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Application of Local and Non-local Kernels: The Optimal Solutions of Water-based Nanoparticles Under Ramped Conditions |
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PP: 317-335 |
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doi:10.18576/pfda/070410
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Author(s) |
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Aziz-Ur-Rehman,
Zaheer Hussain Shah,
Muhammad Bilal Riaz,
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Abstract |
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| Fractional calculus has been rising these days vastly due to its useful and exclusive properties.The classical calculus as per the fact that it is presumed that instant rate of change of the output, when the input level changes. Therefore it is unable to predict the earlier state of the process called memory effect which is absent in classical models, but Fractional Calculus(FC) famous for having memory effects. To predict the solution for fractional order derivative by using fractional calculus tools that has great importance for describing many systems. Due to this reason, we applied the modern definition of fractional derivatives (Local and non-locals kernels). In present paper the influence of energy and velocity on time dependent natural convection flow of magnetohydrodynamic water-based nanoparticles near long vertical plate of infinite length with ramped conditions nested in porous material is discussed. The fractional model of water-based nanofluid in which copper, aluminum oxide and titanium dioxide as nanoparticles using non-integer derivative operators Atangena-Baleanu, Caputo-Fabrizio and Caputo has been examined. Results are derived with the application of inversion algorithm and Laplace transformation method, for dimensionless temperature and velocity equations. The key features for different connected parameters are highlighted to display the graphs. A comparative study is accomplished for all fractional models with an ordinary model.Moreover, it is point out that ramped wall temperature and nanofluid velocity for non-integer models becomes an classical model, when the involving fractional parameter approaches to one, this reveal that fractional order models are more suitable to explain the investigational facts.
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