Heat and mass transfer of fractional second grade fluid with slippage and ramped wall temperature using Caputo-Fabrizio fractional derivative approach

Sami Ul Haq; Saeed Ullah Jan; Syed Inayat Ali Shah; Ilyas Khan; Jagdev Singh; Sami Ul Haq; Saeed Ullah Jan; Syed Inayat Ali Shah; Ilyas Khan; Jagdev Singh

doi:10.3934/math.2020198

AIMS Mathematics

2020, Volume 5, Issue 4: 3056-3088. doi: 10.3934/math.2020198

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Heat and mass transfer of fractional second grade fluid with slippage and ramped wall temperature using Caputo-Fabrizio fractional derivative approach

1.
Department of Mathematics, Islamia College University, Peshawar 25000, Pakistan
2.
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
3.
Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India

Received: 29 September 2019 Accepted: 10 February 2020 Published: 23 March 2020
MSC : 26A33, 35R11, 76D05

Unsteady free convection slip flow of second grade fluid over an infinite heated inclined plate is discussed. The effects of mass diffusions in the flow are also eligible. Caputo-Fabrizio fractional derivative is used in the constitutive equations of heat and mass transfer respectively. Laplace transform is utilized to operate the set of fractional governing equations for both ramped and stepped wall temperature. Expression for Sherwood number and Nusselt number with non-integer order are found by differentiating the analytical solutions of fluid concentration and temperature. Numerical results of Sherwood number, Nusselt number and skin friction are demonstrated in tables. Solutions are plotted graphically to analyze the impact of distinct parameters i.e. Caputo-Fabrizio fractional parameter, second grade parameter, slip parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number to observe the physical behavior of the flow.
- heat and mass transfer,
- second grade fluid,
- constitutive equations,
- Caputo-Fabrizio,
- slip condition,
- ramped wall temperature
Citation: Sami Ul Haq, Saeed Ullah Jan, Syed Inayat Ali Shah, Ilyas Khan, Jagdev Singh. Heat and mass transfer of fractional second grade fluid with slippage and ramped wall temperature using Caputo-Fabrizio fractional derivative approach[J]. AIMS Mathematics, 2020, 5(4): 3056-3088. doi: 10.3934/math.2020198

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Abstract

Unsteady free convection slip flow of second grade fluid over an infinite heated inclined plate is discussed. The effects of mass diffusions in the flow are also eligible. Caputo-Fabrizio fractional derivative is used in the constitutive equations of heat and mass transfer respectively. Laplace transform is utilized to operate the set of fractional governing equations for both ramped and stepped wall temperature. Expression for Sherwood number and Nusselt number with non-integer order are found by differentiating the analytical solutions of fluid concentration and temperature. Numerical results of Sherwood number, Nusselt number and skin friction are demonstrated in tables. Solutions are plotted graphically to analyze the impact of distinct parameters i.e. Caputo-Fabrizio fractional parameter, second grade parameter, slip parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number to observe the physical behavior of the flow.

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