Document Zbl 1514.82142

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Unlike previous investigations on fADE to investigate the suspension distribution, in this study the modified Atangana-Baleanu-Caputo fractional derivative with a non-singular and non-local kernel is employed. The proposed fADE is solved and an analytical model for finding vertical suspension distribution is obtained. The model is validated against experimental as well as field measurements of Missouri River, Mississippi River and Rio Grande conveyance channel and is compared with the Rouse equation and other fractional model found in literature. A quantitative error analysis shows that the proposed model is able to predict the vertical distribution of particles more appropriately than previous models. The validation results shows that the fractional model can be equally applied to all size of particles with an appropriate choice of the order of the fractional derivative $\alpha$. It is also found that besides particle diameter, parameter $\alpha$ depends on the mass density of particle and shear velocity of the flow. To predict this parameter, a multivariate regression is carried out and a relation is proposed for easy application of the model. From the results for sand and plastic particles, it is found that the parameter $\alpha$ is more sensitive to mass density than the particle diameter. The rationality of the dependence of $\alpha$ on particle and flow characteristics has been justified physically.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7550371">Cited in <strong>10</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A82C24" title="MSC2020">82C24</a> </td> <td class="space"> Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R11" title="MSC2020">35R11</a> </td> <td class="space"> Fractional partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76F99" title="MSC2020">76F99</a> </td> <td class="space"> Turbulence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76T20" title="MSC2020">76T20</a> </td> <td class="space"> Suspensions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asuspension+concentration+distribution">suspension concentration distribution</a>; <a href="/?q=ut%3Aopen+channel+flow">open channel flow</a>; <a href="/?q=ut%3Aturbulent+flow">turbulent flow</a>; <a href="/?q=ut%3Afractional+advection-diffusion+equation">fractional advection-diffusion equation</a>; <a href="/?q=ut%3Arouse+equation">rouse equation</a></div> <div class="software"> <h3>Software:</h3><a href="/software/12626">Mittag-Leffler</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1514.82142" data-ciurl="/ci/07550371" data-biburl="/bibtex/07550371.bib" data-amsurl="/amsrefs/07550371.bib" data-xmlurl="/xml/07550371.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07550371.pdf" title="Zbl 1514.82142 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.physa.2018.04.009" aria-label="DOI for “Suspension concentration distribution in turbulent flows: an analytical study using fractional advection-diffusion equation”" title="10.1016/j.physa.2018.04.009">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">O’Brine, M. 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