{"id":61,"date":"2022-12-30T18:15:14","date_gmt":"2022-12-30T18:15:14","guid":{"rendered":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/sherwood-number\/"},"modified":"2023-01-05T03:15:34","modified_gmt":"2023-01-05T03:15:34","slug":"sherwood-number","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/sherwood-number\/","title":{"raw":"5.4 Sherwood Number","rendered":"5.4 Sherwood Number"},"content":{"raw":"
\r\n

The dimensionless Sherwood number (Sh<\/em>) is the ratio of the actual solute mass flux resulting from free convection to the solute mass flux resulting from diffusion and is given by Equation\u00a030 (Prasad and Simmons, 2005).<\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle Sh=\\frac{Q_{m}H}{D_{C}\\Delta C}[\/latex]<\/td>\r\n(30)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

where:<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
Q<\/em>m<\/em><\/sub><\/td>\r\n=<\/td>\r\nmass flux across the source boundary (M\/(TL2<\/sup>)), e.g., kg\u00a0s\u22121<\/sup>\u00a0m\u22122<\/sup><\/td>\r\n<\/tr>\r\n
\u0394C<\/em><\/td>\r\n=<\/td>\r\nconcentration difference over the height H<\/em> (M\/L3<\/sup>), e.g., kg\u00a0m\u22123<\/sup><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

For Sh<\/em>\u00a0<\u00a01, transport is diffusive in the stable regime. For Sh<\/em>\u00a0>\u00a01 transport is in the unstable regime. As one moves from the stable to unstable density configuration, the associated physics become increasingly complicated as the diffusive transport gives way to convective fingering. The Sherwood number is a useful quantitative indicator for comparing the performance of numerical models of free convection (Niederau et al., 2019; Prasad and Simmons, 2005, 2003).<\/p>\r\n\r\n<\/div>","rendered":"

\n

The dimensionless Sherwood number (Sh<\/em>) is the ratio of the actual solute mass flux resulting from free convection to the solute mass flux resulting from diffusion and is given by Equation\u00a030 (Prasad and Simmons, 2005).<\/p>\n\n\n\n
<\/td>\n\"\displaystyle Sh=\frac{Q_{m}H}{D_{C}\Delta C}\"<\/td>\n(30)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n
Q<\/em>m<\/em><\/sub><\/td>\n=<\/td>\nmass flux across the source boundary (M\/(TL2<\/sup>)), e.g., kg\u00a0s\u22121<\/sup>\u00a0m\u22122<\/sup><\/td>\n<\/tr>\n
\u0394C<\/em><\/td>\n=<\/td>\nconcentration difference over the height H<\/em> (M\/L3<\/sup>), e.g., kg\u00a0m\u22123<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

For Sh<\/em>\u00a0<\u00a01, transport is diffusive in the stable regime. For Sh<\/em>\u00a0>\u00a01 transport is in the unstable regime. As one moves from the stable to unstable density configuration, the associated physics become increasingly complicated as the diffusive transport gives way to convective fingering. The Sherwood number is a useful quantitative indicator for comparing the performance of numerical models of free convection (Niederau et al., 2019; Prasad and Simmons, 2005, 2003).<\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":9,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-61","chapter","type-chapter","status-publish","hentry"],"part":131,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/61","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":2,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/61\/revisions"}],"predecessor-version":[{"id":282,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/61\/revisions\/282"}],"part":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/131"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/61\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/media?parent=61"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/pressbooks\/v2\/chapter-type?post=61"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/contributor?post=61"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/wp-json\/wp\/v2\/license?post=61"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}