Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo–Fabrizio derivatives

By Nehad Ali Shah, Ilyas Khan. 2016

191 citations recorded by the source corpus.

This paper presents a Caputo–Fabrizio fractional derivatives approach to the thermal analysis of a second grade fluid over an infinite oscillating vertical flat plate. Together with an oscillating boundary motion, the heat transfer is caused by the buoyancy force induced by temperature differences between the plate and the fluid. Closed form solutions of the fluid velocity and temperature are obtained by means of the Laplace transform. The solutions of ordinary second grade and Newtonian fluids corresponding to time derivatives of integer and fractional orders are obtained as particular cases of the present solutions. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo–Fabrizio time-fractional parameter $$\upalpha $$α, the material parameter $$\alpha _2 $$α2, and the Prandtl and Grashof numbers on the velocity field. A comparison for time derivative of integer order versus fractional order is shown graphically for both Newtonian and second grade fluids. It is found that fractional fluids (second grade and Newtonian) have highest velocities. This shows that the fractional parameter enhances the fluid flow.

Subfields: Biomedical Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b440271e70150a8613098271affbc9205404c767

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In Biomedical Engineering

Dumitru Băleanu

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Application of Shehu transform to Atangana-Baleanu derivatives (2019, background): “Caputo-Fabrizio operator has proved to be effective through some applications [1, 12].”