Applications of fractional derivatives to nanofluids: exact and numerical solutions

Zulkhibri, Ismail and Mohd Zuki, Salleh and Aman, Sidra and Khan, Ilyas (2018) Applications of fractional derivatives to nanofluids: exact and numerical solutions. Mathematical Modelling of Natural Phenomena, 13 (1). pp. 1-12. ISSN 0973-5348 (Print); 1760-6101 (Online). (Published)

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Abstract

In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt heat and mass transfer of nanofluids (sodium alginate (SA) carrier fluid with graphene nanoparticles) are tackled using fractional derivative approach. Exact solutions are determined for temperature, concentration and velocity field, and Nusselt number via Laplace transform technique. The obtained solutions are then expressed in terms of wright function or its fractional derivatives. Numerical solutions for velocity, temperature, concentration and Nusselt number are obtained using finite difference scheme. It is found that these solutions are significantly controlled by the variations of parameters including thermal Grashof number, fractional parameter and nanoparticles volume fraction. It is observed that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters.

Item Type:	Article
Additional Information:	Indexed by SCOPUS
Uncontrolled Keywords:	Heat and mass transfer; Graphene nanoparticles; Finite difference scheme; Time fractional derivatives; Laplace transform
Subjects:	Q Science > QA Mathematics
Faculty/Division:	Faculty of Industrial Sciences And Technology Institute of Postgraduate Studies
Depositing User:	Dr. Zulkhibri Ismail@Mustofa
Date Deposited:	04 Mar 2019 06:47
Last Modified:	18 Oct 2019 02:34
URI:	http://umpir.ump.edu.my/id/eprint/23900
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