Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippage

The velocity slippage with combined effects of buoyancy force plays an important role in the extraction of crude oil since it reduces the pressure drop along the pipelines and well-bore. Due to this, it becomes difficult to push the oil out of the reservoir. So, the main goal is to analyse the veloc...

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Main Authors: Jafar Hasnain, Nomana Abid
Format: Article
Language:English
Published: Elsevier 2025-01-01
Series:Alexandria Engineering Journal
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016824012122
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author Jafar Hasnain
Nomana Abid
author_facet Jafar Hasnain
Nomana Abid
author_sort Jafar Hasnain
collection DOAJ
description The velocity slippage with combined effects of buoyancy force plays an important role in the extraction of crude oil since it reduces the pressure drop along the pipelines and well-bore. Due to this, it becomes difficult to push the oil out of the reservoir. So, the main goal is to analyse the velocity slip and no-slip on two immiscible viscous fluids flowing in a curved channel with viscous dissipation. To the best of the author's knowledge, there is no study given on two non-miscible laminar Newtonian layers of viscous-viscous fluids. The curved channel is divided into two regions and both regions are occupied with viscous fluids. The flow is caused by the constant pressure gradient and buoyancy force. The analytical solutions of highly nonlinear mathematical equations are obtained using perturbation series by taking ε(=PrEc)≪1. The impact of the curvature ratio parameter, velocity slips, Reynolds number, buoyancy force, viscosity ratio parameter, and height ratio parameter on heat and mass transfer are examined and presented through graphs. Moreover, the behaviour of shear stresses, skin drag and Nusselt number on both walls of the channel is analyzed and presented through bar charts. It is concluded that the velocities of the immiscible fluids augment by increasing the curvature parameter whereas the temperatures and shear stresses fall. It is also observed that the shear stress at the lower wall is more significant with a rise in curvature parameter in the case when velocity slippage is not considered as compared to velocity slippage.
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spelling doaj-art-4bd29f788dcb49928ae8e476c0ad45fd2025-01-18T05:03:39ZengElsevierAlexandria Engineering Journal1110-01682025-01-01111238248Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippageJafar Hasnain0Nomana Abid1Department of Computer Science, Bahria University, Islamabad 44000, PakistanCorresponding author.; Department of Computer Science, Bahria University, Islamabad 44000, PakistanThe velocity slippage with combined effects of buoyancy force plays an important role in the extraction of crude oil since it reduces the pressure drop along the pipelines and well-bore. Due to this, it becomes difficult to push the oil out of the reservoir. So, the main goal is to analyse the velocity slip and no-slip on two immiscible viscous fluids flowing in a curved channel with viscous dissipation. To the best of the author's knowledge, there is no study given on two non-miscible laminar Newtonian layers of viscous-viscous fluids. The curved channel is divided into two regions and both regions are occupied with viscous fluids. The flow is caused by the constant pressure gradient and buoyancy force. The analytical solutions of highly nonlinear mathematical equations are obtained using perturbation series by taking ε(=PrEc)≪1. The impact of the curvature ratio parameter, velocity slips, Reynolds number, buoyancy force, viscosity ratio parameter, and height ratio parameter on heat and mass transfer are examined and presented through graphs. Moreover, the behaviour of shear stresses, skin drag and Nusselt number on both walls of the channel is analyzed and presented through bar charts. It is concluded that the velocities of the immiscible fluids augment by increasing the curvature parameter whereas the temperatures and shear stresses fall. It is also observed that the shear stress at the lower wall is more significant with a rise in curvature parameter in the case when velocity slippage is not considered as compared to velocity slippage.http://www.sciencedirect.com/science/article/pii/S1110016824012122Curved channelVelocity slipViscous fluidAnalytical studyShear stressesImmiscible fluids
spellingShingle Jafar Hasnain
Nomana Abid
Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippage
Alexandria Engineering Journal
Curved channel
Velocity slip
Viscous fluid
Analytical study
Shear stresses
Immiscible fluids
title Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippage
title_full Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippage
title_fullStr Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippage
title_full_unstemmed Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippage
title_short Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippage
title_sort analytical study on flow of two non miscible laminar layers of newtonian fluids in a curved channel with wall slippage
topic Curved channel
Velocity slip
Viscous fluid
Analytical study
Shear stresses
Immiscible fluids
url http://www.sciencedirect.com/science/article/pii/S1110016824012122
work_keys_str_mv AT jafarhasnain analyticalstudyonflowoftwononmisciblelaminarlayersofnewtonianfluidsinacurvedchannelwithwallslippage
AT nomanaabid analyticalstudyonflowoftwononmisciblelaminarlayersofnewtonianfluidsinacurvedchannelwithwallslippage