Heat transfer analysis in a non-Newtonian hybrid nanofluid over an exponentially oscillating plate using fractional Caputo–Fabrizio derivative
Open Access
- 15 November 2022
- journal article
- research article
- Published by Springer Science and Business Media LLC in Scientific Reports
- Vol. 12 (1), 1-12
- https://doi.org/10.1038/s41598-022-21082-x
Abstract
In this paper, we have been study a hybrid nanofluid over an exponentially oscillating vertical flat plate. Therefore the fractional derivatives definition of Caputo–Fabrizio approach is applied to transform the classical model for this hybrid nanofluid to fractional model. Together with an oscillating boundary motion, therefore the heat transfer is cause as a result of the buoyancy force produce due temperature differences between the plate and the fluid. The dimensionless classical model is generalized by transforming it to the time fractional model using Caputo–Fabrizio time fractional derivative. Exact analytical solutions are obtained by using Laplace transform method to the set of dimensionless fractional governing equations, containing the momentum and energy equations subjected to the boundary and initial conditions. Numerical computations and graphical illustrations are used to checked the results of the Caputo–Fabrizio time-fractional parameter, the second-grade parameter, the magnetic parameter and the Grashof numbers on the velocity field. An assessment for time spin-off is shown graphically of integer order versus fractional-order for these non-Newtonian hybrid nanofluid through Mathcad software. The fluid velocity increases for increasing the value of the fractional parameter, second-grade parameter and Grashof number. Also for increasing the values of the MHD parameter the fluid velocity decreases.This publication has 30 references indexed in Scilit:
- Effect of Al2O3–Cu/water hybrid nanofluid in heat transferExperimental Thermal and Fluid Science, 2011
- Synthesis of Al2O3–Cu/water hybrid nanofluids using two step method and its thermo physical propertiesColloids and Surfaces A: Physicochemical and Engineering Aspects, 2011
- Threefold Introduction to Fractional DerivativesPublished by Wiley ,2008
- Oscillating flow of a viscoelastic fluid in a pipe with the fractional Maxwell modelApplied Mathematics and Computation, 2006
- Periodic unidirectional flows of a viscoelastic fluid with the fractional Maxwell modelApplied Mathematics and Computation, 2004
- A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel platesInternational Journal of Non-Linear Mechanics, 2003
- Application of Fractional Calculus to Fluid MechanicsJournal of Fluids Engineering, 2002
- Heat transfer enhancement of nanofluidsInternational Journal of Heat and Fluid Flow, 2000
- Free convection boundary-layer flow along a vertical surface in a porous medium with Newtonian heatingInternational Journal of Heat and Mass Transfer, 1999
- Natural-convection boundary-layer flow on a vertical surface with Newtonian heatingInternational Journal of Heat and Fluid Flow, 1994