapman-enskog-theory-integral","tag-engineering","tag-enskog-constant","tag-materials-and-metallurgical","tag-temperature","tag-transport-phenomena","cs-entry"],"yoast_head":"\nHow to Calculate and Solve for Chapman Enskog Theory Integral | Transport Phenomena<\/title>\n<meta name=\"description\" content=\"Master the steps and the formula on How to Calculate Chapman Enskog Theory Integral | Transport Phenomena. 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